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An adult is an animal that has reached full growth. The biological definition of adult is an organism that has reached sexual maturity and thus capable of reproduction.
In the human context, the term adult has meanings associated with legal and social concepts. In contrast to a non-adult or "minor", a legal adult is a person who has attained the age of majority and is therefore regarded as independent, self-sufficient, and responsible. They may also be regarded as "majors". The typical age of attaining adulthood for humans is 18 years, although definition may vary by country. A person may be physically mature and a biological adult by age 16 or so, but not defined as an adult by law until older ages. For example, in the US, you cannot join the armed forces or vote until age 18, and you cannot take on many legal and financial responsibilities until age 21.
Human adulthood encompasses psychological adult development. Definitions of adulthood are often inconsistent and contradictory; a person may be biologically an adult, and have adult behavior, but still be treated as a child if they are under the legal age of majority. Conversely, one may legally be an adult but possess none of the maturity and responsibility that may define an adult character.
In different cultures, there are events that relate passing from being a child to becoming an adult or coming of age. This often encompasses passing a series of tests to demonstrate that a person is prepared for adulthood, or reaching a specified age, sometimes in conjunction with demonstrating preparation. Most modern societies determine legal adulthood based on reaching a legally specified age without requiring a demonstration of physical maturity or preparation for adulthood.
== Biological adulthood ==
Historically and cross-culturally, adulthood has been determined primarily by the start of puberty (the appearance of secondary sex characteristics such as menstruation and the development of breasts in women, ejaculation, the development of facial hair, and a deeper voice in men, and pubic hair in both sexes). In the past, a person usually moved from the status of child directly to the status of adult, often with this shift being marked by some type of coming-of-age test or ceremony. During the Industrial Revolution, children went to work as soon as they could in order to help provide for their family. There was not a huge emphasis on school or education in general. Many children could get a job and were not required to have experience as adults are nowadays. In recent years, studies of adulthood have identified characteristic traits that go far beyond mere physical maturity. These markers for a full, mentally developed, adult include traits of personal responsibilities in multiple aspects of life.
Although few or no established dictionaries provide a definition for the two-word term biological adult, the first definition of adult in multiple dictionaries includes "the stage of the life cycle of an animal after reproductive capacity has been attained". Thus, the base definition of the word adult is the period beginning at physical sexual maturity, which occurs sometime after the onset of puberty. Although this is the primary definition of the base word "adult", the term is also frequently used to refer to social adults. The two-word term biological adult stresses or clarifies that the original definition, based on physical maturity (i.e. having reached reproductive competency), is being used.
The time of puberty varies from child to child, but usually begins between 10 and 12 years old. Girls typically begin the process of puberty at age 10 or 11, and boys at age 11 or 12. Girls generally complete puberty by 1517, and boys by age 16 or 17. Nutrition, genetics and environment also usually play a part in the onset of puberty. Girls will go through a growth spurt and gain weight in several areas of their body. Boys will go through similar spurts in growth, though it is usually not in a similar style or time frame. This is due to the natural processes of puberty, but genetics also plays a part in how much weight they gain or how much taller they get.
One recent area of debate within the science of brain development is the most likely chronological age for full mental maturity, or indeed, if such an age even exists. Common claims repeated in the media since 2005 (based upon interpretations of imaging data) have commonly suggested an "end-point" of age 25, referring to the prefrontal cortex as one area that is not yet fully mature at the age of 18. However, this is based on an interpretation of a brain imaging study by Jay Giedd, dating back to 2004 or 2005, where the only participants were aged up to 21 years, and Giedd assumed this maturing process would be done by the age of 25 years, whereas more recent studies show prefrontal cortex maturation continuing well past the age of 30 years, marking this interpretation as incorrect and outdated.
== Legal adulthood ==

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Legally, adulthood typically means that one has reached the age of majority when parents lose parental rights and responsibilities regarding the person concerned. Depending on one's jurisdiction, the age of majority may or may not be set independently of and should not be confused with the minimum ages applicable to other activities, such as engaging in a contract, marriage, voting, having a job, serving in the military, buying/possessing firearms, driving, traveling abroad, involvement with alcoholic beverages, smoking, sexual activity, gambling, being a model or actor in pornography, running for president, etc. Admission of a young person to a place may be restricted because of danger for that person, concern that the place may lead the person to immoral behavior, or because of the risk that the young person causes damage (for example, at an exhibition of fragile items).
One can distinguish the legality of acts of a young person, or of enabling a young person to carry out that act, by selling, renting out, showing, permitting entrance, allowing participation, etc. There may be distinction between commercially and socially enabling. Sometimes there is the requirement of supervision by a legal guardian, or just by an adult. Sometimes there is no requirement, but rather a recommendation.
Using the example of pornography, one can distinguish between:
being allowed inside an adult establishment
being allowed to purchase pornography
being allowed to possess pornography
another person being allowed to sell, rent out, or show the young person pornography, see disseminating pornography to a minor
being a pornographic actor: rules for the young person, and for other people, regarding production, possession, etc. (see child pornography)
With regard to films with violence, etc.:
another person being allowed to sell, rent out, or show the young person a film; a cinema being allowed to let a young person enter
The age of majority ranges internationally from ages 15 to 21, with 18 being the most common age. Nigeria, Mali, Democratic Republic of Congo and Cameroon define adulthood at age 15, but marriage of girls at an earlier age is common.
In most of the world, the legal adult age is 18 for most purposes, with some notable exceptions:

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The legal age of adulthood in British Columbia, New Brunswick, Newfoundland and Labrador, Northwest Territories, Nova Scotia, Nunavut, and Yukon in Canada is 19 (though there are some exceptions in which Canadians may be considered legal adults in certain situations like sexual consent, which is age 16, and criminal law, federal elections and the military, which is at 18);
The legal age of adulthood in Nebraska and Alabama in the United States is 19. The legal age of adulthood in South Korea is 19. The legal age of adulthood in Mississippi and Puerto Rico in the U.S. and Bahrain is 21. Prior to the 1970s, young people were not classed as adults until 21 in most western nations. For example, in the United States, young citizens could not vote in many elections until 21 until July 1971 when the 26th Amendment passed mandating that the right to vote cannot be abridged for anyone 18 or older. The voting age was lowered in response to the fact that young men between the ages of 18 and 21 were drafted into the army to fight in the Vietnam War, hence the popular slogan "old enough to fight, old enough to vote". Young people under 21 in the US could also not purchase alcohol, purchase handguns, sign a binding contract, or marry without permission from parents. After the voting age was lowered, many states also moved to lower the drinking age (with most states having a minimum age of 18 or 19) and also to lower the age of legal majority (adulthood) to 18. However, there are legal activities where 18 is not the default age of adulthood. There are still some exceptions where 21 (or even higher) is still the benchmark for certain rights or responsibilities. For example, in the US the Gun Control Act of 1968 prohibits those under 21 from purchasing a handgun from a federally licensed dealer (although federal law makes an exception for individuals between the ages of 18 and 20 to obtain one from a private dealer if state law permits.)
As of July 1984, the National Minimum Drinking Age Act mandated that all states raise their respective drinking ages to 21 to create a uniform standard for legally purchasing, drinking, or publicly possessing alcohol with exceptions made for consumption only in private residences under parental supervision and permission. This was done in response to reducing the number of drunk driving fatalities prevalent among young drivers. States that choose not to comply can lose up to 10% of highway funding. The Credit Card Act of 2009 imposed tougher safeguards for young adults between the ages of 18 and 20 obtaining a credit card. Young adults under the age of 21 must either have a co-signer 21 or older or show proof (usually a source of income) that they can repay their credit card balance. Unless that requirement is met, one must wait until 21 to be approved for a credit card on their own. The Affordable Care Act of 2010 expands the age that young adults can remain on their parent's health insurance plan up to age 26. As of December 2019, the federal government raised the legal age to purchase tobacco and vaping products from 18 to 21. In states where recreational marijuana is legalized, the default age is also 21, though those younger may be able to obtain medical marijuana prescriptions or cards upon seeing a physician. Gambling also varies from 18 to 21 depending on the state and many rental car companies do not rent cars to those under 21 and have surcharges for drivers under 25 (although this is not codified, and is company policy). In Quebec, Canada the Quebec legislature in 2020 raised the age one could purchase recreational marijuana from 18 to 21 stepping out of line with most of the country that set a minimum age of 19 (except Alberta, which is 18.) The Quebec government cited the risk that marijuana poses to the brain development of people under 21 as justification for the age raise. In March 2021, the state of Washington in a 54 decision, justices in the Supreme Court of the State of Washington tossed the life without parole sentences of a 19-year-old and a 20-year-old convicted in separate cases of first-degree aggravated murder decades ago, saying, as with juveniles, the court must first consider the age of those under 21 before sentencing them to die behind bars. This comes at a time when there are ongoing debates about whether those between 18 and 20 should be exempted from the death penalty. In Germany, courts largely sentence defendants under the age of 21 according to juvenile law in a bid to help them reintegrate into society and mete out punishments that fit the crime as well as the offender. In May 2021, the state of Texas raised the age that one can be an exotic dancer and work and patronize sexually oriented businesses from 18 to 21. In the UK, there have been many proposals to raise the age that one can buy tobacco from 18 to 21 in an attempt to curb teen and young adult use to get to a "smoke-free" UK by 2030. All of these laws made over the years reflect the growing awareness that young adults, while not children, are still in a transitional stage between adolescence and full adulthood and that there should be policy adjustments or restrictions where necessary, especially where it pertains to activities that carry certain degrees of risk or harm to themselves or others. At the same time, however, even though the generally accepted age of majority is 18 in most nations, there are rights or privileges afforded to adolescents who have not yet reached legal adulthood. In the United States, youth are able to get a part-time job at 14 provided they have a work permit. At 16, one is able to obtain a driver's permit or license depending on state laws and is able to work most jobs (except ones requiring heavy machinery) and consent to sexual activity (depending on the state). At 17, one is able to enlist in the armed forces with parental consent although they cannot be deployed to be in combat roles until age 18. The voting age for local elections in most American cities is 18. But in five localities nationwide — four of which are in Maryland — 16 and 17-year-olds are eligible to vote. The cities are Takoma Park, Riverdale, Greenbelt, and Hyattsville. In 2020, students 16 or older in Oakland, California gained the right to vote in school board elections. There is a growing movement to lower the voting age in the US and many other countries from 18 to 16 in hopes of engaging the youth vote and encouraging greater electoral participation. Some countries already have a voting age of 16 which include Austria, Scotland, Argentina, Brazil, Wales, Cuba, and Ecuador. In Germany, one can purchase beer and wine at the age of 16 although they cannot purchase spirits or hard liquor until 18. The age of consent in Germany is 14 if both partners are under 18.

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Sexual activity with a person under 18 is punishable if the adult is a person of authority over the minor in upbringing, education, care, or employment.

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== Social construction of adulthood ==
In contrast to biological perspectives of aging and adulthood, social scientists conceptualize adulthood as socially constructed. While aging is an established biological process, the attainment of adulthood is social in its criteria. In contrast to other perspectives that conceptualize aging and the attainment of adulthood as a largely universal development, regardless of context, nation, generation, gender, race, or social class. Social scientists regard these aspects as paramount in cultural definitions of adulthood.
Further evidence of adulthood as a social construction is illustrated by the changing criteria of adulthood over time. Historically, adulthood in the U.S. has rested on completing one's education, moving away from the family of origin, and beginning one's career. Other key historical criteria include entering a marriage and becoming a parent. These criteria are social and subjective; they are organized by gender, race, ethnicity, and social class, among other key identity markers. As a result, particular populations feel adult earlier in the life course than do others.
Contemporary experiences of and research on young adults today substitute more seemingly subjective criteria for adulthood which resonate more soundly with young adults' experiences of aging. The criteria are marked by a growing "importance of individualistic criteria and the irrelevance of the demographic markers of normative conceptions of adulthood." In particular, younger cohorts' attainment of adulthood centers on three criteria: gaining a sense of responsibility, independent decision-making, and financial independence.
Jeffrey Arnett, a psychologist and professor at Clark University in Massachusetts, studied the development of adults and argues that there is a new and distinct period of development in between adolescence and adulthood. This stage, which he calls "emerging adulthood", occurs between the ages of 18 and 25. Arnett describes these individuals as able to take some responsibility for their lives, but still not completely feeling like an adult. Arnett articulates five distinct features that are unique to this period of development: identity exploration, feeling in between, instability, self-focus, and having possibilities. Arnett makes it clear that these 5 aspects of emerging adulthood are only relevant during the life stage of emerging adulthood.
The first feature, identity exploration, describes emerging adults making decisions for themselves about their career, education, and love life. This is a time of life when a young person has yet to finalize these decisions but are pondering them, making them feel somewhere in between adolescent and adult. This leads into a second feature of this phase of life—feeling in between. Emerging adults feel that they are taking on responsibilities but do not feel like a 'full' adult quite yet. Next, the instability feature notes that emerging adults often move around after their high school years whether that is to college, friends' houses, or living with a romantic partner, as well as moving back home with their parents/guardians for a time. This moving around often ends once the individual's family and career have been set. Tagging along with the instability feature is having self-focus. Emerging adults, being away from their parental and societal routines, are now able to do what they want when they want and where they want before they are put back into a routine when they start a marriage, family, and career. Arnett's last feature of emerging adulthood, an age of possibilities, characterizes this stage as one where "optimism reigns". These individuals believe they have a good chance of turning out better than their parents did.
== Religion ==
According to Jewish tradition, adulthood is reached at age 13 for Jewish boys and 12 for Jewish girls in accordance with the Bar or Bat Mitzvah; they are expected to demonstrate preparation for adulthood by learning the Torah and other Jewish practices. The Christian Bible and Jewish scripture contain no age requirement for adulthood or marrying, which includes engaging in sexual activity.
The 1983 Code of Canon Law states, "A man before he has completed his sixteenth year of age, and likewise a woman before she has completed her fourteenth year of age, cannot enter a valid marriage". According to The Disappearance of Childhood by Neil Postman, the Christian Church of the Middle Ages considered the age of accountability, when a person could be tried and even executed as an adult, to be age 7. While certain religions have their guidelines on what it means to be an adult, generally speaking, there are trends that occur regarding religiosity as individuals transition from adolescence to adulthood. The role of religion in one's life can impact development during adolescence. The National Library of Medicine (NCBI) highlights some studies that show rates of religiosity declining as people move out of the house and live on their own. Oftentimes when people live on their own, they change their life goals and religion tends to be less important as they discover who they are. Other studies from the NCBI show that as adults get married and have children they settle down, and as they do, there tends to be an increase in religiosity. Everyone's level of religiosity builds at a different pace, meaning that religion relative to adult development varies across cultures and time.
== See also ==
== References ==

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Behavior (American English) or behaviour (British English) is the range of actions of organisms, individuals, systems or artificial entities in some environment. These systems can include other systems or organisms as well as the inanimate physical environment. It is the computed response of the system or organism to various stimuli or inputs, whether internal or external, conscious or subconscious, overt or covert, and voluntary or involuntary. While some behavior is produced in response to an organism's environment (extrinsic motivation), behavior can also be the product of intrinsic motivation, also referred to as "agency" or "free will".
Taking a behavior informatics perspective, a behavior consists of actor, operation, interactions, and their properties. This can be represented as a behavior vector.
== Models ==
=== Biology ===
==== Definition ====
A broader definition of behavior, applicable to plants and other organisms, is similar to the concept of phenotypic plasticity. It describes behavior as a response to an event or environment change during the course of the lifetime of an individual, differing from other physiological or biochemical changes that occur more rapidly, and excluding changes that are a result of development (ontogeny).
Behaviour can be regarded as any action of an organism that changes its relationship to its environment. Behavior provides outputs from the organism to the environment.
==== Determination by genetics or the environment ====
Behaviors can be either innate or learned from the environment, or both, dependent on the organism. The more complex nervous systems (or brains) are, the more influence learning has on behavior. However, even in mammals, a large fraction of behavior is genetically determined. For instance, prairie voles tend to be monogamous while, while meadow voles are more promiscuous, a difference that is strongly determined by a single gene, Avpr1a, encoding a receptor for the peptide hormone Vasopressin.
=== Human behavior ===
The endocrine system and the nervous system likely influence human behavior. Complexity in the behavior of an organism may be correlated to the complexity of its nervous system. Generally, organisms with more complex nervous systems have a greater capacity to learn new responses and thus adjust their behavior.
Consumer behaviour is the behavior of humans when they act or treated as consumers.
=== Animal behavior ===
Ethology is the scientific and objective study of animal behavior, usually with a focus on behavior under natural conditions, and viewing behavior as an evolutionarily adaptive trait. Behaviorism is a term that also describes the scientific and objective study of animal behavior, usually referring to measured responses to stimuli or trained behavioral responses in a laboratory context, without a particular emphasis on evolutionary adaptivity.
== In management ==
=== Organizational ===
In management, behaviors are associated with desired or undesired focuses. Managers generally note what the desired outcome is, but behavioral patterns can take over. These patterns are the reference to how often the desired behavior actually occurs. Before a behavior actually occurs, antecedents focus on the stimuli that influence the behavior that is about to happen. After the behavior occurs, consequences fall into place. Consequences consist of rewards or punishments.
=== Social behavior ===
Social behavior is behavior among two or more organisms within the same species, and encompasses any behavior in which one member affects the other. This is due to an interaction among those members. Social behavior can be seen as similar to an exchange of goods, with the expectation that when one gives, one will receive the same. This behavior can be affected by both the qualities of the individual and the environmental (situational) factors. Therefore, social behavior arises as a result of an interaction between the two—the organism and its environment. This means that, in regards to humans, social behavior can be determined by both the individual characteristics of the person, and the situation they are in.
== Behavior informatics ==
Behavior informatics also called behavior computing, explores behavior intelligence and behavior insights from the informatics and computing perspectives.
Different from applied behavior analysis from the psychological perspective, BI builds computational theories, systems and tools to qualitatively and quantitatively model, represent, analyze, and manage behaviors of individuals, groups and/or organizations.
== Health ==
Health behavior refers to a person's beliefs and actions regarding their health and well-being. Health behaviors are direct factors in maintaining a healthy lifestyle. Health behaviors are influenced by the social, cultural, and physical environments in which we live. They are shaped by individual choices and external constraints. Positive behaviors help promote health and prevent disease, while the opposite is true for risk behaviors. Health behaviors are early indicators of population health. Because of the time lag that often occurs between certain behaviors and the development of disease, these indicators may foreshadow the future burdens and benefits of health-risk and health-promoting behaviors.
=== Correlates ===
A variety of studies have examined the relationship between health behaviors and health outcomes (e.g., Blaxter 1990) and have demonstrated their role in both morbidity and mortality.
These studies have identified seven features of lifestyle which were associated with lower morbidity and higher subsequent long-term survival (Belloc and Breslow 1972):
Avoiding snacks
Eating breakfast regularly
Exercising regularly
Maintaining a desirable body weight
Moderate alcohol intake
Not smoking
Sleeping 78hrs per night
Health behaviors impact upon individuals' quality of life, by delaying the onset of chronic disease and extending active lifespan. Smoking, alcohol consumption, drug use, diet, gaps in primary care services and low screening uptake are all significant determinants of poor health, and changing such behaviors should lead to improved health.
For example, in US, Healthy People 2000, United States Department of Health and Human Services, lists increased physical activity, changes in nutrition and reductions in tobacco, alcohol and drug use as important for health promotion and disease prevention.

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=== Treatment approach ===
Any interventions done are matched with the needs of each individual in an ethical and respected manner. Health belief model encourages increasing individuals' perceived susceptibility to negative health outcomes and making individuals aware of the severity of such negative health behavior outcomes. E.g. through health promotion messages. In addition, the health belief model suggests the need to focus on the benefits of health behaviors and the fact that barriers to action are easily overcome. The theory of planned behavior suggests using persuasive messages for tackling behavioral beliefs to increase the readiness to perform a behavior, called intentions. The theory of planned behavior advocates the need to tackle normative beliefs and control beliefs in any attempt to change behavior. Challenging the normative beliefs is not enough but to follow through the intention with self-efficacy from individual's mastery in problem solving and task completion is important to bring about a positive change. Self efficacy is often cemented through standard persuasive techniques.
== See also ==
== References ==
General
Cao, L. (2014). Behavior Informatics: A New Perspective. IEEE Intelligent Systems (Trends and Controversies), 29(4): 6280.
Clemons, E. K. (2008). "How Information Changes Consumer Behavior and How Consumer Behavior Determines Corporate Strategy". Journal of Management Information Systems. 25 (2): 1340. doi:10.2753/mis0742-1222250202. S2CID 16370526.
Dowhan, D (2013). "Hitting Your Target". Marketing Insights. 35 (2): 3238.
Perner, L. (2008), Consumer behavior. University of Southern California, Marshall School of Business. Retrieved from http://www.consumerpsychologist.com/intro_Consumer_Behavior.html
Szwacka-Mokrzycka, J (2015). "TRENDS IN CONSUMER behavior CHANGES. OVERVIEW OF CONCEPTS". Acta Scientiarum Polonorum. Oeconomia. 14 (3): 149156.
== Further reading ==
Bateson, P. (2017) behavior, Development and Evolution. Open Book Publishers, Cambridge. ISBN 978-1-78374-250-9.
Plomin, Robert; DeFries, John C.; Knopik, Valerie S.; Neiderhiser, Jenae M. (24 September 2012). Behavioral Genetics. Shaun Purcell (Appendix: Statistical Methods in Behavioral Genetics). Worth Publishers. ISBN 978-1-4292-4215-8. Retrieved 4 September 2013.
Flint, Jonathan; Greenspan, Ralph J.; Kendler, Kenneth S. (28 January 2010). How Genes Influence Behavior. Oxford University Press. ISBN 978-0-19-955990-9.
== External links ==
What is behavior? Baby don't ask me, don't ask me, no more at Earthling Nature.
behaviorinformatics.org
Links to review articles by Eric Turkheimer and co-authors on behavior research
Links to IJCAI2013 tutorial on behavior informatics and computing

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Biological processes are processes that are necessary for an organism to live and that shape its capacities for interacting with its environment. Biological processes are made of many chemical reactions or other events that are involved in the persistence and transformation of life forms.
== Regulation ==
Regulation of biological processes occurs when any process is modulated in its frequency, rate or extent. Biological processes are regulated by many means; examples include the control of gene expression, protein modification or interaction with a protein or substrate molecule.
Homeostasis: regulation of the internal environment to maintain a constant state; for example, sweating to reduce temperature
Organization: being structurally composed of one or more cells the basic units of life
Metabolism: transformation of energy by converting chemicals and energy into cellular components (anabolism) and decomposing organic matter (catabolism). Living things require energy to maintain internal organization (homeostasis) and to produce the other phenomena associated with life.
Growth: maintenance of a higher rate of anabolism than catabolism. A growing organism increases in size in all of its parts, rather than simply accumulating matter.
Response to stimuli: a response can take many forms, from the contraction of a unicellular organism to external chemicals, to complex reactions involving all the senses of multicellular organisms. A response is often expressed by motion; for example, the leaves of a plant turning toward the sun (phototropism), and chemotaxis.
Interaction between organisms. the processes by which an organism has an observable effect on another organism of the same or different species.
Adaptation: the ability to change over time in response to the environment. This ability is fundamental to the process of evolution and is determined by the organism's heredity, diet, and external factors.
Also: cellular differentiation, fermentation, fertilisation, germination, tropism, hybridisation, metamorphosis, morphogenesis, photosynthesis, transpiration.
== List of biological processes in humans ==
Breathing
Defecation
Drinking
Eating
Ejaculation
Perspiration
Urination
== See also ==
Cellular process
Chemical process
Life
Organic reaction
== References ==

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In chronobiology, the circannual cycle is characterized by biological processes and behaviors recurring on an approximate annual basis, spanning a period of about one year. This term is particularly relevant in the analysis of seasonal environmental changes and their influence on the physiology, behavior, and life cycles of organisms. Adaptations observed in response to these circannual rhythms include fur color transformation, molting, migration, breeding, fattening and hibernation, all of which are inherently driven and synchronized with external environmental changes.
The regulation of these cycles is linked to internal biological clocks, akin to the circadian rhythm, which respond to external cues such as variations in temperature, daylight length (photoperiod), and food availability. Such environmental signals enable organisms to anticipate seasonal variations and adjust their behaviors and physiological states, thereby optimizing evolutionary fitness and reproductive success.
Circannual rhythms are evident in a range of organisms, including birds, mammals, fish, and insects, facilitating their adaptation to the cyclical nature of their habitats. Circannual cycles can be defined by three primary characteristics: persistence in the absence of apparent time cues, the capacity for phase shifting, and stability against temperature fluctuations. Classified as an infradian rhythm, it occurs less frequently than a circadian rhythm. This cycle was first discovered by Ebo Gwinner and Canadian biologist Ted Pengelley.
Derived from Latin, the term circannual combines circa, meaning approximately, with annual, referring to a period of one year.

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== Examples ==
In one study performed by Eberhard Gwinner, two species of birds were born in a controlled environment without ever being exposed to external stimuli. They were presented with a fixed Photoperiod of 10 hours of light and 14 hours of darkness each day. The birds were exposed to these conditions for eight years and consistently molted at the same time as they would have in the wild, indicating that this physiological cycle is innate rather than governed environmentally.
Researchers Ted Pengelley and Ken Fisher studied the circannual clock in the golden-mantled ground squirrel. They exposed the squirrels to twelve hours of light and 12 hours of darkness and at a constant temperature for three years. Despite this constant cycle, they continued to hibernate once a year with each episode preceded by an increase in body weight and food consumption. During the first year, the squirrels began hibernation in late October. They started hibernating in mid August and early April respectively for the following two years, displaying a circannual rhythm with a period of about 10 months.
An annual rhythm has been observed in humans diagnosed with obsessive compulsive tic disorder (OCTD). The study focused on observing the patients seasonal patterns and how the cycle of seasons affected their behaviors. They observed that there was a statistically significant annual rhythm in patients with OC symptoms but not in patients with tic symptoms. As a result of the study, the researchers concluded that treatments for this disorder can be implemented following an observation of the patients cycle and annual rhythm that they follow.
Gwinner observed the willow warbler (Phylloscopus trochilus) which is a bird species that migrates seasonally to tropical and southern Africa. They follow an annual cycle of migration starting in September and ending in mid-November for the winter and then migrate back between March and May. The willow warblers follow this cycle to maximize reproduction in the spring/summer as well as increasing available resources in the fall/winter. Gwinner observed that even through a lack of environmental cues for migration, the willow warblers followed precise schedules attributed to their circannual rhythm. The willow warblers would consistently molt between January and February, they would have gonadal growth initiate in the winter and continue on their migration back for the spring, and they would begin a fattening process precisely at the same time year after year for their spring migrations.
A classic example in insects is the varied carpet beetle. In a study performed by T. Nisimura and H. Numata in 2003, the seasonal timing and synchrony of pupation in the Varied Carpet Beetle (Anthrenus verbasci) was determined by studying how natural patterns in photoperiod and temperature affected it. The authors first fostered larvae under various constant photoperiods at a constant temperature of 20°C to determine if there was a critical duration of the photophase that affected the phase of circannual rhythm. Secondly, they examined if a decrease in temperature caused a phase-shift in the circannual rhythm. Third, they fostered larvae under a natural photoperiod at a constant temperature of 20°C and compared it to a group under natural photoperiod and temperature. Lastly, to clarify the significance of the circannual control of the A. verbasci life cycle, larvae were reared under natural photoperiod and temperature from the various times of the year. The results showed that the critical day-length was between 13 and 14 hours of light, that a decrease in temperature of 5°C did not affect the phase-shift, that larvae under controlled light but fluctuating temperatures experienced a delay in pupation compared to natural light and natural temperatures and that spring in Japan was the best time of the year for synchronous pupation which slowed as spring turned to summer.
Circannual and circadian rhythms can be influenced by metabolism which is primarily influenced from natural external environmental factors such as daily weather and seasons. Location adaptations are needed to survive in extreme environmental changes. These rhythms are influenced by variable environmental cues, and in some species are influenced by internal cues. In a study conducted by Catalina Reyes, the authors took a further look into how red-eared sliders showed circadian and circannual rhythms in metabolism, and if metabolic rates overall influenced the circadian and circannual cues. These rhythms were studied over one year, and displayed evidence of endogenous circadian and circannual rhythms in metabolism. The understanding was that in order for these rhythms to be expressed, environmental cues influenced these thermo and phyto cycles eliciting circadian and circannual rhythms of the red-eared sliders. The sensitivity to these environmental influences reflect adaptations to migration patterns that could serve as further insight to the cost-and-benefit of transportation and risk of predation.
Environmental external factors are the key drivers into influencing circannual and circadian rhythms. Although they may all differ depending on species, they all are influenced by factors like weather and seasonality. At temperate latitudes, circannual rhythms align with the day lengths, and in mammals, the hormone melatonin is reactive to the proportional length of evenings. Authors that collaborated on this study focused on the circannual alignment of, (Rangifer tarandus tarandus), better known as arctic reindeer. They are known to limit production of a rhythmic melatonin signal when exposed to prolonged periods of midwinter darkness and midsummer light. Areas in temperate regions are known to have prolonged periods of light and darkness, for instance, like in Alaska. They concluded that rhythmical melatonin secretion is a psychological response to the orientation of the sun in early winter months and the delay of circannual programme during the following autumnal months.

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== Biological advantages ==
Generating biological rhythms internally helps organisms anticipate important changes in the environment before they occur, thus providing the organisms with time to prepare and survive. For example, some plants have a very strict time frame in regards to blooming and preparing for spring. If they begin their preparations too early or too late they risk not being pollinated, competing with different species, or other factors that might affect their survival rate. Having a circannual cycle may keep them from making this mistake if a particular geographic region experiences a false spring, where the weather becomes exceptionally warm early for a short period of time before returning to winter temperatures.
Similarly, bird plumage and mammal fur change with the approach of winter, and is triggered by the shortening photoperiod of autumn. The circannual cycle can also be useful for animals that Migrate or Hibernate. Many animals' reproductive organs change in response to changes in photoperiod. Male gonads will grow during the onset of spring to promote reproduction among the species. These enlarged gonads would be nearly impossible to keep year round and would be inefficient for the species. Many female animals will only produce eggs during certain times of the year.
== Interaction with changing climate ==
Changing climate may unravel ecosystems in which different organisms use different internal calendars. Warming temperatures may lead to earlier blooms of flora in spring. For instance, one study performed by Menzel et al., analyzed 125,000 phenological records of 542 plant species in 21 European countries from 1971 to 2000 and found that 78% of all plants studied advanced in flowering, leafing, and fruiting while only three percent were significantly delayed. They determined that the average advance of spring and summer was 2.5 days per decade in Europe. Meanwhile, fauna may breed or migrate based on the length of day, and thus might arrive too late for critical food supplies they co-evolved with.
For example, the Parus major closely times the hatching of their chicks to the emergence of the protein-rich winter moth caterpillar, which in turn hatches to meet the budding of oaks. These birds are a single-brood bird, meaning they breed once a year with about nine chicks per brood. If the birds and caterpillars and buds all emerge at the right time, the caterpillars eat the new oak leaves and their population increases dramatically, and this hopefully will coincide with the arrival of the new chicks, allowing them to eat. But if plants, insects, and birds respond differently to the advance of spring or other phenology changes, the relationship may be altered.
As another example, studies of the Pied Flycatcher (ficedula hypoleuca) have shown that their spring migration timing is triggered by an internal circannual clock that is fine tuned to day length. These particular birds overwinter in dry tropical forest in Western Africa and breed in temperate forests in Europe, over 4,500 km away. From 1980-2000, temperatures at the time of arrival and the start of breeding have warmed significantly. They have advanced their mean laying date by ten days, but have not advanced the spring arrival on their breeding grounds because their migration behavior is triggered by photoperiod rather than temperature.
In short, even if each individual species can easily live with elevated temperatures, disruptions of phenology timing at ecosystem level may still imperil them.
== Challenges for scientific study ==
One reason for the paucity of research on circannual cycles is the duration of required efforts. The ratio of the period length of a circannual cycle to the length of the productive life of a scientist makes this branch of chronobiology difficult. It takes an entire year to get a time series which makes it difficult to see how these cycles adjust over the years. To put this into perspective, a two-week experiment for a circadian biologist would take fourteen years for a circannual researcher, in order to achieve the same level of data robustness for the conclusions.
== Related Topics ==
Circadian Rhythm - If circadian rhythm enables animals to prepare physiologically and behaviorally for certain predictable daily changes in the environment, might not some animals possess a circannual rhythm that runs on an approximately 365 cycle? A circannual clock mechanism could be similar to the circadian master clock, with an environment-independent timer capable of generating a circannual rhythm in conjunction with a mechanism that keeps the clock entertained to local conditions.
Nocturnality is when animals are active during the night, and inactive during the day. This adaptation allows for animals to avoid predators that may not have this adaptability, as well as having availability to resources that are otherwise not harvested by non-nocturnal animals. Some animals that are nocturnal have disadvantages in animal sensory systems, such as bats, they have poor vision and use other adaptations such as echolocation, something a non-nocturnal animal would not have.
Photoperiodism is the ability of plants and animals to use the length of day or night, resulting in the modification of their activities. A response from an organism to the length in daylight and time that allows for adaptations to seasonal variations and environmental changes. It orchestrates seasonal growth, development, reproduction, migration, and dormancy that affect survivorship and reproductive success. Changes in photoperiod over days and seasons created the opportunity for the development of internal clocks and eventually create circadian and circannual rhythms. Photoperiod can affect the circannual rhythms of animals if changed significantly.
== References ==

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A compilospecies is a genetically aggressive species which acquires the heredities of a closely related sympatric species by means of hybridisation and comprehensive introgression. The concept has in practice been applied to plants. The target species may be incorporated to the point of despeciation, rendering it extinct. This type of genetic aggression is associated with species in newly disturbed habitats (such as pioneering species), weed species and domestication. They can be diploid or polyploid, as well as sexual or primarily asexual. The term compilospecies derives from the Latin word compilo, which means to seize, to collect, to rob or to plunder. A proposed explanation for the existence of such a species with weak reproductive barriers and frequent introgression is that it allows for genetic variation. An increase in the gene pool through viable hybrids can facilitate new phenotypes and the colonisation of novel habitats. The concept of compilospecies is not frequent in scientific literature and may not be fully regarded by the biological community as a true evolutionary concept, especially due to low supporting evidence.
== History ==
Compilospecies were first described by Harlan and de Wet in 1962, who examined a wide range of grasses and other species such as Bothriochloa intermedia, otherwise known as Australian bluestem grass. B. intermedia was found to introgress heavily with neighboring sympatric grass species and even genera, particularly in geographically restricted areas. The species itself is of hybrid origin, containing genetic material from five or more different grass species. Harlan and de Wet examined the interactions between the genera Bothriochloa, Dichanthium and Capillipedium - an apomictic complex of grasses from the tribe Andropogoneae - and used the cytogenetic model of these as a basis for the compilospecies concept. Species within these genera exhibit both sexual and asexual reproduction, high heterozygosity, ploidies from 2x to 6x, and gene flow between bordering populations as evidence of ongoing introgression. However, this gene flow is only made possible in the presence of B. intermedia, which introgression moves towards, and the absence of which keeps the other species reproductively isolated. B. intermedia is identified as the compilospecies in this model.
=== Further examples ===
Other researched examples of compilospecies include;
Helianthus (sunflowers)
Draba (whitlow-grasses)
Armeria villosa
== References ==

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Within biological systems, degeneracy occurs when structurally dissimilar components/pathways can perform similar functions (i.e. are effectively interchangeable) under certain conditions, but perform distinct functions in other conditions. Degeneracy is thus a relational property that requires comparing the behavior of two or more components. In particular, if degeneracy is present in a pair of components, then there will exist conditions where the pair will appear functionally redundant but other conditions where they will appear functionally distinct.
This use of the term has practically no relevance to the questionably meaningful concept of evolutionarily degenerate populations that have lost ancestral functions.
== Biological examples ==
Examples of degeneracy are found in the genetic code, when many different nucleotide sequences encode the same polypeptide; in protein folding, when different polypeptides fold to be structurally and functionally equivalent; in protein functions, when overlapping binding functions and similar catalytic specificities are observed; in metabolism, when multiple, parallel biosynthetic and catabolic pathways may coexist.
More generally, degeneracy is observed in proteins of every functional class (e.g. enzymatic, structural, or regulatory), protein complex assemblies, ontogenesis, the nervous system, cell signalling (crosstalk) and numerous other biological contexts.
== Contribution to robustness ==
Degeneracy contributes to the robustness of biological traits through several mechanisms. Degenerate components compensate for one another under conditions where they are functionally redundant, thus providing robustness against component or pathway failure. Because degenerate components are somewhat different, they tend to harbor unique sensitivities so that a targeted attack such as a specific inhibitor is less likely to present a risk to all components at once. There are numerous biological examples where degeneracy contributes to robustness in this way. For instance, gene families can encode for diverse proteins with many distinctive roles yet sometimes these proteins can compensate for each other during lost or suppressed gene expression, as seen in the developmental roles of the adhesins gene family in Saccharomyces. Nutrients can be metabolized by distinct metabolic pathways that are effectively interchangeable for certain metabolites even though the total effects of each pathway are not identical. In cancer, therapies targeting the EGF receptor are thwarted by the co-activation of alternate receptor tyrosine kinases (RTK) that have partial functional overlap with the EGF receptor (and are therefore degenerate), but are not targeted by the same specific EGF receptor inhibitor.
== Theory ==
Several theoretical developments have outlined links between degeneracy and important biological measurements related to robustness, complexity, and evolvability. These include:
Theoretical arguments supported by simulations have proposed that degeneracy can lead to distributed forms of robustness in protein interaction networks. Those authors suggest that similar phenomena is likely to arise in other biological networks and potentially may contribute to the resilience of ecosystems as well.
Tononi et al. have found evidence that degeneracy is inseparable from the existence of hierarchical complexity in neural populations. They argue that the link between degeneracy and complexity is likely to be much more general.
Fairly abstract simulations have supported the hypothesis that degeneracy fundamentally alters the propensity for a genetic system to access novel heritable phenotypes and that degeneracy could therefore be a precondition for open-ended evolution.
The three hypotheses above have been integrated in where they propose that degeneracy plays a central role in the open-ended evolution of biological complexity. In the same article, it was argued that the absence of degeneracy within many designed (abiotic) complex systems may help to explain why robustness appears to be in conflict with flexibility and adaptability, as seen in software, systems engineering, and artificial life.
== See also ==
Canalisation
Equifinality
== References ==
== Further reading ==
Because there are many distinct types of systems that undergo heritable variation and selection (see Universal Darwinism), degeneracy has become a highly interdisciplinary topic. The following provides a brief roadmap to the application and study of degeneracy within different disciplines.
Animal Communication
Hebets E. A., Barron A. B., Balakrishnan C. N., Hauber M. E., Mason P. H., Hoke K. L. (2016). "A systems approach to animal communication". Proc. R. Soc. B. 283 (1826) 20152889. doi:10.1098/rspb.2015.2889. PMC 4810859. PMID 26936240.{{cite journal}}: CS1 maint: multiple names: authors list (link)
Cultural Variation
Downey G (2012). "Cultural variation in rugby skills: A preliminary neuroanthropological report". Annals of Anthropological Practice. 36 (1): 2644. doi:10.1111/j.2153-9588.2012.01091.x.
Ecosystems
Atamas S., Bell J. (2009). "Degeneracy-Driven Self-Structuring Dynamics in Selective Repertoires". Bulletin of Mathematical Biology. 71 (6): 13491365. doi:10.1007/s11538-009-9404-z. PMC 3707519. PMID 19337776.
Epigenetics
Maleszka R., Mason P.H., Barron A.B. (2014). "Epigenomics and the concept of degeneracy in biological systems". Briefings in Functional Genomics. 13 (3): 191202. doi:10.1093/bfgp/elt050. PMC 4031454. PMID 24335757.{{cite journal}}: CS1 maint: multiple names: authors list (link)
History and philosophy of science
Mason P.H. (2010). "Degeneracy at Multiple Levels of Complexity". Biological Theory. 5 (3): 277288. doi:10.1162/biot_a_00041. S2CID 83846240.
Systems biology
Solé R.V., Ferrer-Cancho R., Montoya J.M., Valverde S. (2002). "Selection, tinkering, and emergence in complex networks" (PDF). Complexity. 8 (1): 2033. Bibcode:2002Cmplx...8a..20S. doi:10.1002/cplx.10055. hdl:2117/176298.{{cite journal}}: CS1 maint: multiple names: authors list (link)
Whitacre J.M., Bender A. (2010). "Networked buffering: a basic mechanism for distributed robustness in complex adaptive systems". Theoretical Biology and Medical Modelling. 7 (20): 20. arXiv:0912.1961. Bibcode:2009arXiv0912.1961W. doi:10.1186/1742-4682-7-20. PMC 2901314. PMID 20550663.
Mason P.H. (2015). "Degeneracy: Demystifying and destigmatizing a core concept in systems biology". Complexity. 20 (3): 1221. Bibcode:2015Cmplx..20c..12M. doi:10.1002/cplx.21534.
Mason P.H., Domínguez D. J.F., Winter B., Grignolio A. (2015). "Hidden in plain view: degeneracy in complex systems". BioSystems. 128: 18. Bibcode:2015BiSys.128....1M. doi:10.1016/j.biosystems.2014.12.003. PMID 25543071.{{cite journal}}: CS1 maint: multiple names: authors list (link)
Evolution

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Edelman G.M., Gally J.A. (2001). "Degeneracy and complexity in biological systems". Proceedings of the National Academy of Sciences, USA. 98 (24): 1376313768. Bibcode:2001PNAS...9813763E. doi:10.1073/pnas.231499798. PMC 61115. PMID 11698650.
Whitacre J.M. (2010). "Degeneracy: a link between evolvability, robustness and complexity in biological systems". Theoretical Biology and Medical Modelling. 7 (6): 6. arXiv:0910.2586. Bibcode:2009arXiv0910.2586W. doi:10.1186/1742-4682-7-6. PMC 2830971. PMID 20167097.
Whitacre J.M., Bender A. (2010). "Degeneracy: a design principle for achieving robustness and evolvability". Journal of Theoretical Biology. 263 (1): 14353. arXiv:0907.0510. Bibcode:2010JThBi.263..143W. doi:10.1016/j.jtbi.2009.11.008. PMID 19925810. S2CID 11511132.
Whitacre J.M., Atamas S.P. (2011). "The Diversity Paradox: How Nature Resolves an Evolutionary Dilemma". arXiv:1112.3115. Bibcode:2011arXiv1112.3115W. {{cite journal}}: Cite journal requires |journal= (help)
Immunology
Cohn M (2005). "Degeneracy, mimicry and crossreactivity in immune recognition". Molecular Immunology. 42 (5): 651655. doi:10.1016/j.molimm.2004.09.010. PMID 15607824.
Cohen, I.R., U. Hershberg, and S. Solomon, 2004 Antigen-receptor degeneracy and immunological paradigms. Molecular Immunology, . 40(1415) pp. 993996.
Tieri, P., G.C. Castellani, D. Remondini, S. Valensin, J. Loroni, S. Salvioli, and C. Franceschi, Capturing degeneracy of the immune system. In Silico Immunology. Springer, 2007.
Tieri P., Grignolio A., Zaikin A., Mishto M., Remondini D., Castellani G.C., Franceschi C. (2010). "Network, degeneracy and bow tie. Integrating paradigms and architectures to grasp the complexity of the immune system". Theor Biol Med Model. 7: 32. doi:10.1186/1742-4682-7-32. PMC 2927512. PMID 20701759.{{cite journal}}: CS1 maint: multiple names: authors list (link)
Artificial life, Computational intelligence
Andrews, P.S. and J. Timmis, A Computational Model of Degeneracy in a Lymph Node. Lecture Notes in Computer Science, 2006. 4163: p. 164.
Mendao, M., J. Timmis, P.S. Andrews, and M. Davies. The Immune System in Pieces: Computational Lessons from Degeneracy in the Immune System. in Foundations of Computational Intelligence (FOCI). 2007.
Whitacre, J.M. and A. Bender. Degenerate neutrality creates evolvable fitness landscapes. in WorldComp-2009. 2009. Las Vegas, Nevada, USA.
Whitacre, J.M., P. Rohlfshagen, X. Yao, and A. Bender. The role of degenerate robustness in the evolvability of multi-agent systems in dynamic environments. in PPSN XI. 2010. Kraków, Poland.
Macia J., Solé R. (2009). "Distributed robustness in cellular networks: insights from synthetic evolved circuits". Journal of the Royal Society Interface. 6 (33): 393400. doi:10.1098/rsif.2008.0236. PMC 2658657. PMID 18796402.
Fernandez-Leon, J.A. (2011). Evolving cognitive-behavioural dependencies in situated agents for behavioural robustness. BioSystems 106, pp. 94110.
Fernandez-Leon, J.A. (2011). Behavioural robustness: a link between distributed mechanisms and coupled transient dynamics. BioSystems 105, Elsevier, pp. 4961.
Fernandez-Leon, J.A. (2010). Evolving experience-dependent robust behaviour in embodied agents. BioSystems 103:1, Elsevier, pp. 4556.
Brain
Price, C. and K. Friston, Degeneracy and cognitive anatomy. Trends in Cognitive Sciences, 2002. 6(10) pp. 416421.
Tononi, G., O. Sporns, and G.M. Edelman, Measures of degeneracy and redundancy in biological networks. Proceedings of the National Academy of Sciences, USA, 1999. 96(6) pp. 32573262.
Mason, P.H. (2014) What is normal? A historical survey and neuroanthropological perspective, in Jens Clausen and Neil Levy. (Eds.) Handbook of Neuroethics, Springer, pp. 343363.
Linguistics
Winter B (2014). "Spoken language achieves robustness and evolvability by exploiting degeneracy and neutrality". BioEssays. 36 (10): 960967. doi:10.1002/bies.201400028. PMID 25088374. S2CID 27876941.
Oncology
Tian, T., S. Olson, J.M. Whitacre, and A. Harding, The origins of cancer robustness and evolvability. Integrative Biology, 2011. 3: pp. 1730.
Peer Review
Lehky, S., Peer Evaluation and Selection Systems: Adaptation and Maladaptation of Individuals and Groups through Peer Review. 2011: BioBitField Press.
=== Researchers ===
Duarte Araujo
Sergei Atamas
Andrew Barron
Keith Davids
Gerald Edelman
Ryszard Maleszka Archived 2013-03-19 at the Wayback Machine
Paul Mason
Ludovic Seifert
Ricard Sole
Giulio Tononi
James Whitacre
== External links ==
degeneracy research community

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Field metabolic rate (FMR) refers to a measurement of the metabolic rate of a free-living animal.
== Method ==
Measurement of the field metabolic rate is made using the doubly labeled water method, although alternative techniques, such as monitoring heart rates, can also be used. The advantages and disadvantages of the alternative approaches have been reviewed by Butler et al. Several summary reviews have been published.
== References ==

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A globoid is a spherical crystalline inclusion in a protein body found in seed tissues that contains phytate and other nutrients for plant growth. These are found in several plants, including wheat and the genus Cucurbita. These nutrients are eventually completely depleted during seedling growth. In Cucurbita maxima, globoids form as early as the 3rd day of seedling growth. They are located in conjunction with a larger crystalloid. They are electrondense and vary widely in size.
== References ==

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Hydrodynamic Delivery (HD) is a method of DNA insertion in rodent models. Genes are delivered via injection into the bloodstream of the animal, and are expressed in the liver. This protocol is helpful to determine gene function, regulate gene expression, and develop pharmaceuticals in vivo.
== Methods ==
Hydrodynamic Delivery was developed as a way to insert genes without viral infection (transfection). The procedure requires a high-volume DNA solution to be inserted into the veins of the rodent using a high-pressure needle. The volume of the DNA is typically 8-10% equal to 8-10% of the animal's body weight, and is injected within 5-7 seconds. The pressure of the insertion leads to cardiac congestion (increased pressure in the heart), allowing the DNA solution to flow through the bloodstream and accumulate in the liver. The pressure expands the pores in the cell membrane, forcing the DNA molecules into the parenchyma, or the functional cells of the organ. In the liver, these cells are the hepatocytes. In less than two minutes after the injection, the pressure returns to natural levels, and the pores shrink back, trapping the DNA inside of the cell. After injection, the majority of genes are expressed in the liver of the animal over a long period of time.
Originally developed to insert DNA, further developments in HD have enabled the insertion of RNA, proteins, and short oligonucleotides into cells.
== Applications ==
The development of Hydrodynamic Delivery methods allows an alternative way to study in vivo experiments. This method has shown to be effective in small mammals, without the potential risks and complications of viral transfection. Applications of these studies include: testing regulatory elements, generating antibodies, analyzing gene therapy techniques, and developing models for diseases. Typically, genes are expressed in the liver, but the procedure can be altered to express genes in kidneys, lungs, muscles, heart, and pancreas.
=== Gene therapy ===
Hydrodynamic Delivery has been used to insert genes in an effort to combat genetic diseases. Since HD has mainly focused on small mammals such as rodents, its application in humans is limited. Ongoing research is increasing applications in large mammals and future clinical studies. Computer-assisted image-guided techniques allow surgeons to insert the needle or catheter in the precise site, while an automated injection device monitors and adjusts the pressure needed for optimal gene transmission.. With more precise injections, the volume of DNA solution can be reduced to about 1% of the organism's body weight
By using a catheter to conduct the injection, surgeons are able to express genes in organs other than the liver. Placing the catheter in alternate locations allows the DNA solution to reach the target, although genes are still expressed in the liver.
=== Developing model organisms ===
Hydrodynamic DNA delivery is a useful tool for creating model systems for human disease. Using this technique, laboratories are able to study genetic diseases in vivo. Studies are able to insert oncogenes into lab animals to study treatments. In addition to gene transfer, HD has also been shown to work in tumor cells. Metastatic cancer cells can be successfully delivered in model organisms in order to study specific cancers.
== Alternative non-viral transfection methods ==
Alternative methods can be used to insert genes into an organism without a viral vector. These can be split into physical and chemical techniques.
Physical methods:
Electroporation
Gene gun
Sonoporation
Microneedle
Magnetofection
Chemical methods:
Cationic lipids
Cationic polymers
Dendrimer-based vectors
Polypeptide-based vectors
Inorganic, polymeric, and lipid nanoparticles
Gemini surfactants
== References ==

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Injury is physiological damage to the living tissue of any organism, whether in humans, in other animals, or in plants.
Injuries can be caused in many ways, including mechanically with penetration by sharp objects such as teeth or with blunt objects, by heat or cold, or by venoms and biotoxins. Injury prompts an inflammatory response in many taxa of animals; this prompts wound healing. In both plants and animals, substances are often released to help to occlude the wound, limiting loss of fluids and the entry of pathogens such as bacteria. Many organisms secrete antimicrobial chemicals which limit wound infection; in addition, animals have a variety of immune responses for the same purpose. Both plants and animals have regrowth mechanisms which may result in complete or partial healing over the injury. Cells too can repair damage to a certain degree.
== Taxonomic range ==
=== Animals ===
Injury in animals is sometimes defined as mechanical damage to anatomical structure, but it has a wider connotation of physical damage with any cause, including drowning, burns, and poisoning. Such damage may result from attempted predation, territorial fights, falls, and abiotic factors.
Injury prompts an inflammatory response in animals of many different phyla; this prompts coagulation of the blood or body fluid, followed by wound healing, which may be rapid, as in the cnidaria. Arthropods are able to repair injuries to the cuticle that forms their exoskeleton to some extent.
Animals in several phyla, including annelids, arthropods, cnidaria, molluscs, nematodes, and vertebrates are able to produce antimicrobial peptides to fight off infection following an injury.
==== Humans ====
Injury in humans has been studied extensively for its importance in medicine. Much of medical practice, including emergency medicine and pain management, is dedicated to the treatment of injuries. The World Health Organization has developed a classification of injuries in humans by categories including mechanism, objects/substances producing injury, place of occurrence, activity when injured and the role of human intent. In addition to physical harm, injuries can cause psychological harm, including post-traumatic stress disorder.
=== Plants ===
In plants, injuries result from the eating of plant parts by herbivorous animals including insects and mammals, from damage to tissues by plant pathogens such as bacteria and fungi, which may gain entry after herbivore damage or in other ways, and from abiotic factors such as heat, freezing, flooding, lightning, and pollutants such as ozone. Plants respond to injury by signalling that damage has occurred, by secreting materials to seal off the damaged area, by producing antimicrobial chemicals, and in woody plants by regrowing over wounds.
== Cell injury ==
Cell injury is a variety of changes of stress that a cell suffers due to external as well as internal environmental changes. Amongst other causes, this can be due to physical, chemical, infectious, biological, nutritional or immunological factors. Cell damage can be reversible or irreversible. Depending on the extent of injury, the cellular response may be adaptive and where possible, homeostasis is restored. Cell death occurs when the severity of the injury exceeds the cell's ability to repair itself. Cell death is relative to both the length of exposure to a harmful stimulus and the severity of the damage caused.
== References ==

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Intersex is a general term for an organism that has sex characteristics that are between male and female. It typically applies to a minority of members of gonochoric animal species such as mammals (as opposed to hermaphroditic species in which the majority of members can have both male and female sex characteristics). Such organisms are usually sterile.
Intersexuality can occur due to both genetic and environmental factors and has been reported in mammals, fish, nematodes, crustaceans, and birds.
== Mammals ==
Intersex can occur in mammals such as pigs, with it being estimated that 0.1% to 1.4% of pigs are intersex. In Vanuatu, Narave pigs are sacred intersex pigs that are found on Malo Island. An analysis of Narave pig mitochondrial DNA by Lum et al. (2006) found that they are descended from Southeast Asian pigs. Female spotted hyenas have a pseudo-penis which led to a myth that they are hermaphroditic.
In cattle, a freemartin is the infertile female twin of a bull. Freemartins have both XX and XY chromosomes, non-functional ovaries, and exhibit masculine behavior.
At least six different mole species have an adaption where by the female mole has an ovotestis, "a hybrid organ made up of both ovarian and testicular tissue. The evolved purpose of this adoption is to give them an extra dose of testosterone to make them just as muscular and aggressive as male moles". Only the ovarian part of the ovotestis is reproductively functional.
Intersexuality in humans is relatively rare. Depending on the definition, the prevalence of intersex among humans has been reported to range around a figure of 0.018%.
== Nematodes ==
Intersex is known to occur in all main groups of nematodes. Most of them are functionally female. Male intersexes with female characteristics have been reported but are less common.
== Fishes ==
Gonadal intersex occurs in fishes, where the individual has both ovarian and testicular tissue. Although it is a rare anomaly among gonochoric fishes, it is a transitional state in fishes that are protandric or protogynous. Intersexuality has been reported in 23 fish families.
== Crustaceans ==
The oldest evidence for intersexuality in crustaceans comes from fossils dating back 70 million years ago. Intersex has been reported in gonochoric crustaceans as early as 1729. A large amount of literature exists on intersexuality for isopoda and amphipoda, with there being reports of both intersex males and intersex females.
== See also ==
Gynandromorphism
Hermaphrodite
Sexual differentiation
== References ==

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In taxonomy, a kleptotype is an unofficial term referring to a stolen, unrightfully displaced type specimen or part of a type specimen.
== Etymology ==
The term is composed of klepto-, from the Ancient Greek κλέπτω (kléptō) meaning "to steal", and -type referring to type specimens. It translates to "stolen type".
== History ==
During the Second World War biological collections, like the herbarium in Berlin have been destroyed. This led to the loss of type specimens. In some cases only kleptotypes have survived the destruction, as the type material had been removed from their original collections. For instance, the type of Taxus celebica was thought to be destroyed during the Second World War, but a kleptotype has survived the war in Stockholm.
Kleptotypes have been taken by researchers, who subsequently added their unauthorised type duplicates to their own collections.
== Consequences ==
Taking kleptotypes has been criticised as destructive, wasteful, and unethical. The displacement of type material complicates the work of taxonomists, as species identities may become ambiguous due to the lacking type material. It can cause problems, as researchers have to search in multiple collections to get a complete perspective on the displaced material. To combat this issue it has been proposed to weigh specimens before loaning types, and to identify loss of material through comparing the types weight upon return. Also, in some herbaria, such as the herbarium Kew, specimens are glued to the herbarium sheets to hinder the removal of plant material. However, this also makes it difficult to handle the specimens.
== Rules concerning type specimens ==
The International Code of Nomenclature for algae, fungi, and plants (ICN) does not explicitly prohibit the removal of material from type specimens, however it strongly recommends to conserve the type specimens properly. It is paramount that types remain intact, as they are an irreplaceable resource and point of reference.
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Locus suicide recombination (LSR) constitutes a variant form of class switch recombination that eliminates all immunoglobulin heavy chain constant genes. It thus terminates immunoglobulin and B-cell receptor (BCR) expression in B-lymphocytes and results in B-cell death since survival of such cells requires BCR expression. This process is initiated by the enzyme activation-induced deaminase upon B-cell activation. LSR is thus one of the pathways that can result into activation-induced cell death in the B-cell lineage.
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In biology, a mechanism is a system of causally interacting parts and processes that produce one or more effects. Phenomena can be explained by describing their mechanisms. For example, natural selection is a mechanism of evolution; other mechanisms of evolution include genetic drift, mutation, and gene flow. In ecology, mechanisms such as predation and host-parasite interactions produce change in ecological systems. In practice, no description of a mechanism is ever complete because not all details of the parts and processes of a mechanism are fully known. For example, natural selection is a mechanism of evolution that includes countless, inter-individual interactions with other individuals, components, and processes of the environment in which natural selection operates.
== Characterizations/ definitions ==
Many characterizations/definitions of mechanisms in the philosophy of science/biology have been provided in the past decades. For example, one influential characterization of neuro- and molecular biological mechanisms by Peter K. Machamer, Lindley Darden and Carl Craver is as follows: mechanisms are entities and activities organized such that they are productive of regular changes from start to termination conditions. Other characterizations have been proposed by Stuart Glennan (1996, 2002), who articulates an interactionist account of mechanisms, and William Bechtel (1993, 2006), who emphasizes parts and operations.
The characterization by Machemer et al. is as follows: mechanisms are entities and activities organized such that they are predictive of changes from start conditions to termination conditions. There are three distinguishable aspects of this characterization:
Ontic aspect
The ontic constituency of biological mechanisms includes entities and activities. Thus, this conception postulates a dualistic ontology of mechanisms, where entities are substantial components, and activities are reified components of mechanisms. This augmented ontology increases the explanatory power of this conception.
Descriptive aspect
Most descriptions of mechanisms (as found in the scientific literature) include specifications of the entities and activities involved, as well as the start and termination conditions. This aspect is mostly limited to linear mechanisms, which have relatively unambiguous beginning and end points between which they produce their phenomenon, although it may be possible to arbitrarily select such points in cyclical mechanisms (e.g., the Krebs cycle).
Epistemic aspect
Mechanisms are dynamic producers of phenomena. This conception emphasizes activities, which are causes that are reified. It is because of activities that this conception of mechanisms is able to capture the dynamicity of mechanisms as they bring about a phenomenon.
== Analysis ==
Mechanisms in science/biology have reappeared as a subject of philosophical analysis and discussion in the last several decades because of a variety of factors, many of which relate to metascientific issues such as explanation and causation. For example, the decline of Covering Law (CL) models of explanation, e.g., Hempel's deductive-nomological model, has stimulated interest how mechanisms might play an explanatory role in certain domains of science, especially higher-level disciplines such as biology (i.e., neurobiology, molecular biology, neuroscience, and so on). This is not just because of the philosophical problem of giving some account of what "laws of nature," which CL models encounter, but also the incontrovertible fact that most biological phenomena are not characterizable in nomological terms (i.e., in terms of lawful relationships). For example, protein biosynthesis does not occur according to any law, and therefore, on the DN model, no explanation for the biosynthesis phenomenon could be given.
== Explanations ==
Mechanistic explanations come in many forms. Wesley Salmon proposed what he called the "ontic" conception of explanation, which states that explanations are mechanisms and causal processes in the world. There are two such kinds of explanation: etiological and constitutive. Salmon focused primarily on etiological explanation, with respect to which one explains some phenomenon P by identifying its causes (and, thus, locating it within the causal structure of the world). Constitutive (or componential) explanation, on the other hand, involves describing the components of a mechanism M that is productive of (or causes) P. Indeed, whereas (a) one may differentiate between descriptive and explanatory adequacy, where the former is characterized as the adequacy of a theory to account for at least all the items in the domain (which need explaining), and the latter as the adequacy of a theory to account for no more than those domain items, and (b) past philosophies of science differentiate between descriptions of phenomena and explanations of those phenomena, in the non-ontic context of mechanism literature, descriptions and explanations seem to be identical. This is to say, to explain a mechanism M is to describe it (specify its components, as well as background, enabling, and so on, conditions that constitute, in the case of a linear mechanism, its "start conditions").
== See also ==
Aristotle's biology
== Notes and references ==

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In paleoecology and ecological forecasting, a no-analog community or climate is one that is compositionally different from a (typically modern) baseline for measurement. Alternative naming conventions to describe no-analog communities and climates may include novel, emerging, mosaic, disharmonious and intermingled.
Modern climates, communities and ecosystems are often studied in an attempt to understand no-analogs that have happened in the past and those that may occur in the future. This use of a modern analog to study the past draws on the concept of uniformitarianism. Along with the use of these modern analogs, actualistic studies and taphonomy are additional tools that are used in understanding no-analogs. Statistical tools are also used to identify no-analogs and their baselines, often through the use of dissimilarity analyses or analog matching Study of no-analog fossil remains are often carefully evaluated as to rule out mixing of fossils in an assemblage due to erosion, animal activity or other processes.
== No-analog climates ==
Conditions that are considered no-analog climates are those that have no modern analog, such as the climate during the last glaciation. Glacial climates varied from current climates in seasonality and temperature, having an overall more steady climate without as many extreme temperatures as today's climate.
Climates with no modern analog may be used to infer species range shifts, biodiversity changes, ecosystem arrangements and help in understanding species fundamental niche space. Past climates are often studied to understand how changes in a species' fundamental niche may lead to the formation of no analog communities. Seasonality and temperatures that are outside the climates at present provide opportunity for no-analog communities to arise, as is seen in the late Holocene plant communities. Evidence of deglacial temperature controls having significant effects on the formation of no-analog communities in the midwestern United States provides example of how intertwined climate and species assemblage are when studying no-analogs.
== No-analog communities ==
No-analog communities are defined by the existence of extant species in groupings that are not currently seen in modern biomes, or populations that have history of species assemblages that are no longer seen in the modern world. Formation of no-analog communities can be due to multiple factors, including climate conditions, environmental changes, human action, disease or species interactions. Migrations of species causes displacement and colonization into areas that may have been outside of what was known to be their fundamental niche, such as northern species moving south and mountain fauna being removed entirely or isolated to the peaks.
=== Quaternary no-analogs ===
Quaternary fossil records from the Pleistocene present a developed history of no-analogs. Records of plants, mammals, coleopterans, mollusks and foraminifera with no modern analogs are abundant in the fossil record. In the last glacial maximum, species aggregations were different from previous time periods due to a unique set of climate conditions. The development of no-analog plant and mammal communities is often interconnected, and also tied to occurrence of no-analog climates. Changes in plant community compositions may also lead to no-analog conditions with addition of biotic pressures such as competition and disease, or enhanced fire regimes.
The North American pollen record provides examples of detailed no-analog plant assemblages from the late quaternary. Pollen assemblages that contain no modern analog are present from many late glacial and early Holocene records, and extend from 14,000 to 12,000 years ago. Pollen is a commonly used proxy in studying plant no-analogs. These assemblages are marked by high abundances of taxa such as Betula, the co-occurrence of now allopatric species such as Fraxinus and Picea, and the low abundance of taxa that are now modernly abundant, such as Pinus. These associations are evident across Alaska, eastern North America, Europe and the southwestern US.
The environmental conditions during the Pleistocene offered a climate that was more productive for plant species than climate conditions that exist today. This is evident through extensive records of high abundances of broadleaved trees Ulmus, Ostrya, Fraxinus and Quercus mixed with boreal conifers such as Picea and Larix during the late Holocene. New evidence states that deglacial temperatures are now hypothesized to be a major contributor to the formation of no-analog plant communities in the Midwestern US. Christensen bog fauna during this time period also represent a significant example of no-analog assemblages from the Pleistocene. It is also possible that these plant assemblages formed due to influence from megafaunal extinctions during the late quaternary, and there is also evidence that shows connection between novel plant assemblages and new fire regimes.
=== Mammal no-analogs ===
Pleistocene mammal assemblages had high levels of diversity and abundance of megafauna. During the late quaternary extinction there was a loss of many megafauna. This extinction has led to the creation of a no-analog for modern ecosystems, which are lacking high diversity or abundance of large herbivores.
These no-analog mammal assemblages and the loss of megafauna coincides with no-analog plant community rise. The shifts in these groups has been hypothesized to have direct relationship to one another, with the possibility of a release from herbivory pressures causing the bloom in novel plant assemblages during the late quaternary.
== Future no-analog climates ==
Modern ecologists looking to study future climates and ecosystem assemblages use modern analogs to understand how species distributions will change and how to infer management of ecosystems with climate change. Along with modern analogs, studying past climates and how they've changed is being used to understand future novel climates due to climate changes. Species distribution models are currently being tested with no-analog climates to get more predictive estimates of species range shifts and biodiversity loss.
Examples of modern conditions that are considered no-analogs are also present. Accelerated tree growth due to environmental conditions and pollutants that are present today provide no analog to past conditions of tree growth.
=== Emerging ecosystems ===
The concept of emerging ecosystems originated from the discussion of the ecological and economical fate of agricultural land once it is no longer in use. Similarly to the definition of a no-analog, emerging ecosystems are considered as those that have species composition and abundances that are not seen in modern analogs. Emerging ecosystems not only encompass the understanding of ecological consequences, but also those social, economic and cultural associations. These ecosystems may provide opportunities for species to colonize new niche space.
=== Additional examples ===
Projections of future no-analog communities based on two climate models and two species-distribution-model algorithms indicate that by 2070 over half of California could be occupied by novel assemblages of bird species, implying the potential for dramatic community reshuffling and altered patterns of species interactions
== See also ==
Axel Heiberg Island ~80°N is known for its large ~45-million-year-old 'fossil forests'.
Biogeography
Ecology
Effects of global warming
Ellesmere Island ~80°N is known for its ~55-million-year-old 'fossil forest'.
Extinction risk from global warming
La Brea Tar Pits are well known for their fossils of extinct North American megafauna.
Paleoclimatology
Paleontology
Pleistocene rewilding
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A star is a luminous spheroid of plasma held together by self-gravity. The nearest star to Earth is the Sun. Many other stars are visible to the naked eye at night; their immense distances from Earth make them appear as fixed points of light. The most prominent stars have been categorised into constellations and asterisms, and many of the brightest stars have proper names. Astronomers have assembled star catalogues that identify the known stars and provide standardized stellar designations. The observable universe contains an estimated 1022 to 1024 stars. Only about 4,000 of these stars are visible to the naked eye—all within the Milky Way galaxy.
A star's life begins with the gravitational collapse of a gaseous nebula of material largely comprising hydrogen, helium, and traces of heavier elements. Its total mass mainly determines its evolution and eventual fate. A star shines for most of its active life due to the thermonuclear fusion of hydrogen into helium in its core. This process releases energy that traverses the star's interior and radiates into outer space. At the end of a star's lifetime, fusion ceases and its core becomes a stellar remnant: a white dwarf, a neutron star, or—if it is sufficiently massive—a black hole.
Stellar nucleosynthesis in stars or their remnants creates almost all naturally occurring chemical elements heavier than lithium. Stellar mass loss or supernova explosions return chemically enriched material to the interstellar medium. These elements are then recycled into new stars. Astronomers can determine stellar properties—including mass, age, metallicity (chemical composition), variability, distance, and motion through space—by carrying out observations of a star's apparent brightness, spectrum, and changes in its position in the sky over time.
Stars can form orbital systems with other astronomical objects, as in planetary systems and star systems with two or more stars. When two such stars orbit closely, their gravitational interaction can significantly impact their evolution. Stars often form part of much larger gravitationally bound structures, such as star clusters and galaxies.
== Etymology ==
The English word star ultimately derives from the Proto-Indo-European root *h₂stḗr, also meaning 'star' which is further analyzable as *h₂eh₁s- 'to burn' (also the source of the word ash) plus *-tēr (the agentive suffix). Its cognates in other languages include Latin stella, Greek aster, and German Stern; further cognates in English include asterisk, asteroid, astral, constellation, and Esther.
== Observation history ==
Historically, stars have been important to civilizations throughout the world. They have been part of religious practices, divination rituals, mythology, used for celestial navigation and orientation, to mark the passage of seasons, and to define calendars.
Early astronomers recognized a difference between "fixed stars", whose position on the celestial sphere does not change, and "wandering stars" (planets), which move noticeably relative to the fixed stars over days or weeks. Many ancient astronomers believed that the stars were permanently affixed to a heavenly sphere and that they were immutable. By convention, astronomers grouped prominent stars into asterisms and constellations and used them to track the motions of the planets and the inferred position of the Sun. The motion of the Sun against the background stars (and the horizon) was used to create calendars, which could be used to regulate agricultural practices. The Gregorian calendar, currently used nearly everywhere in the world, is a solar calendar based on the angle of the Earth's rotational axis relative to its local star, the Sun.
The oldest accurately dated star chart was the result of ancient Egyptian astronomy in 1534 BC. The earliest known star catalogues were compiled by the ancient Babylonian astronomers of Mesopotamia in the late 2nd millennium BC, during the Kassite Period (c.1531 BC c.1155 BC).

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The first star catalogue in Greek astronomy was created by Aristillus in approximately 300 BC, with the help of Timocharis. The star catalog of Hipparchus (2nd century BC) included 1,020 stars, and was used to assemble Ptolemy's star catalogue. Hipparchus is known for the discovery of the first recorded nova (new star). Many of the constellations and star names in use today derive from Greek astronomy.
Despite the apparent immutability of the heavens, Chinese astronomers were aware that new stars could appear. In 185 AD, they were the first to observe and write about a supernova, now known as SN 185. The brightest stellar event in recorded history was the SN 1006 supernova, which was observed in 1006 and written about by the Egyptian astronomer Ali ibn Ridwan and several Chinese astronomers. The SN 1054 supernova, which gave birth to the Crab Nebula, was also observed by Chinese and Islamic astronomers.
Medieval Islamic astronomers gave Arabic names to many stars that are still used today and they invented numerous astronomical instruments that could compute the positions of the stars. They built the first large observatory research institutes, mainly to produce Zij star catalogues. Among these, the Book of Fixed Stars (964) was written by the Persian astronomer Abd al-Rahman al-Sufi, who observed a number of stars, star clusters (including the Omicron Velorum and Brocchi's Clusters) and galaxies (including the Andromeda Galaxy). According to A. Zahoor, in the 11th century, the Persian polymath scholar Abu Rayhan Biruni described the Milky Way galaxy as a multitude of fragments having the properties of nebulous stars, and gave the latitudes of various stars during a lunar eclipse in 1019.
According to Josep Puig, the Andalusian astronomer Ibn Bajjah proposed that the Milky Way was made up of many stars that almost touched one another and appeared to be a continuous image due to the effect of refraction from sublunary material, citing his observation of the conjunction of Jupiter and Mars during the year 1106/1107 as evidence.
Early European astronomers such as Tycho Brahe identified new stars in the night sky (later termed novae), suggesting that the heavens were not immutable. In 1584, Giordano Bruno suggested that the stars were like the Sun, and may have other planets, possibly even Earth-like, in orbit around them, an idea that had been suggested earlier by the ancient Greek philosophers, Democritus and Epicurus, and by medieval Islamic cosmologists such as Fakhr al-Din al-Razi. By the following century, the idea of the stars being the same as the Sun was reaching a consensus among astronomers. To explain why these stars exerted no net gravitational pull on the Solar System, Isaac Newton suggested that the stars were equally distributed in every direction, an idea prompted by the theologian Richard Bentley.
The Italian astronomer Geminiano Montanari recorded observing variations in luminosity of the star Algol in 1667. Edmond Halley published the first measurements of the proper motion of a pair of nearby "fixed" stars, demonstrating that they had changed positions since the time of the ancient Greek astronomers Ptolemy and Hipparchus.
William Herschel was the first astronomer to attempt to determine the distribution of stars in the sky. During the 1780s, he established a series of gauges in 600 directions and counted the stars observed along each line of sight. From this, he deduced that the number of stars steadily increased toward one side of the sky, in the direction of the Milky Way core. His son John Herschel repeated this study in the southern hemisphere and found a corresponding increase in the same direction. In addition to his other accomplishments, William Herschel is noted for his discovery that some stars do not merely lie along the same line of sight, but are physical companions that form binary star systems.
The science of stellar spectroscopy was pioneered by Joseph von Fraunhofer and Angelo Secchi. By comparing the spectra of stars such as Sirius to the Sun, they found differences in the strength and number of their absorption lines—the dark lines in stellar spectra caused by the atmosphere's absorption of specific frequencies. In 1865, Secchi began classifying stars into spectral types. The modern version of the stellar classification scheme was developed by Annie J. Cannon during the early 1900s.
The first direct measurement of the distance to a star (61 Cygni at 11.4 light-years) was made in 1838 by Friedrich Bessel using the parallax technique. Parallax measurements demonstrated the vast separation of the stars in the heavens. Observation of double stars gained increasing importance during the 19th century. In 1834, Friedrich Bessel observed changes in the proper motion of the star Sirius and inferred a hidden companion. Edward Pickering discovered the first spectroscopic binary in 1899 when he observed the periodic splitting of the spectral lines of the star Mizar in a 104-day period. Detailed observations of many binary star systems were collected by astronomers such as Friedrich Georg Wilhelm von Struve and S. W. Burnham, allowing the masses of stars to be determined from computation of orbital elements. The first solution to the problem of deriving an orbit of binary stars from telescope observations was made by Felix Savary in 1827.
The twentieth century saw increasingly rapid advances in the scientific study of stars. The photograph became a valuable astronomical tool. Karl Schwarzschild discovered that the color of a star and, hence, its temperature, could be determined by comparing the visual magnitude against the photographic magnitude. The development of the photoelectric photometer allowed precise measurements of magnitude at multiple wavelength intervals. In 1921 Albert A. Michelson made the first measurements of a stellar diameter using an interferometer on the Hooker telescope at Mount Wilson Observatory.
Important theoretical work on the physical structure of stars occurred during the first decades of the twentieth century. In 1913, the HertzsprungRussell diagram was developed, propelling the astrophysical study of stars. Successful models were developed to explain the interiors of stars and stellar evolution. Cecilia Payne-Gaposchkin first proposed that stars were made primarily of hydrogen and helium in her 1925 PhD thesis. The spectra of stars were further understood through advances in quantum physics. This allowed the chemical composition of the stellar atmosphere to be determined.

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The interior of a stable star is in a state of hydrostatic equilibrium: the forces on any small volume almost exactly counterbalance each other. The balanced forces are inward gravitational force and an outward force due to the pressure gradient within the star. The pressure gradient is established by the temperature gradient of the plasma; the outer part of the star is cooler than the core. The temperature at the core of a main-sequence or giant star is at least on the order of 107 K. The resulting temperature and pressure at the hydrogen-burning core of a main-sequence star are sufficient for nuclear fusion to occur and for sufficient energy to be produced to prevent further collapse of the star.
As atomic nuclei are fused in the core, they emit energy in the form of gamma rays. These photons interact with the surrounding plasma, adding to the thermal energy at the core. Stars on the main sequence convert hydrogen into helium, creating a slowly but steadily increasing proportion of helium in the core. Eventually the helium content becomes predominant, and energy production ceases at the core. Instead, for stars of more than 0.4 M☉, fusion occurs in a slowly expanding shell around the degenerate helium core.
In addition to hydrostatic equilibrium, the interior of a stable star will maintain an energy balance of thermal equilibrium. There is a radial temperature gradient throughout the interior that results in a flux of energy flowing toward the exterior. The outgoing flux of energy leaving any layer within the star will exactly match the incoming flux from below.
The radiation zone is the region of the stellar interior where the flux of energy outward is dependent on radiative heat transfer, since convective heat transfer is inefficient in that zone. In this region the plasma will not be perturbed, and any mass motions will die out. Where this is not the case, then the plasma becomes unstable and convection will occur, forming a convection zone. This can occur, for example, in regions where very high energy fluxes occur, such as near the core or in areas with high opacity (making radiatative heat transfer inefficient) as in the outer envelope.
The occurrence of convection in the outer envelope of a main-sequence star depends on the star's mass. Stars with several times the mass of the Sun have a convection zone deep within the interior and a radiative zone in the outer layers. Smaller stars such as the Sun are just the opposite, with the convective zone located in the outer layers. Red dwarf stars with less than 0.4 M☉ are convective throughout, which prevents the accumulation of a helium core. For most stars the convective zones will vary over time as the star ages and the constitution of the interior is modified.
The photosphere is that portion of a star that is visible to an observer. This is the layer at which the plasma of the star becomes transparent to photons of light. From here, the energy generated at the core becomes free to propagate into space. It is within the photosphere that sun spots, regions of lower than average temperature, appear.
Above the level of the photosphere is the stellar atmosphere. In a main-sequence star such as the Sun, the lowest level of the atmosphere, just above the photosphere, is the thin chromosphere region, where spicules appear and stellar flares begin. Above this is the transition region, where the temperature rapidly increases within a distance of only 100 km (62 mi). Beyond this is the corona, a volume of super-heated plasma that can extend outward to several million kilometres. The existence of a corona appears to be dependent on a convective zone in the outer layers of the star. Despite its high temperature, the corona emits very little light, due to its low gas density. The corona region of the Sun is normally only visible during a solar eclipse.
From the corona, a stellar wind of plasma particles expands outward from the star, until it interacts with the interstellar medium. For the Sun, the influence of its solar wind extends throughout a bubble-shaped region called the heliosphere.
== Nuclear fusion reaction pathways ==
When nuclei fuse, the mass of the fused product is less than the mass of the original parts. This lost mass is converted to electromagnetic energy, according to the massenergy equivalence relationship
E
=
m
c
2
{\displaystyle E=mc^{2}}
. A variety of nuclear fusion reactions take place in the cores of stars, that depend upon their mass and composition.
The hydrogen fusion process is temperature-sensitive, so a moderate increase in the core temperature will result in a significant increase in the fusion rate. As a result, the core temperature of main-sequence stars only varies from 4 million kelvin for a small M-class star to 40 million kelvin for a massive O-class star.
In the Sun, with a 16-million-kelvin core, hydrogen fuses to form helium in the protonproton chain reaction:
41H → 22H + 2e+ + 2νe(2 x 0.4 MeV)
2e+ + 2e → 2γ (2 x 1.0 MeV)
21H + 22H → 23He + 2γ (2 x 5.5 MeV)
23He → 4He + 21H (12.9 MeV)
There are a couple other paths, in which 3He and 4He combine to form 7Be, which eventually (with the addition of another proton) yields two 4He, a gain of one.
All these reactions result in the overall reaction:

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41H → 4He + 2γ + 2νe (26.7 MeV)
where γ is a gamma ray photon, νe is a neutrino, and H and He are isotopes of hydrogen and helium, respectively. The energy released by this reaction is in millions of electron volts. Each individual reaction produces only a tiny amount of energy, but because enormous numbers of these reactions occur constantly, they produce all the energy necessary to sustain the star's radiation output. In comparison, the combustion of two hydrogen gas molecules with one oxygen gas molecule releases only 5.7 eV.
In more massive stars, helium is produced in a cycle of reactions catalyzed by carbon called the carbon-nitrogen-oxygen cycle.
In evolved stars with cores at 100 million kelvin and masses between 0.5 and 10 M☉, helium can be transformed into carbon in the triple-alpha process that uses the intermediate element beryllium:
4He + 4He + 92 keV → 8*Be
4He + 8*Be + 67 keV → 12*C
12*C → 12C + γ + 7.4 MeV
For an overall reaction of:
34He → 12C + γ + 7.2 MeV
In massive stars, heavier elements can be burned in a contracting core through the neon-burning process and oxygen-burning process. The final stage in the stellar nucleosynthesis process is the silicon-burning process that results in the production of the stable isotope iron-56. Any further fusion would be an endothermic process that consumes energy, and so further energy can only be produced through gravitational collapse.
== See also ==
List of proper names of stars
Outline of astronomy
Sidereal time
Star clocks
Star count
Stars in fiction
== References ==
== External links ==
"How To Decipher Classification Codes". Astronomical Society of South Australia. Retrieved 20 August 2010.
Kaler, James. "Portraits of Stars and their Constellations". University of Illinois. Retrieved 20 August 2010.
Pickover, Cliff (2001). The Stars of Heaven. Oxford University Press. ISBN 978-0-19-514874-9.
Prialnick, Dina; et al. (2001). "Stars: Stellar Atmospheres, Structure, & Evolution". University of St. Andrews. Archived from the original on 11 February 2021. Retrieved 20 August 2010.
"Query star by identifier, coordinates or reference code". SIMBAD. Centre de Données astronomiques de Strasbourg. Retrieved 20 August 2010.

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With the exception of rare events such as supernovae and supernova impostors, individual stars have primarily been observed in the Local Group, and especially in the visible part of the Milky Way (as demonstrated by the detailed star catalogues available for the Milky Way galaxy) and its satellites. Individual stars such as Cepheid variables have been observed in the M87 and M100 galaxies of the Virgo Cluster, as well as luminous stars in some other relatively nearby galaxies. With the aid of gravitational lensing, a single star (named Icarus) has been observed at 9 billion light-years away.
== Designations ==
The concept of a constellation was known to exist during the Babylonian period. Ancient sky watchers imagined that prominent arrangements of stars formed patterns, and they associated these with particular aspects of nature or their myths. Twelve of these formations lay along the band of the ecliptic and these became the basis of astrology. Many of the more prominent individual stars were given names, particularly with Arabic or Latin designations.
As well as certain constellations and the Sun itself, individual stars have their own myths. To the Ancient Greeks, some "stars", known as planets (Greek πλανήτης (planētēs), meaning "wanderer"), represented various important deities, from which the names of the planets Mercury, Venus, Mars, Jupiter and Saturn were taken. (Uranus and Neptune were Greek and Roman gods, but neither planet was known in Antiquity because of their low brightness. Their names were assigned by later astronomers.)
Circa 1600, the names of the constellations were used to name the stars in the corresponding regions of the sky. The German astronomer Johann Bayer created a series of star maps and applied Greek letters as designations to the stars in each constellation. Later a numbering system based on the star's right ascension was invented and added to John Flamsteed's star catalogue in his book "Historia coelestis Britannica" (the 1712 edition), whereby this numbering system came to be called Flamsteed designation or Flamsteed numbering.
The internationally recognized authority for naming celestial bodies is the International Astronomical Union (IAU). The International Astronomical Union maintains the Working Group on Star Names (WGSN) which catalogs and standardizes proper names for stars. A number of private companies sell names of stars which are not recognized by the IAU, professional astronomers, or the amateur astronomy community. The British Library calls this an unregulated commercial enterprise, and the New York City Department of Consumer and Worker Protection issued a violation against one such star-naming company for engaging in a deceptive trade practice.
== Units of measurement ==
Although stellar parameters can be expressed in SI units or Gaussian units, it is often most convenient to express mass, luminosity, and radii in solar units, based on the characteristics of the Sun. In 2015, the IAU defined a set of nominal solar values (defined as SI constants, without uncertainties) which can be used for quoting stellar parameters:
The solar mass M☉ was not explicitly defined by the IAU due to the large relative uncertainty (104) of the Newtonian constant of gravitation G. Since the product of the Newtonian constant of gravitation and solar mass
together (GM☉) has been determined to much greater precision, the IAU defined the nominal solar mass parameter to be:
The nominal solar mass parameter can be combined with the most recent (2014) CODATA estimate of the Newtonian constant of gravitation G to derive the solar mass to be approximately 1.9885×1030 kg. Although the exact values for the luminosity, radius, mass parameter, and mass may vary slightly in the future due to observational uncertainties, the 2015 IAU nominal constants will remain the same SI values as they remain useful measures for quoting stellar parameters.
Large lengths, such as the radius of a giant star or the semi-major axis of a binary star system, are often expressed in terms of the astronomical unit—approximately equal to the mean distance between the Earth and the Sun (150 million km or approximately 93 million miles). In 2012, the IAU defined the astronomical constant to be an exact length in meters: 149,597,870,700 m.
== Formation and evolution ==
Stars condense from regions of space of higher matter density, yet those regions are less dense than within a vacuum chamber. These regions—known as molecular clouds—consist mostly of hydrogen, with about 23 to 28 percent helium and a few percent heavier elements. One example of such a star-forming region is the Orion Nebula. Most stars form in groups of dozens to hundreds of thousands of stars. Massive stars in these groups may powerfully illuminate those clouds, ionizing the hydrogen, and creating H II regions. Such feedback effects, from star formation, may ultimately disrupt the cloud and prevent further star formation.
All stars spend the majority of their existence as main-sequence stars, fueled primarily by the nuclear fusion of hydrogen into helium within their cores. However, stars of different masses have markedly different properties at various stages of their development. The ultimate fate of more massive stars differs from that of less massive stars, as do their luminosities and the impact they have on their environment. Accordingly, astronomers often group stars by their mass:

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Very low mass stars, with masses below 0.5 M☉, are fully convective and distribute helium evenly throughout the whole star while on the main sequence. Therefore, they never undergo shell burning and never become red giants. After exhausting their hydrogen they become helium white dwarfs and slowly cool. As the lifetime of 0.5 M☉ stars is longer than the age of the universe, no such star has yet reached the white dwarf stage.
Low mass stars (including the Sun), with a mass between 0.5 M☉ and ~2.25 M☉ depending on composition, do become red giants as their core hydrogen is depleted and they begin to burn helium in core in a helium flash; they develop a degenerate carbon-oxygen core later on the asymptotic giant branch; they finally blow off their outer shell as a planetary nebula and leave behind their core in the form of a white dwarf.
Intermediate-mass stars, between ~2.25 M☉ and ~8 M☉, pass through evolutionary stages similar to low mass stars, but after a relatively short period on the red-giant branch they ignite helium without a flash and spend an extended period in the red clump before forming a degenerate carbon-oxygen core.
Massive stars generally have a minimum mass of ~8 M☉. After exhausting the hydrogen at the core these stars become supergiants and go on to fuse elements heavier than helium. Many end their lives when their cores collapse and they explode as supernovae.
=== Star formation ===
The formation of a star begins with gravitational instability within a molecular cloud, caused by regions of higher density—often triggered by compression of clouds by radiation from massive stars, expanding bubbles in the interstellar medium, the collision of different molecular clouds, or the collision of galaxies (as in a starburst galaxy). When a region reaches a sufficient density of matter to satisfy the criteria for Jeans instability, it begins to collapse under its own gravitational force.
As the cloud collapses, individual conglomerations of dense dust and gas form "Bok globules". As a globule collapses and the density increases, the gravitational energy converts into heat and the temperature rises. When the protostellar cloud has approximately reached the stable condition of hydrostatic equilibrium, a protostar forms at the core. These pre-main-sequence stars are often surrounded by a protoplanetary disk and powered mainly by the conversion of gravitational energy. The period of gravitational contraction lasts about 10 million years for a star like the Sun, up to 100 million years for a red dwarf.
Early stars of less than 2 M☉ are called T Tauri stars, while those with greater mass are Herbig Ae/Be stars. These newly formed stars emit jets of gas along their axis of rotation, which may reduce the angular momentum of the collapsing star and result in small patches of nebulosity known as HerbigHaro objects.
These jets, in combination with radiation from nearby massive stars, may help to drive away the surrounding cloud from which the star was formed.
Early in their development, T Tauri stars follow the Hayashi track—they contract and decrease in luminosity while remaining at roughly the same temperature. Less massive T Tauri stars follow this track to the main sequence, while more massive stars turn onto the Henyey track.
Most stars are observed to be members of binary star systems, and the properties of those binaries are the result of the conditions in which they formed. A gas cloud must lose its angular momentum in order to collapse and form a star. The fragmentation of the cloud into multiple stars distributes some of that angular momentum. The primordial binaries transfer some angular momentum by gravitational interactions during close encounters with other stars in young stellar clusters. These interactions tend to split apart more widely separated (soft) binaries while causing hard binaries to become more tightly bound. This produces the separation of binaries into their two observed populations distributions.
=== Main sequence ===
Stars spend about 90% of their lifetimes fusing hydrogen into helium in high-temperature-and-pressure reactions in their cores. Such stars are said to be on the main sequence and are called dwarf stars. Starting at zero-age main sequence, the proportion of helium in a star's core will steadily increase, the rate of nuclear fusion at the core will slowly increase, as will the star's temperature and luminosity.
The Sun, for example, is estimated to have increased in luminosity by about 40% since it reached the main sequence 4.6 billion (4.6×109) years ago.
Every star generates a stellar wind of particles that causes a continual outflow of gas into space. For most stars, the mass lost is negligible. The Sun loses 1014 M☉ every year, or about 0.01% of its total mass over its entire lifespan. However, very massive stars can lose 107 to 105 M☉ each year, significantly affecting their evolution. Stars that begin with more than 50 M☉ can lose over half their total mass while on the main sequence.

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The time a star spends on the main sequence depends primarily on the amount of fuel it has and the rate at which it fuses it. The Sun is expected to live 10 billion (1010) years. Massive stars consume their fuel very rapidly and are short-lived. Low mass stars consume their fuel very slowly. Stars less massive than 0.25 M☉, called red dwarfs, are able to fuse nearly all of their mass while stars of about 1 M☉ can only fuse about 10% of their mass. The combination of their slow fuel-consumption and relatively large usable fuel supply allows low mass stars to last about one trillion (10×1012) years; the most extreme of 0.08 M☉ will last for about 12 trillion years. Red dwarfs become hotter and more luminous as they accumulate helium. When they eventually run out of hydrogen, they contract into a white dwarf and decline in temperature. Since the lifespan of such stars is greater than the current age of the universe (13.8 billion years), no stars under about 0.85 M☉ are expected to have moved off the main sequence.
Besides mass, the elements heavier than helium can play a significant role in the evolution of stars. Astronomers label all elements heavier than helium "metals", and call the chemical concentration of these elements in a star, its metallicity. A star's metallicity can influence the time the star takes to burn its fuel, and controls the formation of its magnetic fields, which affects the strength of its stellar wind. Older, population II stars have substantially less metallicity than the younger, population I stars due to the composition of the molecular clouds from which they formed. Over time, such clouds become increasingly enriched in heavier elements as older stars die and shed portions of their atmospheres.
=== Postmain sequence ===
As stars of at least 0.4 M☉ exhaust the supply of hydrogen at their core, they start to fuse hydrogen in a shell surrounding the helium core. The outer layers of the star expand and cool greatly as they transition into a red giant. In some cases, they will fuse heavier elements at the core or in shells around the core. As the stars expand, they throw part of their mass, enriched with those heavier elements, into the interstellar environment, to be recycled later as new stars. In about 5 billion years, when the Sun enters the helium burning phase, it will expand to a maximum radius of roughly 1 astronomical unit (150 million kilometres), 250 times its present size, and lose 30% of its current mass.
As the hydrogen-burning shell produces more helium, the core increases in mass and temperature. In a red giant of up to 2.25 M☉, the mass of the helium core becomes degenerate prior to helium fusion. Finally, when the temperature increases sufficiently, core helium fusion begins explosively in what is called a helium flash, and the star rapidly shrinks in radius, increases its surface temperature, and moves to the horizontal branch of the HR diagram. For more massive stars, helium core fusion starts before the core becomes degenerate, and the star spends some time in the red clump, slowly burning helium, before the outer convective envelope collapses and the star then moves to the horizontal branch.
After a star has fused the helium of its core, it begins fusing helium along a shell surrounding the hot carbon core. The star then follows an evolutionary path called the asymptotic giant branch (AGB) that parallels the other described red-giant phase, but with a higher luminosity. The more massive AGB stars may undergo a brief period of carbon fusion before the core becomes degenerate. During the AGB phase, stars undergo thermal pulses due to instabilities in the core of the star. In these thermal pulses, the luminosity of the star varies and matter is ejected from the star's atmosphere, ultimately forming a planetary nebula. As much as 50 to 70% of a star's mass can be ejected in this mass loss process. Because energy transport in an AGB star is primarily by convection, this ejected material is enriched with the fusion products dredged up from the core. Therefore, the planetary nebula is enriched with elements like carbon and oxygen. Ultimately, the planetary nebula disperses, enriching the general interstellar medium. Therefore, future generations of stars are made of the "star stuff" from past stars.
==== Massive stars ====
During their helium-burning phase, a star of more than 9 solar masses expands to form first a blue supergiant and then a red supergiant. Particularly massive stars (exceeding 40 solar masses, like Alnilam, the central blue supergiant of Orion's Belt) do not become red supergiants due to high mass loss. These may instead evolve to a WolfRayet star, characterised by spectra dominated by emission lines of elements heavier than hydrogen, which have reached the surface due to strong convection and intense mass loss, or from stripping of the outer layers.
When helium is exhausted at the core of a massive star, the core contracts and the temperature and pressure rises enough to fuse carbon (see Carbon-burning process). This process continues, with the successive stages being fueled by neon (see neon-burning process), oxygen (see oxygen-burning process), and silicon (see silicon-burning process). Near the end of the star's life, fusion continues along a series of onion-layer shells within a massive star. Each shell fuses a different element, with the outermost shell fusing hydrogen; the next shell fusing helium, and so forth.
The final stage occurs when a massive star begins producing iron. Since iron nuclei are more tightly bound than any heavier nuclei, any fusion beyond iron does not produce a net release of energy.
Some massive stars, particularly luminous blue variables, are very unstable to the extent that they violently shed their mass into space in events known as supernova impostors, becoming significantly brighter in the process. Eta Carinae is known for having undergone a supernova impostor event, the Great Eruption, in the 19th century.

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==== Collapse ====
As a star's core shrinks, the intensity of radiation from that surface increases, creating such radiation pressure on the outer shell of gas that it will push those layers away, forming a planetary nebula. If what remains after the outer atmosphere has been shed is less than roughly 1.4 M☉, it shrinks to a relatively tiny object about the size of Earth, known as a white dwarf. White dwarfs lack the mass for further gravitational compression to take place. The electron-degenerate matter inside a white dwarf is no longer a plasma. Eventually, white dwarfs fade into black dwarfs over a very long period of time.
In massive stars, fusion continues until the iron core has grown so large (more than 1.4 M☉) that it can no longer support its own mass. This core will suddenly collapse as its electrons are driven into its protons, forming neutrons, neutrinos, and gamma rays in a burst of electron capture and inverse beta decay. The shockwave formed by this sudden collapse causes the rest of the star to explode in a supernova. Supernovae become so bright that they may briefly outshine the star's entire home galaxy. When they occur within the Milky Way, supernovae have historically been observed by naked-eye observers as "new stars" where none seemingly existed before.
A supernova explosion blows away the star's outer layers, leaving a remnant such as the Crab Nebula. The core is compressed into a neutron star, which sometimes manifests itself as a pulsar or X-ray burster. In the case of the largest stars, the remnant is a black hole greater than 4 M☉. In a neutron star the matter is in a state known as neutron-degenerate matter, with a more exotic form of degenerate matter, QCD matter, possibly present in the core.
The blown-off outer layers of dying stars include heavy elements, which may be recycled during the formation of new stars. These heavy elements allow the formation of rocky planets. The outflow from supernovae and the stellar wind of large stars play an important part in shaping the interstellar medium.
==== Binary stars ====
Binary stars' evolution may significantly differ from that of single stars of the same mass. For example, when any star expands to become a red giant, it may overflow its Roche lobe, the surrounding region where material is gravitationally bound to it; if stars in a binary system are close enough, some of that material may overflow to the other star, yielding phenomena including contact binaries, common-envelope binaries, cataclysmic variables, blue stragglers, and Type Ia supernovae. Mass transfer leads to cases such as the Algol paradox, where the most-evolved star in a system is the least massive.
The evolution of binary star and higher-order star systems is intensely researched since so many stars have been found to be members of binary systems. Around half of Sun-like stars, and an even higher proportion of more massive stars, form in multiple systems, and this may greatly influence such phenomena as novae and supernovae, the formation of certain types of star, and the enrichment of space with nucleosynthesis products.
The influence of binary star evolution on the formation of evolved massive stars such as luminous blue variables, WolfRayet stars, and the progenitors of certain classes of core collapse supernova is still disputed. Single massive stars may be unable to expel their outer layers fast enough to form the types and numbers of evolved stars that are observed, or to produce progenitors that would explode as the supernovae that are observed. Mass transfer through gravitational stripping in binary systems is seen by some astronomers as the solution to that problem.
== Distribution ==
Stars are not spread uniformly across the universe but are normally grouped into galaxies along with interstellar gas and dust. A typical large galaxy like the Milky Way contains hundreds of billions of stars. There are more than 2 trillion (1012) galaxies, though most are less than 10% the mass of the Milky Way. Overall, there are likely to be between 1022 and 1024 stars, which are more stars than all the grains of sand on planet Earth. Most stars are within galaxies, but between 10 and 50% of the starlight in large galaxy clusters may come from stars outside of any galaxy.
A multi-star system consists of two or more gravitationally bound stars that orbit each other. The simplest and most common multi-star system is a binary star, but systems of three or more stars exist. For reasons of orbital stability, such multi-star systems are often organized into hierarchical sets of binary stars. Larger groups are called star clusters. These range from loose stellar associations with only a few stars to open clusters with dozens to thousands of stars, up to enormous globular clusters with hundreds of thousands of stars. Such systems orbit their host galaxy. The stars in an open or globular cluster all formed from the same giant molecular cloud, so all members normally have similar ages and compositions.
Many stars are observed, and most or all may have originally formed in gravitationally bound, multiple-star systems. This is particularly true for very massive O and B class stars, 80% of which are believed to be part of multiple-star systems. The proportion of single star systems increases with decreasing star mass, so that only 25% of red dwarfs are known to have stellar companions. As 85% of all stars are red dwarfs, more than two thirds of stars in the Milky Way are likely single red dwarfs. In a 2017 study of the Perseus molecular cloud, astronomers found that most of the newly formed stars are in binary systems. In the model that best explained the data, all stars initially formed as binaries, though some binaries later split up and leave single stars behind.

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The nearest star to the Earth, apart from the Sun, is Proxima Centauri, 4.2465 light-years (40.175 trillion kilometres) away. Travelling at the orbital speed of the Space Shuttle, 8 kilometres per second (29,000 kilometres per hour), it would take about 150,000 years to arrive. This is typical of stellar separations in galactic discs. Stars can be much closer to each other in the centres of galaxies and in globular clusters, or much farther apart in galactic halos.
Due to the relatively vast distances between stars outside the galactic nucleus, collisions between stars are thought to be rare. In denser regions such as the core of globular clusters or the galactic center, collisions can be more common. Such collisions can produce what are known as blue stragglers. These abnormal stars have higher surface temperatures and thus are bluer than stars at the main sequence turnoff in the cluster to which they belong; in standard stellar evolution, blue stragglers would already have evolved off the main sequence and thus would not be seen in the cluster.
== Characteristics ==
Almost everything about a star is determined by its initial mass, including such characteristics as luminosity, size, evolution, lifespan, and its eventual fate.
=== Age ===
Most stars are between 1 billion and 10 billion years old. Some stars may even be close to 13.8 billion years old—the observed age of the universe. The oldest star yet discovered, HD 140283, nicknamed Methuselah star, is an estimated 14.46 ± 0.8 billion years old. (Due to the uncertainty in the value, this age for the star does not conflict with the age of the universe, determined by the Planck satellite as 13.799 ± 0.021).
The more massive the star, the shorter its lifespan, primarily because massive stars have greater pressure on their cores, causing them to burn hydrogen more rapidly. The most massive stars last an average of a few million years, while stars of minimum mass (red dwarfs) burn their fuel very slowly and can last tens to hundreds of billions of years.
=== Chemical composition ===
When stars form in the present Milky Way galaxy, they are composed of about 71% hydrogen and 27% helium, as measured by mass, with a small fraction of heavier elements. Typically the portion of heavy elements is measured in terms of the iron content of the stellar atmosphere, as iron is a common element and its absorption lines are relatively easy to measure. The portion of heavier elements may be an indicator of the likelihood that the star has a planetary system.
As of 2005 the star with the lowest iron content ever measured is the dwarf HE1327-2326, with only 1/200,000th the iron content of the Sun. By contrast, the super-metal-rich star μ Leonis has nearly double the abundance of iron as the Sun, while the planet-bearing star 14 Herculis has nearly triple the iron. Chemically peculiar stars show unusual abundances of certain elements in their spectrum; especially chromium and rare earth elements. Stars with cooler outer atmospheres, including the Sun, can form various diatomic and polyatomic molecules.
=== Diameter ===
Due to their great distance from the Earth, all stars except the Sun appear to the unaided eye as shining points in the night sky that twinkle because of the effect of the Earth's atmosphere. The Sun is close enough to the Earth to appear as a disk instead, and to provide daylight. Other than the Sun, the star with the largest apparent size is R Doradus, with an angular diameter of only 0.057 arcseconds.
The disks of most stars are much too small in angular size to be observed with current ground-based optical telescopes, so interferometer telescopes are required to produce images of these objects. Another technique for measuring the angular size of stars is through occultation. By precisely measuring the drop in brightness of a star as it is occulted by the Moon (or the rise in brightness when it reappears), the star's angular diameter can be computed.
Stars range in size from neutron stars, which vary anywhere from 20 to 40 km (25 mi) in diameter, to supergiants like Betelgeuse in the Orion constellation, which has a diameter about 640 times that of the Sun with a much lower density.
=== Kinematics ===
The motion of a star relative to the Sun can provide useful information about the origin and age of a star, as well as the structure and evolution of the surrounding galaxy. The components of motion of a star consist of the radial velocity toward or away from the Sun, and the traverse angular movement, which is called its proper motion.
Radial velocity is measured by the doppler shift of the star's spectral lines and is given in units of km/s. The proper motion of a star, its parallax, is determined by precise astrometric measurements in units of milli-arc seconds (mas) per year. With knowledge of the star's parallax and its distance, the proper motion velocity can be calculated. Together with the radial velocity, the total velocity can be calculated. Stars with high rates of proper motion are likely to be relatively close to the Sun, making them good candidates for parallax measurements.
When both rates of movement are known, the space velocity of the star relative to the Sun or the galaxy can be computed. Among nearby stars, it has been found that younger population I stars have generally lower velocities than older, population II stars. The latter have elliptical orbits that are inclined to the plane of the galaxy. A comparison of the kinematics of nearby stars has allowed astronomers to trace their origin to common points in giant molecular clouds; such groups with common points of origin are referred to as stellar associations.
=== Magnetic field ===

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The magnetic field of a star is generated within regions of the interior where convective circulation occurs. This movement of conductive plasma functions like a dynamo, wherein the movement of electrical charges induce magnetic fields, as does a mechanical dynamo. Those magnetic fields have a great range that extend throughout and beyond the star. The strength of the magnetic field varies with the mass and composition of the star, and the amount of magnetic surface activity depends upon the star's rate of rotation. This surface activity produces starspots, which are regions of strong magnetic fields and lower than normal surface temperatures. Coronal loops are arching magnetic field flux lines that rise from a star's surface into the star's outer atmosphere, its corona. The coronal loops can be seen due to the plasma they conduct along their length. Stellar flares are bursts of high-energy particles that are emitted due to the same magnetic activity.
Young, rapidly rotating stars tend to have high levels of surface activity because of their magnetic field. The magnetic field can act upon a star's stellar wind, functioning as a brake to gradually slow the rate of rotation with time. Thus, older stars such as the Sun have a much slower rate of rotation and a lower level of surface activity. The activity levels of slowly rotating stars tend to vary in a cyclical manner and can shut down altogether for periods of time. During the Maunder Minimum, for example, the Sun underwent a 70-year period with almost no sunspot activity.
=== Mass ===
Stars have masses ranging from less than half the solar mass to over 200 solar masses (see List of most massive stars). One of the most massive stars known is Eta Carinae, which, with 100150 times as much mass as the Sun, will have a lifespan of only several million years. Studies of the most massive open clusters suggests 150 M☉ as a rough upper limit for stars in the current era of the universe. This represents an empirical value for the theoretical limit on the mass of forming stars due to increasing radiation pressure on the accreting gas cloud. Several stars in the R136 cluster in the Large Magellanic Cloud have been measured with larger masses, but it has been determined that they could have been created through the collision and merger of massive stars in close binary systems, sidestepping the 150 M☉ limit on massive star formation.
The first stars to form after the Big Bang may have been larger, up to 300 M☉, due to the complete absence of elements heavier than lithium in their composition. This generation of supermassive population III stars is likely to have existed in the very early universe (i.e., they are observed to have a high redshift), and may have started the production of chemical elements heavier than hydrogen that are needed for the later formation of planets and life. In June 2015, astronomers reported evidence for Population III stars in the Cosmos Redshift 7 galaxy at z = 6.60.
With a mass only 80 times that of Jupiter (MJ), 2MASS J0523-1403 is the smallest known star undergoing nuclear fusion in its core. For stars with metallicity similar to the Sun, the theoretical minimum mass the star can have and still undergo fusion at the core, is estimated to be about 75 MJ. When the metallicity is very low, the minimum star size seems to be about 8.3% of the solar mass, or about 87 MJ. Smaller bodies called brown dwarfs, occupy a poorly defined grey area between stars and gas giants.
The combination of the radius and the mass of a star determines its surface gravity. Giant stars have much lower surface gravity than do main-sequence stars, while the opposite is the case for degenerate, compact stars such as white dwarfs. The surface gravity can influence the appearance of a star's spectrum, with higher gravity causing a broadening of the absorption lines.
=== Rotation ===
The rotation rate of stars can be determined through spectroscopic measurement, or more exactly determined by tracking their starspots. Young stars can have a rotation greater than 100 km/s at the equator. The B-class star Achernar, for example, has an equatorial velocity of about 225 km/s or greater, causing its equator to bulge outward and giving it an equatorial diameter that is more than 50% greater than between the poles. This rate of rotation is just below the critical velocity of 300 km/s at which speed the star would break apart. By contrast, the Sun rotates once every 2535 days depending on latitude, with an equatorial velocity of 1.93 km/s. A main-sequence star's magnetic field and the stellar wind serve to slow its rotation by a significant amount as it evolves on the main sequence.
Degenerate stars have contracted into a compact mass, resulting in a rapid rate of rotation. However they have relatively low rates of rotation compared to what would be expected by conservation of angular momentum—the tendency of a rotating body to compensate for a contraction in size by increasing its rate of spin. A large portion of the star's angular momentum is dissipated as a result of mass loss through the stellar wind. In spite of this, the rate of rotation for a pulsar can be very rapid. The pulsar at the heart of the Crab nebula, for example, rotates 30 times per second. The rotation rate of the pulsar will gradually slow due to the emission of radiation.

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=== Temperature ===
The surface temperature of a main-sequence star is determined by the rate of energy production of its core and by its radius, and is often estimated from the star's color index. The temperature is normally given in terms of an effective temperature, which is the temperature of an idealized black body that radiates its energy at the same luminosity per surface area as the star. The effective temperature is only representative of the surface, as the temperature increases toward the core. The temperature in the core region of a star is several million kelvins.
The stellar temperature will determine the rate of ionization of various elements, resulting in characteristic absorption lines in the spectrum. The surface temperature of a star, along with its visual absolute magnitude and absorption features, is used to classify a star (see classification below).
Massive main-sequence stars can have surface temperatures of 50,000 K. Smaller stars such as the Sun have surface temperatures of a few thousand K. Red giants have relatively low surface temperatures of about 3,600 K; but they have a high luminosity due to their large exterior surface area.
== Radiation ==
The energy produced by stars, a product of nuclear fusion, radiates to space as both electromagnetic radiation and particle radiation. The particle radiation emitted by a star is manifested as the stellar wind, which streams from the outer layers as electrically charged protons and alpha and beta particles. A steady stream of almost massless neutrinos emanate directly from the star's core.
The production of energy at the core is the reason stars shine so brightly: every time two or more atomic nuclei fuse together to form a single atomic nucleus of a new heavier element, gamma ray photons are released from the nuclear fusion product. This energy is converted to other forms of electromagnetic energy of lower frequency, such as visible light, by the time it reaches the star's outer layers.
The color of a star, as determined by the most intense frequency of the visible light, depends on the temperature of the star's outer layers, including its photosphere. Besides visible light, stars emit forms of electromagnetic radiation that are invisible to the human eye. In fact, stellar electromagnetic radiation spans the entire electromagnetic spectrum, from the longest wavelengths of radio waves through infrared, visible light, ultraviolet, to the shortest of X-rays, and gamma rays. From the standpoint of total energy emitted by a star, not all components of stellar electromagnetic radiation are significant, but all frequencies provide insight into the star's physics.
Using the stellar spectrum, astronomers can determine the surface temperature, surface gravity, metallicity and rotational velocity of a star. If the distance of the star is found, such as by measuring the parallax, then the luminosity of the star can be derived. The mass, radius, surface gravity, and rotation period can then be estimated based on stellar models. (Mass can be calculated for stars in binary systems by measuring their orbital velocities and distances. Gravitational microlensing has been used to measure the mass of a single star.) With these parameters, astronomers can estimate the age of the star.
=== Luminosity ===
The luminosity of a star is the amount of light and other forms of radiant energy it radiates per unit of time. It has units of power. The luminosity of a star is determined by its radius and surface temperature. Many stars do not radiate uniformly across their entire surface. The rapidly rotating star Vega, for example, has a higher energy flux (power per unit area) at its poles than along its equator.
Patches of the star's surface with a lower temperature and luminosity than average are known as starspots. Small, dwarf stars such as the Sun generally have essentially featureless disks with only small starspots. Giant stars have much larger, more obvious starspots, and they exhibit strong stellar limb darkening. That is, the brightness decreases towards the edge of the stellar disk. Red dwarf flare stars such as UV Ceti may possess prominent starspot features.
=== Magnitude ===
The apparent brightness of a star is expressed in terms of its apparent magnitude. It is a function of the star's luminosity, its distance from Earth, the extinction effect of interstellar dust and gas, and the altering of the star's light as it passes through Earth's atmosphere. Intrinsic or absolute magnitude is directly related to a star's luminosity, and is the apparent magnitude a star would be if the distance between the Earth and the star were 10 parsecs (32.6 light-years).
Both the apparent and absolute magnitude scales are logarithmic units: one whole number difference in magnitude is equal to a brightness variation of about 2.5 times (the 5th root of 100 or approximately 2.512). This means that a first magnitude star (+1.00) is about 2.5 times brighter than a second magnitude (+2.00) star, and about 100 times brighter than a sixth magnitude star (+6.00). The faintest stars visible to the naked eye under good seeing conditions are about magnitude +6.
On both apparent and absolute magnitude scales, the smaller the magnitude number, the brighter the star; the larger the magnitude number, the fainter the star. The brightest stars, on either scale, have negative magnitude numbers. The variation in brightness (ΔL) between two stars is calculated by subtracting the magnitude number of the brighter star (mb) from the magnitude number of the fainter star (mf), then using the difference as an exponent for the base number 2.512; that is to say:
Δ
m
=
m
f
m
b
{\displaystyle \Delta {m}=m_{\mathrm {f} }-m_{\mathrm {b} }}
2.512
Δ
m
=
Δ
L
{\displaystyle 2.512^{\Delta {m}}=\Delta {L}}

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Relative to both luminosity and distance from Earth, a star's absolute magnitude (M) and apparent magnitude (m) are not equivalent; for example, the bright star Sirius has an apparent magnitude of 1.44, but it has an absolute magnitude of +1.41.
The Sun has an apparent magnitude of 26.7, but its absolute magnitude is only +4.83. Sirius, the brightest star in the night sky as seen from Earth, is approximately 23 times more luminous than the Sun, while Canopus, the second brightest star in the night sky with an absolute magnitude of 5.53, is approximately 14,000 times more luminous than the Sun. Despite Canopus being vastly more luminous than Sirius, the latter star appears the brighter of the two. This is because Sirius is merely 8.6 light-years from the Earth, while Canopus is much farther away at a distance of 310 light-years.
The most luminous known stars have absolute magnitudes of roughly 12, corresponding to 6 million times the luminosity of the Sun. Theoretically, the least luminous stars are at the lower limit of mass at which stars are capable of supporting nuclear fusion of hydrogen in the core; stars just above this limit have been located in the NGC 6397 cluster. The faintest red dwarfs in the cluster are absolute magnitude 15, while a 17th absolute magnitude white dwarf has been discovered.
== Classification ==
The current stellar classification system originated in the early 20th century, when stars were classified from A to Q based on the strength of the hydrogen line. It was thought that the hydrogen line strength was a simple linear function of temperature. Instead, it was more complicated: it strengthened with increasing temperature, peaked near 9000 K, and then declined at greater temperatures. The classifications were since reordered by temperature, on which the modern scheme is based.
Stars are given a single-letter classification according to their spectra, ranging from type O, which are very hot, to M, which are so cool that molecules may form in their atmospheres. The main classifications in order of decreasing surface temperature are: O, B, A, F, G, K, and M. A variety of rare spectral types are given special classifications. The most common of these are types L and T, which classify the coldest low-mass stars and brown dwarfs. Each letter has 10 sub-divisions, numbered from 0 to 9, in order of decreasing temperature. However, this system breaks down at extreme high temperatures as classes O0 and O1 may not exist.
In addition, stars may be classified by the luminosity effects found in their spectral lines, which correspond to their spatial size and is determined by their surface gravity. These range from 0 (hypergiants) through III (giants) to V (main-sequence dwarfs); some authors add VII (white dwarfs). Main-sequence stars fall along a narrow, diagonal band when graphed according to their absolute magnitude and spectral type. The Sun is a main-sequence G2V yellow dwarf of intermediate temperature and ordinary size.
There is additional nomenclature in the form of lower-case letters added to the end of the spectral type to indicate peculiar features of the spectrum. For example, an "e" can indicate the presence of emission lines; "m" represents unusually strong levels of metals, and "var" can mean variations in the spectral type.
White dwarf stars have their own class that begins with the letter D. This is further sub-divided into the classes DA, DB, DC, DO, DZ, and DQ, depending on the types of prominent lines found in the spectrum. This is followed by a numerical value that indicates the temperature.
== Variable stars ==
Variable stars have periodic or random changes in luminosity because of intrinsic or extrinsic properties. Of the intrinsically variable stars, the primary types can be subdivided into three principal groups.
During their stellar evolution, some stars pass through phases where they can become pulsating variables. Pulsating variable stars vary in radius and luminosity over time, expanding and contracting with periods ranging from minutes to years, depending on the size of the star. This category includes Cepheid and Cepheid-like stars, and long-period variables such as Mira.
Eruptive variables are stars that experience sudden increases in luminosity because of flares or mass ejection events. This group includes protostars, Wolf-Rayet stars, and flare stars, as well as giant and supergiant stars.
Cataclysmic or explosive variable stars are those that undergo a dramatic change in their properties. This group includes novae and supernovae. A binary star system that includes a nearby white dwarf can produce certain types of these spectacular stellar explosions, including the nova and a Type Ia supernova. The explosion is created when the white dwarf accretes hydrogen from the companion star, building up mass until the hydrogen undergoes fusion. Some novae are recurrent, having periodic outbursts of moderate amplitude.
Stars can vary in luminosity because of extrinsic factors, such as eclipsing binaries, as well as rotating stars that produce extreme starspots. A notable example of an eclipsing binary is Algol, which regularly varies in magnitude from 2.1 to 3.4 over a period of 2.87 days.
== Structure ==

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Star formation is the process by which dense regions within molecular clouds in interstellar space—sometimes referred to as "stellar nurseries" or "star-forming regions"—collapse and form stars. As a branch of astronomy, star formation includes the study of the interstellar medium (ISM) and giant molecular clouds (GMC) as precursors to the star formation process, and the study of protostars and young stellar objects as its immediate products. It is closely related to planet formation, another branch of astronomy. Star formation theory, as well as accounting for the formation of a single star, must also account for the statistics of binary stars and the initial mass function. Most stars do not form in isolation but as part of a group of stars referred to as star clusters or stellar associations.
== First stars ==
Star formation is divided into three groups called "Populations". Population III stars formed from primordial hydrogen after the Big Bang. These stars are poorly understood but should contain only hydrogen and helium. Population II stars formed from the debris of the first stars and they in turn created more higher atomic number chemical elements. Population I stars are young metal-rich (contain elements other than hydrogen and helium) stars like the Sun.
The initial star formation was driven by gravitational attraction of hydrogen within local areas of higher gravity called dark matter halos. As the hydrogen lost energy through atomic or molecular energy transitions, the temperature of local clumps fell allowing more gravitational condensation. Eventually the process leads to collapse into a star. Details of the dynamics of the Population III stars is now believed to be as complex as star formation today.
== Stellar nurseries ==
=== Interstellar clouds ===
Spiral galaxies like the Milky Way contain stars, stellar remnants, and a diffuse interstellar medium (ISM) of gas and dust. The interstellar medium consists of 104 to 106 particles per cm3, and is typically composed of roughly 70% hydrogen, 28% helium, and 1.5% heavier elements by mass. The trace amounts of heavier elements were and are produced within stars via stellar nucleosynthesis and ejected as the stars pass beyond the end of their main sequence lifetime. Higher density regions of the interstellar medium form clouds, or diffuse nebulae, where star formation takes place. In contrast to spiral galaxies, elliptical galaxies lose the cold component of its interstellar medium within roughly a billion years, which hinders the galaxy from forming diffuse nebulae except through mergers with other galaxies.
In the dense nebulae where stars are produced, much of the hydrogen is in the molecular (H2) form, so these nebulae are called molecular clouds. The Herschel Space Observatory has revealed that filaments, or elongated dense gas structures, are truly ubiquitous in molecular clouds and central to the star formation process. They fragment into gravitationally bound cores, most of which will evolve into stars. Continuous accretion of gas, geometrical bending, and magnetic fields may control the detailed manner in which the filaments are fragmented. Observations of supercritical filaments have revealed quasi-periodic chains of dense cores with spacing comparable to the filament inner width, and embedded protostars with outflows.
Observations indicate that the coldest clouds tend to form low-mass stars, which are first observed via the infrared light they emit inside the clouds, and then as visible light when the clouds dissipate. Giant molecular clouds, which are generally warmer, produce stars of all masses. These giant molecular clouds have typical densities of 100 particles per cm3, diameters of 100 light-years (9.5×1014 km), masses of up to 6 million solar masses (M☉), or six million times the mass of the Sun. The average interior temperature is 10 K (441.7 °F).
About half the total mass of the Milky Way's galactic ISM is found in molecular clouds and the galaxy includes an estimated 6,000 molecular clouds, each with more than 100,000 M☉. The nebula nearest to the Sun where massive stars are being formed is the Orion Nebula, 1,300 light-years (1.2×1016 km) away. However, lower mass star formation is occurring about 400450 light-years distant in the ρ Ophiuchi cloud complex.
A more compact site of star formation is the opaque clouds of dense gas and dust known as Bok globules, so named after the astronomer Bart Bok. These can form in association with collapsing molecular clouds or possibly independently. The Bok globules are typically up to a light-year across and contain a few solar masses. They can be observed as dark clouds silhouetted against bright emission nebulae or background stars. Over half the known Bok globules have been found to contain newly forming stars.
=== Cloud collapse ===
An interstellar cloud of gas will remain in hydrostatic equilibrium as long as the kinetic energy of the gas pressure is in balance with the potential energy of the internal gravitational force. Mathematically this is expressed using the virial theorem, which states that, to maintain equilibrium, the gravitational potential energy must equal twice the internal thermal energy. If a cloud is massive enough that the gas pressure is insufficient to support it, the cloud will undergo gravitational collapse. The mass above which a cloud will undergo such collapse is called the Jeans mass. The Jeans mass depends on the temperature and density of the cloud, but is typically thousands to tens of thousands of solar masses. During cloud collapse dozens to tens of thousands of stars form more or less simultaneously which is observable in so-called embedded clusters. The end product of a core collapse is an open cluster of stars.

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In triggered star formation, one of several events might occur to compress a molecular cloud and initiate its gravitational collapse. Molecular clouds may collide with each other, or a nearby supernova explosion can be a trigger, sending shocked matter into the cloud at very high speeds. (The resulting new stars may themselves soon produce supernovae, producing self-propagating star formation.) Alternatively, galactic collisions can trigger massive starbursts of star formation as the gas clouds in each galaxy are compressed and agitated by tidal forces. The latter mechanism may be responsible for the formation of globular clusters.
A supermassive black hole at the core of a galaxy may serve to regulate the rate of star formation in a galactic nucleus. A black hole that is accreting infalling matter can become active, emitting a strong wind through a collimated relativistic jet. This can limit further star formation. Massive black holes ejecting radio-frequency-emitting particles at near-light speed can also block the formation of new stars in aging galaxies. However, the radio emissions around the jets may also trigger star formation. Likewise, a weaker jet may trigger star formation when it collides with a cloud.
As it collapses, a molecular cloud breaks into smaller and smaller pieces in a hierarchical manner, until the fragments reach stellar mass. In each of these fragments, the collapsing gas radiates away the energy gained by the release of gravitational potential energy. As the density increases, the fragments become opaque and are thus less efficient at radiating away their energy. This raises the temperature of the cloud and inhibits further fragmentation. The fragments now condense into rotating spheres of gas that serve as stellar embryos.
Complicating this picture of a collapsing cloud are the effects of turbulence, macroscopic flows, rotation, magnetic fields and the cloud geometry. Both rotation and magnetic fields can hinder the collapse of a cloud. Turbulence is instrumental in causing fragmentation of the cloud, and on the smallest scales it promotes collapse.
== Protostar ==
A protostellar cloud will continue to collapse as long as the gravitational binding energy can be eliminated. This excess energy is primarily lost through radiation. However, the collapsing cloud will eventually become opaque to its own radiation, and the energy must be removed through some other means. The dust within the cloud becomes heated to temperatures of 60100 K, and these particles radiate at wavelengths in the far infrared where the cloud is transparent. Thus the dust mediates the further collapse of the cloud.
During the collapse, the density of the cloud increases towards the center and thus the middle region becomes optically opaque first. This occurs when the density is about 1013 g / cm3. A core region, called the first hydrostatic core, forms where the collapse is essentially halted. It continues to increase in temperature as determined by the virial theorem. The gas falling toward this opaque region collides with it and creates shock waves that further heat the core.
When the core temperature reaches about 2000 K, the thermal energy dissociates the H2 molecules. This is followed by the ionization of the hydrogen and helium atoms. These processes absorb the energy of the contraction, allowing it to continue on timescales comparable to the period of collapse at free fall velocities. After the density of infalling material has reached about 108 g / cm3, that material is sufficiently transparent to allow energy radiated by the protostar to escape. The combination of convection within the protostar and radiation from its exterior allow the star to contract further. This continues until the gas is hot enough for the internal pressure to support the protostar against further gravitational collapse—a state called hydrostatic equilibrium. When this accretion phase is nearly complete, the resulting object is known as a protostar.
Accretion of material onto the protostar continues partially from the newly formed circumstellar disc. When the density and temperature are high enough, deuterium fusion begins, and the outward pressure of the resultant radiation slows (but does not stop) the collapse. Material comprising the cloud continues to "rain" onto the protostar. In this stage bipolar jets are produced called HerbigHaro objects. This is probably the means by which excess angular momentum of the infalling material is expelled, allowing the star to continue to form.
When the surrounding gas and dust envelope disperses and accretion process stops, the star is considered a pre-main-sequence star (PMS star). The energy source of these objects is (gravitational contraction) KelvinHelmholtz mechanism, as opposed to hydrogen burning in main sequence stars. The PMS star follows a Hayashi track on the HertzsprungRussell (HR) diagram. The contraction will proceed until the Hayashi limit is reached, and thereafter contraction will continue on a KelvinHelmholtz timescale with the temperature remaining stable. Stars with less than 0.5 M☉ thereafter join the main sequence. For more massive PMS stars, at the end of the Hayashi track they will slowly collapse in near hydrostatic equilibrium, following the Henyey track.
Finally, hydrogen begins to fuse in the core of the star, and the rest of the enveloping material is cleared away. This ends the protostellar phase and begins the star's main sequence phase on the HR diagram.
The stages of the process are well defined in stars with masses around 1 M☉ or less. In high mass stars, the length of the star formation process is comparable to the other timescales of their evolution, much shorter, and the process is not so well defined. The later evolution of stars is studied in stellar evolution.
== Observations ==

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Key elements of star formation are only available by observing in wavelengths other than the optical. The protostellar stage of stellar existence is almost invariably hidden away deep inside dense clouds of gas and dust left over from the GMC. Often, these star-forming cocoons known as Bok globules, can be seen in silhouette against bright emission from surrounding gas. Early stages of a star's life can be seen in infrared light, which penetrates the dust more easily than visible light.
Observations from the Wide-field Infrared Survey Explorer (WISE) have thus been especially important for unveiling numerous galactic protostars and their parent star clusters. Examples of such embedded star clusters are FSR 1184, FSR 1190, Camargo 14, Camargo 74, Majaess 64, and Majaess 98.
The structure of the molecular cloud and the effects of the protostar can be observed in near-IR extinction maps (where the number of stars are counted per unit area and compared to a nearby zero extinction area of sky), continuum dust emission and rotational transitions of CO and other molecules; these last two are observed in the millimeter and submillimeter range. The radiation from the protostar and early star has to be observed in infrared astronomy wavelengths, as the extinction caused by the rest of the cloud in which the star is forming is usually too big to allow us to observe it in the visual part of the spectrum. This presents considerable difficulties as the Earth's atmosphere is almost entirely opaque from 20μm to 850μm, with narrow windows at 200μm and 450μm. Even outside this range, atmospheric subtraction techniques must be used.
X-ray observations have proven useful for studying young stars, since X-ray emission from these objects is about 100100,000 times stronger than X-ray emission from main-sequence stars. The earliest detections of X-rays from T Tauri stars were made by the Einstein X-ray Observatory. For low-mass stars X-rays are generated by the heating of the stellar corona through magnetic reconnection, while for high-mass O and early B-type stars X-rays are generated through supersonic shocks in the stellar winds. Photons in the soft X-ray energy range covered by the Chandra X-ray Observatory and XMM-Newton may penetrate the interstellar medium with only moderate absorption due to gas, making the X-ray a useful wavelength for seeing the stellar populations within molecular clouds. X-ray emission as evidence of stellar youth makes this band particularly useful for performing censuses of stars in star-forming regions, given that not all young stars have infrared excesses. X-ray observations have provided near-complete censuses of all stellar-mass objects in the Orion Nebula Cluster and Taurus Molecular Cloud.
The formation of individual stars can only be directly observed in the Milky Way Galaxy, but in distant galaxies star formation has been detected through its unique spectral signature.
Initial research indicates star-forming clumps start as giant, dense areas in turbulent gas-rich matter in young galaxies, live about 500 million years, and may migrate to the center of a galaxy, creating the central bulge of a galaxy.
On February 21, 2014, NASA announced a greatly upgraded database for tracking polycyclic aromatic hydrocarbons (PAHs) in the universe. According to scientists, more than 20% of the carbon in the universe may be associated with PAHs, possible starting materials for the formation of life. PAHs seem to have been formed shortly after the Big Bang, are widespread throughout the universe, and are associated with new stars and exoplanets.
In February 2018, astronomers reported, for the first time, a signal of the reionization epoch, an indirect detection of light from the earliest stars formed about 180 million years after the Big Bang.
An article published on October 22, 2019, reported on the detection of 3MM-1, a massive star-forming galaxy about 12.5 billion light-years away that is obscured by clouds of dust. At a mass of about 1010.8 solar masses, it showed a star formation rate about 100 times as high as in the Milky Way.
=== Notable pathfinder objects ===
MWC 349 was first discovered in 1978, and is estimated to be only 1,000 years old.
VLA 1623 The first exemplar Class 0 protostar, a type of embedded protostar that has yet to accrete the majority of its mass. Found in 1993, is possibly younger than 10,000 years.
L1014 An extremely faint embedded object representative of a new class of sources that are only now being detected with the newest telescopes. Their status is still undetermined, they could be the youngest low-mass Class 0 protostars yet seen or even very low-mass evolved objects (like brown dwarfs or even rogue planets).
GCIRS 8* The youngest known main sequence star in the Galactic Center region, discovered in August 2006. It is estimated to be 3.5 million years old.
== Low mass and high mass star formation ==

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Stars of different masses are thought to form by slightly different mechanisms. The theory of low-mass star formation, which is well-supported by observation, suggests that low-mass stars form by the gravitational collapse of rotating density enhancements within molecular clouds. As described above, the collapse of a rotating cloud of gas and dust leads to the formation of an accretion disk through which matter is channeled onto a central protostar. For stars with masses higher than about 8 M☉, however, the mechanism of star formation is not well understood.
Massive stars emit copious quantities of radiation which pushes against infalling material. In the past, it was thought that this radiation pressure might be substantial enough to halt accretion onto the massive protostar and prevent the formation of stars with masses more than a few tens of solar masses. Theoretical work has shown that the production of a jet and outflow clears a cavity through which much of the radiation from a massive protostar can escape without hindering accretion through the disk and onto the protostar. Present thinking is that massive stars may therefore be able to form by a mechanism similar to that by which low mass stars form.
There is mounting evidence that at least some massive protostars are indeed surrounded by accretion disks. Disk accretion in high-mass protostars, similar to their low-mass counterparts, is expected to exhibit bursts of episodic accretion as a result of a gravitationally instability leading to clumpy and in-continuous accretion rates. Accretion bursts in high-mass protostars have been confirmed observationally. Detection of high-mass protostellar disk candidates around high-mass protostars is consistent with theories that the total mass of a protostar contributes to the properties of their protostellar disk. Several other theories of massive star formation remain to be tested observationally. Of these, perhaps the most prominent is the theory of competitive accretion, which suggests that massive protostars are "seeded" by low-mass protostars which compete with other protostars to draw in matter from the entire parent molecular cloud, instead of simply from a small local region. Magnetic properties of high mass binary systems show that the fields are more prominent at larger distances, possibly causing disk fragmentation. Other research shows that a stronger magnetic field can alter gas cloud fragmentation as well as increase the production of high-mass stars. However, this is still an active area of research.
Another theory of massive star formation suggests that massive stars may form by the coalescence of two or more stars of lower mass. Contact binary systems are suggested as candidate sources of some massive star formations.
== Filamentary nature of star formation ==
Simulations suggest that star forming filaments are commonly created when a shock velocity passes through a cloud of gas. When shock velocity is high (
{\displaystyle \gtrsim }
5 km/s) from Supernova or a H II region expanding the dominate filament creation process is molecular clouds being shock compressed. When shock velocity is less than 5 km/s, filaments form from converging gas moving within local magnetic fields.
Filamentary structures in molecular clouds are important initial conditions for star formation. The spatial relationship between cores and filaments indicates that the majority of prestellar cores are located within 0.1 pc of supercritical filaments. This supports the hypothesis that filamentary structures act as pathways for the accumulation of gas and dust, leading to core formation.
Both the core mass function (CMF) and filament line mass function (FLMF) observed in the California GMC follow power-law distributions at the high-mass end, consistent with the Salpeter initial mass function (IMF). Current results strongly support the existence of a connection between the FLMF and the CMF/IMF, demonstrating that this connection holds at the level of an individual cloud, specifically the California GMC. The FLMF presented is a distribution of local line masses for a complete, homogeneous sample of filaments within the same cloud. It is the local line mass of a filament that defines its ability to fragment at a particular location along its spine, not the average line mass of the filament. This connection is more direct and provides tighter constraints on the origin of the CMF/IMF.
== See also ==
Accretion Accumulation of particles into a massive object by gravitationally attracting more matter
Champagne flow model
Chronology of the universe History and future of the universe
Formation and evolution of the Solar System
Galaxy formation and evolution Subfield of cosmology
List of star-forming regions in the Local Group Regions in the Milky Way galaxy and Local Group where new stars are forming
Pea galaxy Possible type of luminous blue compact galaxy
Star evolution Changes to stars over their lifespansPages displaying short descriptions of redirect targets
== References ==

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In astronomy, stellar classification is the classification of stars based on their spectral characteristics. Electromagnetic radiation from the star is analyzed by splitting it with a prism or diffraction grating into a spectrum exhibiting the rainbow of colors interspersed with spectral lines. Each line indicates a particular chemical element or molecule, with the line strength indicating the abundance of that element. The strengths of the different spectral lines vary mainly due to the temperature of the photosphere, although in some cases there are true abundance differences. The spectral class of a star is a short code primarily summarizing the ionization state, giving an objective measure of the photosphere's temperature.
Most stars are currently classified under the MorganKeenan (MK) system using the letters O, B, A, F, G, K, and M, a sequence from the hottest (O-type) to the coolest (M-type). Each letter class is then subdivided using a numeric digit with 0 being hottest and 9 being coolest (e.g., A8, A9, F0, and F1 form a sequence from hotter to cooler). The sequence has been expanded with three classes for other stars that do not fit in the classical system: W, S and C. Some stellar remnants or objects of deviating mass have also been assigned letters: D for white dwarfs and L, T and Y for brown dwarfs (and exoplanets).
In the MK system, a luminosity class is added to the spectral class using Roman numerals. This is based on the width of certain absorption lines in the star's spectrum, which vary with the density of the atmosphere and so distinguish giant stars from dwarfs. Luminosity class 0 or Ia+ is used for hypergiants, class I for supergiants, class II for bright giants, class III for regular giants, class IV for subgiants, class V for main-sequence stars, class sd (or VI) for subdwarfs, and class D (or VII) for white dwarfs. The full spectral class for the Sun is then G2V, indicating a main-sequence star with a surface temperature around 5,800 K.
== Conventional colour description ==
The conventional colour description takes into account only the peak of the stellar spectrum. In actuality, however, stars radiate in all parts of the spectrum. Because all spectral colours combined appear white, the actual apparent colours the human eye would observe are far lighter than the conventional colour descriptions would suggest. This characteristic of 'lightness' indicates that the simplified assignment of colours within the spectrum can be misleading. Excluding colour-contrast effects in dim light, in typical viewing conditions there are no green, cyan, indigo, or violet stars. "Yellow" dwarfs such as the Sun are white, "red" dwarfs are a deep shade of yellow/orange, and "brown" dwarfs do not literally appear brown, but hypothetically would appear dim red or grey/black to a nearby observer.
== Modern classification ==
The modern classification system is known as the MorganKeenan (MK) classification. Each star is assigned a spectral class (from the older Harvard spectral classification, which did not include luminosity) and a luminosity class using Roman numerals as explained below, forming the star's spectral type.
Other modern stellar classification systems, such as the UBV system, are based on color indices—the measured differences in three or more color magnitudes. Those numbers are given labels such as "UV" or "BV", which represent the colors passed by two standard filters (e.g. Ultraviolet, Blue and Visual).
=== Harvard spectral classification ===
The Harvard system is a one-dimensional classification scheme by astronomer Annie Jump Cannon, who re-ordered and simplified the prior alphabetical system by Draper (see History). Stars are grouped according to their spectral characteristics by single letters of the alphabet, optionally with numeric subdivisions. Main-sequence stars vary in surface temperature from approximately 2,000 to 50,000 K, whereas more-evolved stars in particular, newly-formed white dwarfs can have surface temperatures above 100,000 K. Physically, the classes indicate the temperature of the star's atmosphere and are normally listed from hottest to coldest.
The traditional mnemonic for remembering the order of the spectral type letters, from hottest to coolest, is "Oh, Be A Fine Guy/Girl: Kiss Me!". Many alternative mnemonics have been proposed, in contests held by astronomy courses and organizations, but the traditional mnemonic remains the most popular.
The spectral classes O through M, as well as other more specialized classes discussed later, are subdivided by Arabic numerals (09), where 0 denotes the hottest stars of a given class. For example, A0 denotes the hottest stars in class A and A9 denotes the coolest ones. Fractional numbers are allowed; for example, the star Mu Normae is classified as O9.7. The Sun is classified as G2.
The fact that the Harvard classification of a star indicated its surface or photospheric temperature (or more precisely, its effective temperature) was not fully understood until after its development, though by the time the first HertzsprungRussell diagram was formulated (by 1914), this was generally suspected to be true. In the 1920s, the Indian physicist Meghnad Saha derived a theory of ionization by extending well-known ideas in physical chemistry pertaining to the dissociation of molecules to the ionization of atoms. First he applied it to the solar chromosphere, then to stellar spectra.
Harvard astronomer Cecilia Payne then demonstrated that the O-B-A-F-G-K-M spectral sequence is actually a sequence in temperature. Because the classification sequence predates our understanding that it is a temperature sequence, the placement of a spectrum into a given subtype, such as B3 or A7, depends upon (largely subjective) estimates of the strengths of absorption features in stellar spectra. As a result, these subtypes are not evenly divided into any sort of mathematically representable intervals.

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=== MorganKeenan classification ===
The Yerkes spectral classification, also called the MK, or Morgan-Keenan (alternatively referred to as the MKK, or Morgan-Keenan-Kellman) system from the authors' initials, is a system of stellar spectral classification introduced in 1943 by William Wilson Morgan, Philip C. Keenan, and Edith Kellman from Yerkes Observatory. This two-dimensional (temperature and luminosity) classification scheme is based on spectral lines sensitive to stellar temperature and surface gravity, which is related to luminosity (whilst the Harvard classification is based on just surface temperature). Later, in 1953, after some revisions to the list of standard stars and classification criteria, the scheme was named the MorganKeenan classification, or MK, which remains in use today.
Denser stars with higher surface gravity exhibit greater pressure broadening of spectral lines. The gravity, and hence the pressure, on the surface of a giant star is much lower than for a dwarf star because the radius of the giant is much greater than a dwarf of similar mass. Therefore, differences in the spectrum can be interpreted as luminosity effects and a luminosity class can be assigned purely from examination of the spectrum.
A number of different luminosity classes are distinguished, as listed in the table below.
Marginal cases are allowed; for example, a star may be either a supergiant or a bright giant, or may be in between the subgiant and main-sequence classifications.
In these cases, two special symbols are used between the two luminosity classes:
A slash (/) means that a star is either one class or the other.
A hyphen (-) means that the star is in between the two classes.
For example, a star classified as A3-4III/IV would be in between spectral types A3 and A4, while being either a giant star or a subgiant.
Sub-dwarf classes have also been used: VI for sub-dwarfs (stars slightly less luminous than the main sequence).
Nominal luminosity class VII (and sometimes higher numerals) is now rarely used for white dwarf or "hot sub-dwarf" classes, since the temperature-letters of the main sequence and giant stars no longer apply to white dwarfs.
Occasionally, letters a and b are applied to luminosity classes other than supergiants; for example, a giant star slightly less luminous than typical may be given a luminosity class of IIIb, while a luminosity class IIIa indicates a star slightly brighter than a typical giant.
A sample of extreme V stars with strong absorption in He II λ4686 spectral lines have been given the Vz designation. An example star is HD 93129 B.
=== Spectral peculiarities ===
Additional nomenclature, in the form of lower-case letters, can follow the spectral type to indicate peculiar features of the spectrum.
For example, 59 Cygni is listed as spectral type B1.5Vnne, indicating a spectrum with the general classification B1.5V, as well as very broad absorption lines and certain emission lines.
== History ==
The reason for the odd arrangement of letters in the Harvard classification is historical, having evolved from the earlier Secchi classes and been progressively modified as understanding improved.
=== Secchi classes ===
During the 1860s and 1870s, pioneering stellar spectroscopist Angelo Secchi created the Secchi classes in order to classify observed spectra. By 1866, he had developed three classes of stellar spectra, shown in the table below.
In the late 1890s, this classification began to be superseded by the Harvard classification, which is discussed in the remainder of this article.
The Roman numerals used for Secchi classes should not be confused with the completely unrelated Roman numerals used for Yerkes luminosity classes and the proposed neutron star classes.
=== Draper system ===
After the death of her husband, Mary Anna Draper began to fund the creation of the Harvard Plate Stacks and the study of these plates at the Harvard College Observatory. The director of the Observatory, Edward C. Pickering began to hire pioneering female astronomers collectively known as the Harvard Computers. Though they would study many different astronomical subjects, an early result of this work was the first edition of The Henry Draper Memorial Catalogue of Stellar Spectra, first published in 1890. Williamina Fleming classified most of the spectra in the first edition of the catalogue and is credited with classifying over 10,000 featured stars and discovering 10 novae and more than 200 variable stars. With the help of the Harvard Computers, especially Williamina Fleming, the first iteration of the Henry Draper catalogue was devised to replace the Roman-numeral scheme established by Angelo Secchi.
The catalogue used a scheme in which the previously used Secchi classes (I to V) were subdivided into more specific classes, given letters from A to P. Also, the letter Q was used for stars not fitting into any other class. Fleming worked with Pickering to differentiate 17 different classes based on the intensity of hydrogen spectral lines, which causes variation in the wavelengths emanated from stars and results in variation in color appearance. The spectra in class A tended to produce the strongest hydrogen absorption lines while spectra in class O produced virtually no visible lines. The lettering system displayed the gradual decrease in hydrogen absorption in the spectral classes when moving down the alphabet. This classification system was later modified by Annie Jump Cannon and Antonia Maury to produce the Harvard spectral classification scheme.
=== The old Harvard system (1897) ===
In 1897, another astronomer at Harvard, Antonia Maury, placed the Orion subtype of Secchi class I ahead of the remainder of Secchi class I, thus placing the modern type B ahead of the modern type A. She was the first to do so, although she did not use lettered spectral types, but rather a series of twenty-two types numbered from IXXII.
Because the 22 Roman numeral groupings did not account for additional variations in spectra, three additional divisions were made to further specify differences: Lowercase letters were added to differentiate relative line appearance in spectra; the lines were defined as:

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(a): average width
(b): hazy
(c): sharp
Antonia Maury published her own stellar classification catalogue in 1897 called "Spectra of Bright Stars Photographed with the 11 inch Draper Telescope as Part of the Henry Draper Memorial", which included 4,800 photographs and Maury's analyses of 681 bright northern stars. This was the first instance in which a woman was credited for an observatory publication.
=== The current Harvard system (1912) ===
In 1901, Annie Jump Cannon returned to the lettered types, but dropped all letters except O, B, A, F, G, K, M, and N used in that order, as well as P for planetary nebulae and Q for some peculiar spectra. She also used types such as B5A for stars halfway between types B and A, F2G for stars one fifth of the way from F to G, and so on.
Finally, by 1912, Cannon had changed the types B, A, B5A, F2G, etc. to B0, A0, B5, F2, etc. This is essentially the modern form of the Harvard classification system. This system was developed through the analysis of spectra on photographic plates, which could convert light emanated from stars into a readable spectrum.
=== Mount Wilson classes ===
A luminosity classification known as the Mount Wilson system was used to distinguish between stars of different luminosities. This notation system is still sometimes seen on modern spectra.
sd: subdwarf
d: dwarf
sg: subgiant
g: giant
c: supergiant
== Spectral types ==
The stellar classification system is taxonomic, based on type specimens, similar to classification of species in biology: The categories are defined by one or more standard stars for each category and sub-category, with an associated description of the distinguishing features.
Types F, G, and K are sometimes grouped into the category of "FGK stars" due to their similar stellar structures. Similarly, types G, K, and M are sometimes grouped into "GKM stars", as they are of solar mass or less.
=== "Early" and "late" nomenclature ===
Stars are often referred to as early or late types. "Early" is a synonym for hotter, while "late" is a synonym for cooler.
Depending on the context, "early" and "late" may be absolute or relative terms. "Early" as an absolute term would therefore refer to O or B, and possibly A stars. As a relative reference it relates to stars hotter than others, such as "early K" being perhaps K0, K1, K2 and K3.
"Late" is used in the same way, with an unqualified use of the term indicating stars with spectral types such as K and M, but it can also be used for stars that are cool relative to other stars, as in using "late G" to refer to G7, G8, and G9.
In the relative sense, "early" means a lower Arabic numeral following the class letter, and "late" means a higher number.
This obscure terminology is a hold-over from a late nineteenth century model of stellar evolution, which supposed that stars were powered by gravitational contraction via the KelvinHelmholtz mechanism, which is now known to not apply to main-sequence stars. If that were true, then stars would start their lives as very hot "early-type" stars and then gradually cool down into "late-type" stars. This mechanism provided ages of the Sun that were much smaller than what is observed in the geologic record, and was rendered obsolete by the discovery that stars are powered by nuclear fusion. The terms "early" and "late" were carried over, beyond the demise of the model they were based on.
=== Class O ===
O-type stars are very hot and extremely luminous, with most of their radiated output in the ultraviolet range. These are the rarest of all main-sequence stars. About 1 in 3,000,000 (0.00003%) of the main-sequence stars in the solar neighborhood are O-type stars. Some of the most massive stars lie within this spectral class. O-type stars frequently have complicated surroundings that make measurement of their spectra difficult.
O-type spectra formerly were defined by the ratio of the strength of the He II λ4541 relative to that of He I λ4471, where λ is the radiation wavelength. Spectral type O7 was defined to be the point at which the two intensities are equal, with the He I line weakening towards earlier types. Type O3 was, by definition, the point at which said line disappears altogether, although it can be seen very faintly with modern technology. Due to this, the modern definition uses the ratio of the nitrogen line N IV λ4058 to N III λλ4634-40-42.
O-type stars have dominant lines of absorption and sometimes emission for He II lines, prominent ionized (Si IV, O III, N III, and C III) and neutral helium lines, strengthening from O5 to O9, and prominent hydrogen Balmer lines, although not as strong as in later types. Higher-mass O-type stars do not retain extensive atmospheres due to the extreme velocity of their stellar wind, which may reach 2,000 km/s. Because they are so massive, O-type stars have very hot cores and burn through their hydrogen fuel very quickly, so they are the first stars to leave the main sequence.
When the MKK classification scheme was first described in 1943, the only subtypes of class O used were O5 to O9.5. The MKK scheme was extended to O9.7 in 1971 and O4 in 1978, and new classification schemes that add types O2, O3, and O3.5 have subsequently been introduced.
Example spectral standards:
O7V S Monocerotis
O9V 10 Lacertae
=== Class B ===

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B-type stars are very luminous and blue. Their spectra have neutral helium lines, which are most prominent at the B2 subclass, and moderate hydrogen lines. As O- and B-type stars are so energetic, they only live for a relatively short time. Thus, due to the low probability of kinematic interaction during their lifetime, they are unable to stray far from the area in which they formed, apart from runaway stars.
The transition from class O to class B was originally defined to be the point at which the He II λ4541 disappears. However, with modern equipment, the line is still apparent in the early B-type stars. Today for main-sequence stars, the B class is instead defined by the intensity of the He I violet spectrum, with the maximum intensity corresponding to class B2. For supergiants, lines of silicon are used instead; the Si IV λ4089 and Si III λ4552 lines are indicative of early B. At mid-B, the intensity of the latter relative to that of Si II λλ4128-30 is the defining characteristic, while for late B, it is the intensity of Mg II λ4481 relative to that of He I λ4471.
These stars tend to be found in their originating OB associations, which are associated with giant molecular clouds. The Orion OB1 association occupies a large portion of a spiral arm of the Milky Way and contains many of the brighter stars of the constellation Orion. About 1 in 800 (0.125%) of the main-sequence stars in the solar neighborhood are B-type main-sequence stars. B-type stars are relatively uncommon and the closest is Regulus, at around 80 light years.
Massive yet non-supergiant stars known as Be stars have been observed to show one or more Balmer lines in emission, with the hydrogen-related electromagnetic radiation series projected out by the stars being of particular interest. Be stars are generally thought to feature unusually strong stellar winds, high surface temperatures, and significant attrition of stellar mass as the objects rotate at a curiously rapid rate.
Objects known as B[e] stars or B(e) stars for typographic reasons possess distinctive neutral or low ionisation emission lines that are considered to have forbidden mechanisms, undergoing processes not normally allowed under current understandings of quantum mechanics.
Example spectral standards:
B0V Upsilon Orionis
B0Ia Alnilam
B2Ia Chi2 Orionis
B2Ib 9 Cephei
B3V Alkaid
B3V Haedus
B3Ia Omicron2 Canis Majoris
B5Ia Aludra
B8Ia Rigel
=== Class A ===
A-type stars are among the more common naked eye stars, and are white or bluish-white. They have strong hydrogen lines, at a maximum by A0, and also lines of ionized metals (Fe II, Mg II, Si II) at a maximum at A5. The presence of Ca II lines is notably strengthening by this point. About 1 in 160 (0.625%) of the main-sequence stars in the solar neighborhood are A-type stars, which includes 9 stars within 15 parsecs.
Example spectral standards:
A0Van Phecda
A0Va Vega
A0Ib Eta Leonis
A0Ia HD 21389
A1V Sirius A
A2Ia Deneb
A3Va Fomalhaut
=== Class F ===
F-type stars have strengthening spectral lines H and K of Ca II. Neutral metals (Fe I, Cr I) beginning to gain on ionized metal lines by late F. Their spectra are characterized by the weaker hydrogen lines and ionized metals. Their color is white. About 1 in 33 (3.03%) of the main-sequence stars in the solar neighborhood are F-type stars, including 1 star Procyon A within 20 ly.
Example spectral standards:
F0IIIa Adhafera
F0Ib Arneb
F1V - 37 Ursae Majoris
F2V 78 Ursae Majoris
F7V - Iota Piscium
F9V - Zavijava
F9V - HD 10647
=== Class G ===
G-type stars, including the Sun, have prominent spectral lines H and K of Ca II, which are most pronounced at G2.
They have even weaker hydrogen lines than F, but along with the ionized metals, they have neutral metals.
There is a prominent spike in the G band of CN molecules.
Class G main-sequence stars make up about 7.5%, nearly one in thirteen, of the main-sequence stars in the solar neighborhood.
There are 21 G-type stars within 10pc.
Class G contains the "Yellow Evolutionary Void". Supergiant stars often swing between O or B (blue) and K or M (red). While they do this, they do not stay for long in the unstable yellow supergiant class.
Example spectral standards:
G0V Chara
G0IV Muphrid
G0Ib Sadalsuud
G2V Sun
G5V Kappa1 Ceti
G5IV Mu Herculis
G5Ib 9 Pegasi
G8V 61 Ursae Majoris
G8IV Alshain
G8IIIa Kappa Geminorum
G8IIIab Vindemiatrix
G8Ib Mebsuta
=== Class K ===
K-type stars are orangish stars that are slightly cooler than the Sun. They make up about 12% of the main-sequence stars in the solar neighborhood. There are also giant K-type stars, which range from hypergiants like RW Cephei, to giants and supergiants, such as Arcturus, whereas orange dwarfs, like Alpha Centauri B, are main-sequence stars.
They have extremely weak hydrogen lines, if those are present at all, and mostly neutral metals (Mn I, Fe I, Si I). By late K, molecular bands of titanium oxide become present. Mainstream theories (those rooted in lower harmful radioactivity and star longevity) would thus suggest such stars have the optimal chances of heavily evolved life developing on orbiting planets (if such life is directly analogous to Earth's) due to a broad habitable zone yet much lower harmful periods of emission compared to those with the broadest such zones.
Example spectral standards:
K0V Alsafi
K0III Pollux
K0III Aljanah
K2V Ran
K2III Kappa Ophiuchi
K3III Rho Boötis
K5V 61 Cygni A
K5III Eltanin
=== Class M ===

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Class M stars are by far the most common. About 76% of the main-sequence stars in the solar neighborhood are class M stars. However, class M main-sequence stars (red dwarfs) have such low luminosities that none are bright enough to be seen with the unaided eye, unless under exceptional conditions. The brightest-known M class main-sequence star is Lacaille 8760, class M0V, with magnitude 6.7 (the limiting magnitude for typical naked-eye visibility under good conditions being typically quoted as 6.5), and it is extremely unlikely that any brighter examples will be found.
Although most class M stars are red dwarfs, most of the largest-known supergiant stars in the Milky Way are class M stars, such as VY Canis Majoris, VV Cephei, Antares, and Betelgeuse. Furthermore, some larger, hotter brown dwarfs are late class M, usually in the range of M6.5 to M9.5.
The spectrum of a class M star contains lines from oxide molecules (in the visible spectrum, especially TiO) and all neutral metals, but absorption lines of hydrogen are usually absent. TiO bands can be strong in class M stars, usually dominating their visible spectrum by about M5. Vanadium(II) oxide bands become present by late M.
Example spectral standards:
M3V Gliese 581
M0IIIa Mirach
M2III Chi Pegasi
M1-M2Ia-Iab Betelgeuse
M2Ia Mu Cephei ("Herschel's garnet")
== Extended spectral types ==
A number of new spectral types have been taken into use from newly discovered types of stars.
=== Hot blue emission star classes ===
Spectra of some very hot and bluish stars exhibit marked emission lines from carbon or nitrogen, or sometimes oxygen.
==== Class WR (or W): WolfRayet ====
Once included as type O stars, the WolfRayet stars of class W or WR are notable for spectra lacking hydrogen lines. Instead their spectra are dominated by broad emission lines of highly ionized helium, nitrogen, carbon, and sometimes oxygen. They are thought to mostly be dying supergiants with their hydrogen layers blown away by stellar winds, thereby directly exposing their hot helium shells. Class WR is further divided into subclasses according to the relative strength of nitrogen and carbon emission lines in their spectra (and outer layers).
WR spectra range is listed below:
WN spectrum dominated by N III-V and He I-II lines
WNE (WN2 to WN5 with some WN6) hotter or "early"
WNL (WN7 to WN9 with some WN6) cooler or "late"
Extended WN classes WN10 and WN11 sometimes used for the Ofpe/WN9 stars
h tag used (e.g. WN9h) for WR with hydrogen emission and ha (e.g. WN6ha) for both hydrogen emission and absorption
WN/C WN stars plus strong C IV lines, intermediate between WN and WC stars
WC spectrum with strong C II-IV lines
WCE (WC4 to WC6) hotter or "early"
WCL (WC7 to WC9) cooler or "late"
WO (WO1 to WO4) strong O VI lines, extremely rare, extension of the WCE class into incredibly hot temperatures (up to 200 kK or more)
Although the central stars of most planetary nebulae (CSPNe) show O-type spectra, around 10% are hydrogen-deficient and show WR spectra. These are low-mass stars and to distinguish them from the massive WolfRayet stars, their spectra are enclosed in square brackets: e.g. [WC]. Most of these show [WC] spectra, some [WO], and very rarely [WN].
==== Slash stars ====
The slash stars are O-type stars with WN-like lines in their spectra. The name "slash" comes from their printed spectral type having a slash in it (e.g. "Of/WNL")).
There is a secondary group found with these spectra, a cooler, "intermediate" group designated "Ofpe/WN9". These stars have also been referred to as WN10 or WN11, but that has become less popular with the realisation of the evolutionary difference from other WolfRayet stars. Recent discoveries of even rarer stars have extended the range of slash stars as far as O2-3.5If*/WN5-7, which are even hotter than the original "slash" stars.
==== Magnetic O stars ====
They are O stars with strong magnetic fields. Designation is Of?p.
=== Cool red and brown dwarf classes ===
The new spectral types L, T, and Y were created to classify infrared spectra of cool stars. This includes both red dwarfs and brown dwarfs that are very faint in the visible spectrum.
Brown dwarfs, stars that do not undergo hydrogen fusion, cool as they age and so progress to later spectral types. Brown dwarfs start their lives with M-type spectra and will cool through the L, T, and Y spectral classes, faster the less massive they are; the highest-mass brown dwarfs cannot have cooled to Y or even T dwarfs within the age of the universe. Because this leads to an unresolvable overlap between spectral types' effective temperature and luminosity for some masses and ages of different L-T-Y types, no distinct temperature or luminosity values can be given.
==== Class L ====
Class L dwarfs get their designation because they are cooler than M stars and L is the remaining letter alphabetically closest to M. Some of these objects have masses large enough to support hydrogen fusion and are therefore stars, but most are of substellar mass and are therefore brown dwarfs. They are a very dark red in color and brightest in infrared. Their atmosphere is cool enough to allow metal hydrides and alkali metals to be prominent in their spectra.
Due to low surface gravity in giant stars, TiO- and VO-bearing condensates never form. Thus, L-type stars larger than dwarfs can never form in an isolated environment. However, it may be possible for these L-type supergiants to form through stellar collisions, an example of which is V838 Monocerotis while in the height of its luminous red nova eruption.
==== Class T ====

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Class T dwarfs are cool brown dwarfs with surface temperatures between approximately 550 and 1,300 K (277 and 1,027 °C; 530 and 1,880 °F). Their emission peaks in the infrared. Methane is prominent in their spectra.
Study of the number of proplyds (protoplanetary disks, clumps of gas in nebulae from which stars and planetary systems are formed) indicates that the number of stars in the galaxy should be several orders of magnitude higher than what was previously conjectured. It is theorized that these proplyds are in a race with each other. The first one to form will become a protostar, which are very violent objects and will disrupt other proplyds in the vicinity, stripping them of their gas. The victim proplyds will then probably go on to become main-sequence stars or brown dwarfs of the L and T classes, which are quite invisible to us.
==== Class Y ====
Brown dwarfs of spectral class Y are cooler than those of spectral class T and have qualitatively different spectra from them. A total of 17 objects have been placed in class Y as of August 2013. Although such dwarfs have been modelled and detected within forty light-years by the Wide-field Infrared Survey Explorer (WISE) there is no well-defined spectral sequence yet and no prototypes. Nevertheless, several objects have been proposed as spectral classes Y0, Y1, and Y2.
The spectra of these prospective Y objects display absorption around 1.55 micrometers. Delorme et al. have suggested that this feature is due to absorption from ammonia, and that this should be taken as the indicative feature for the T-Y transition. In fact, this ammonia-absorption feature is the main criterion that has been adopted to define this class. However, this feature is difficult to distinguish from absorption by water and methane, and other authors have stated that the assignment of class Y0 is premature.
The latest brown dwarf proposed for the Y spectral type, WISE 1828+2650, is a > Y2 dwarf with an effective temperature originally estimated around 300 K, the temperature of the human body. Parallax measurements have, however, since shown that its luminosity is inconsistent with it being colder than ~400 K. The coolest Y dwarf currently known is WISE 08550714 with an approximate temperature of 250 K, and a mass just seven times that of Jupiter.
The mass range for Y dwarfs is 925 Jupiter masses, but young objects might reach below one Jupiter mass (although they cool to become planets), which means that Y class objects straddle the 13 Jupiter mass deuterium-fusion limit that marks the current IAU division between brown dwarfs and planets.
==== Peculiar brown dwarfs ====
Young brown dwarfs have low surface gravities because they have larger radii and lower masses compared to the field stars of similar spectral type. These sources are marked by a letter beta (β) for intermediate surface gravity and gamma (γ) for low surface gravity. Indication for low surface gravity are weak CaH, KI and NaI lines, as well as strong VO line. Alpha (α) stands for normal surface gravity and is usually dropped. Sometimes an extremely low surface gravity is denoted by a delta (δ). The suffix "pec" stands for peculiar. The peculiar suffix is still used for other features that are unusual and summarizes different properties, indicative of low surface gravity, subdwarfs and unresolved binaries.
The prefix sd stands for subdwarf and only includes cool subdwarfs. This prefix indicates a low metallicity and kinematic properties that are more similar to halo stars than to disk stars. Subdwarfs appear bluer than disk objects.
The red suffix describes objects with red color, but an older age. This is not interpreted as low surface gravity, but as a high dust content. The blue suffix describes objects with blue near-infrared colors that cannot be explained with low metallicity. Some are explained as L+T binaries, others are not binaries, such as 2MASS J112639915003550 and are explained with thin and/or large-grained clouds.
=== Late giant carbon-star classes ===
Carbon-stars are stars whose spectra indicate production of carbon a byproduct of triple-alpha helium fusion. With increased carbon abundance, and some parallel s-process heavy element production, the spectra of these stars become increasingly deviant from the usual late spectral classes G, K, and M. Equivalent classes for carbon-rich stars are S and C.
The giants among those stars are presumed to produce this carbon themselves, but some stars in this class are double stars, whose odd atmosphere is suspected of having been transferred from a companion that is now a white dwarf, when the companion was a carbon-star.
==== Class C ====
Originally classified as R and N stars, these are also known as carbon stars. These are red giants, near the end of their lives, in which there is an excess of carbon in the atmosphere. The old R and N classes ran parallel to the normal classification system from roughly mid-G to late M. These have more recently been remapped into a unified carbon classifier C with N0 starting at roughly C6. Another subset of cool carbon stars are the CJ-type stars, which are characterized by the strong presence of molecules of 13 CN in addition to those of 12 CN. A few main-sequence carbon stars are known, but the overwhelming majority of known carbon stars are giants or supergiants. There are several subclasses:
C-R Formerly its own class (R) representing the carbon star equivalent of late G- to early K-type stars.
C-N Formerly its own class representing the carbon star equivalent of late K- to M-type stars.
C-J A subtype of cool C stars with a high content of 13C.
C-H Population II analogues of the C-R stars.
C-Hd Hydrogen-deficient carbon stars, similar to late G supergiants with CH and C2 bands added.
==== Class S ====

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Class S stars form a continuum between class M stars and carbon stars. Those most similar to class M stars have strong ZrO absorption bands analogous to the TiO bands of class M stars, whereas those most similar to carbon stars have strong sodium D lines and weak C2 bands. Class S stars have excess amounts of zirconium and other elements produced by the s-process, and have more similar carbon and oxygen abundances to class M or carbon stars. Like carbon stars, nearly all known class S stars are asymptotic-giant-branch stars.
The spectral type is formed by the letter S and a number between zero and ten. This number corresponds to the temperature of the star and approximately follows the temperature scale used for class M giants. The most common types are S3 to S5. The non-standard designation S10 has only been used for the star Chi Cygni when at an extreme minimum.
The basic classification is usually followed by an abundance indication, following one of several schemes: S2,5; S2/5; S2 Zr4 Ti2; or S2*5. A number following a comma is a scale between 1 and 9 based on the ratio of ZrO and TiO. A number following a slash is a more-recent but less-common scheme designed to represent the ratio of carbon to oxygen on a scale of 1 to 10, where a 0 would be an MS star. Intensities of zirconium and titanium may be indicated explicitly. Also occasionally seen is a number following an asterisk, which represents the strength of the ZrO bands on a scale from 1 to 5.
==== Classes MS and SC: Intermediate carbon-related classes ====
In between the M and S classes, border cases are named MS stars. In a similar way, border cases between the S and C-N classes are named SC or CS. The sequence M → MS → S → SC → C-N is hypothesized to be a sequence of increased carbon abundance with age for carbon stars in the asymptotic giant branch.
=== White dwarf classifications ===
The class D (for Degenerate) is the modern classification used for white dwarfs—low-mass stars that are no longer undergoing nuclear fusion and have shrunk to planetary size, slowly cooling down. Class D is further divided into spectral types DA, DB, DC, DO, DQ, DX, and DZ. The letters are not related to the letters used in the classification of other stars, but instead indicate the composition of the white dwarf's visible outer layer or atmosphere.
The white dwarf types are as follows:
DA a hydrogen-rich atmosphere or outer layer, indicated by strong Balmer hydrogen spectral lines.
DB a helium-rich atmosphere, indicated by neutral helium, He I, spectral lines.
DO a helium-rich atmosphere, indicated by ionized helium, He II, spectral lines.
DQ a carbon-rich atmosphere, indicated by atomic or molecular carbon lines.
DZ a metal-rich atmosphere, indicated by metal spectral lines (a merger of the obsolete white dwarf spectral types, DG, DK, and DM).
DC no strong spectral lines indicating one of the above categories.
DX spectral lines are insufficiently clear to classify into one of the above categories.
The type is followed by a number giving the white dwarf's surface temperature. This number is a rounded form of 50400/Teff, where Teff is the effective surface temperature, measured in kelvins. Originally, this number was rounded to one of the digits 1 through 9, but more recently fractional values have started to be used, as well as values below 1 and above 9.(For example DA1.5 for IK Pegasi B)
Two or more of the type letters may be used to indicate a white dwarf that displays more than one of the spectral features above.
==== Extended white dwarf spectral types ====
DAB a hydrogen- and helium-rich white dwarf displaying neutral helium lines
DAO a hydrogen- and helium-rich white dwarf displaying ionized helium lines
DAZ a hydrogen-rich metallic white dwarf
DBZ a helium-rich metallic white dwarf
A different set of spectral peculiarity symbols are used for white dwarfs than for other types of stars:
=== Luminous blue variables ===
Luminous blue variables (LBVs) are rare, massive and evolved stars that show unpredictable and sometimes dramatic variations in their spectra and brightness. During their "quiescent" states, they are usually similar to B-type stars, although with unusual spectral lines. During outbursts, they are more similar to F-type stars, with significantly lower temperatures. Many papers treat LBV as its own spectral type.
=== Spectral types of non-single objects: Classes P and Q ===
Finally, the classes P and Q are left over from the system developed by Cannon for the Henry Draper Catalogue. They are occasionally used for certain objects, not associated with a single star: Type P objects are stars within planetary nebulae (typically young white dwarfs or hydrogen-poor M giants); type Q objects are novae.
== Stellar remnants ==

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Stellar remnants are objects associated with the death of stars. Included in the category are white dwarfs, and as can be seen from the radically different classification scheme for class D, stellar remnants are difficult to fit into the MK system.
The HertzsprungRussell diagram, which the MK system is based on, is observational in nature so these remnants cannot easily be plotted on the diagram, or cannot be placed at all. Old neutron stars are relatively small and cold, and would fall on the far right side of the diagram. Planetary nebulae are dynamic and tend to quickly fade in brightness as the progenitor star transitions to the white dwarf branch. If shown, a planetary nebula would be plotted to the right of the diagram's upper right quadrant. A black hole emits no visible light of its own, and therefore would not appear on the diagram.
A classification system for neutron stars using Roman numerals has been proposed: type I for less massive neutron stars with low cooling rates, type II for more massive neutron stars with higher cooling rates, and a proposed type III for more massive neutron stars (possible exotic star candidates) with higher cooling rates. The more massive a neutron star is, the higher neutrino flux it carries. These neutrinos carry away so much heat energy that after only a few years the temperature of an isolated neutron star falls from the order of billions to only around a million Kelvin. This proposed neutron star classification system is not to be confused with the earlier Secchi spectral classes and the Yerkes luminosity classes.
== Replaced spectral classes ==
Several spectral types, all previously used for non-standard stars in the mid-20th century, have been replaced during revisions of the stellar classification system. They may still be found in old editions of star catalogs: R and N have been subsumed into the new C class as C-R and C-N.
== Stellar classification, habitability, and the search for life ==
While humans may eventually be able to colonize any kind of stellar habitat, this section will address the probability of life arising around other stars.
Stability, luminosity, and lifespan are all factors in stellar habitability. Humans know of only one star that hosts life, the G-class Sun, a star with an abundance of heavy elements and low variability in brightness. The Solar System is also unlike many stellar systems in that it only contains one star (see Habitability of binary star systems).
Working from these constraints and the problems of having an empirical sample set of only one, the range of stars that are predicted to be able to support life is limited by a few factors. Of the main-sequence star types, stars more massive than 1.5 times that of the Sun (spectral types O, B, and A) age too quickly for advanced life to develop (using Earth as a guideline). On the other extreme, dwarfs of less than half the mass of the Sun (spectral type M) are likely to tidally lock planets within their habitable zone, along with other problems (see Habitability of red dwarf systems). While there are many problems facing life on red dwarfs, many astronomers continue to model these systems due to their sheer numbers and longevity.
For these reasons NASA's Kepler Mission is searching for habitable planets at nearby main-sequence stars that are less massive than spectral type A but more massive than type M—making the most probable stars to host life dwarf stars of types F, G, and K.
== See also ==
Astrograph Type of telescope
Guest star Ancient Chinese name for cataclysmic variable stars
Spectral signature Variation of reflectance or emittance of a material with respect to wavelengths
Star count Bookkeeping survey of stars, survey of stars
Stellar dynamics Branch of astrophysics
== Notes ==
== References ==
== Further reading ==
Harre, Jan-Vincent; Heller, René (2021). "Digital color codes of stars". Astronomische Nachrichten. 342 (3): 578587. arXiv:2101.06254. Bibcode:2021AN....342..578H. doi:10.1002/asna.202113868. S2CID 231627588.
== External links ==
Libraries of stellar spectra by D. Montes, UCM
Spectral Types for Hipparcos Catalogue Entries
Stellar Spectral Classification Archived 31 October 2010 at the Wayback Machine by Richard O. Gray and Christopher J. Corbally
Spectral models of stars by P. Coelho
Merrifield, Michael; Bauer, Amanda; Häußler, Boris (2010). "Star Classification". Sixty Symbols. Brady Haran for the University of Nottingham.
Stellar classification table

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Stellar evolution is the process by which a star changes over the course of time. Depending on the mass of the star, its lifetime can range from a few million years for the most massive to trillions of years for the least massive, which is considerably longer than the current age of the universe. The table shows the lifetimes of stars as a function of their masses. All stars are formed from collapsing clouds of gas and dust, often called nebulae or molecular clouds. Over the course of millions of years, these protostars settle down into a state of equilibrium, becoming what is known as a main sequence star.
Nuclear fusion powers a star for most of its existence. Initially the energy is generated by the fusion of hydrogen atoms at the core of the main-sequence star. Later, as the preponderance of atoms at the core becomes helium, stars like the Sun begin to fuse hydrogen along a spherical shell surrounding the core. This process causes the star to gradually grow in size, passing through the subgiant stage until it reaches the red-giant phase. Stars with at least half the mass of the Sun can also begin to generate energy through the fusion of helium at their core, whereas more-massive stars can fuse heavier elements along a series of concentric shells. Once a star like the Sun has exhausted its nuclear fuel, its core collapses into a dense white dwarf and the outer layers are expelled as a planetary nebula. Stars with around ten or more times the mass of the Sun can explode in a supernova as their inert iron cores collapse into an extremely dense neutron star or black hole. Although the universe is not old enough for any of the smallest red dwarfs to have reached the end of their existence, stellar models suggest they will slowly become brighter and hotter before running out of hydrogen fuel and becoming low-mass white dwarfs.
Stellar evolution is not studied by observing the life of a single star, as most stellar changes occur too slowly to be detected, even over many centuries. Instead, astrophysicists come to understand how stars evolve by observing numerous stars at various points in their lifetime, and by simulating stellar structure using computer models.
== Star formation ==
=== Protostar ===
Stellar evolution starts with the gravitational collapse of a giant molecular cloud. Typical giant molecular clouds are roughly 100 light-years (9.5×1014 km) across and contain up to 6,000,000 solar masses (1.2×1037 kg). As it collapses, a giant molecular cloud breaks into smaller and smaller pieces. In each of these fragments, the collapsing gas releases gravitational potential energy as heat. As its temperature and pressure increase, a fragment condenses into a rotating ball of superhot gas known as a protostar. Filamentary structures are truly ubiquitous in the molecular cloud. Dense molecular filaments will fragment into gravitationally bound cores, which are the precursors of stars. Continuous accretion of gas, geometrical bending, and magnetic fields may control the detailed fragmentation manner of the filaments. In supercritical filaments, observations have revealed quasi-periodic chains of dense cores with spacing comparable to the filament inner width, and embedded two protostars with gas outflows.
A protostar continues to grow by accretion of gas and dust from the molecular cloud, becoming a pre-main-sequence star as it reaches its final mass. Further development is determined by its mass. Mass is typically compared to the mass of the Sun: 1.0 M☉ (2.0×1030 kg) means 1 solar mass.
Protostars are encompassed in dust, and are thus more readily visible at infrared wavelengths.
Observations from the Wide-field Infrared Survey Explorer (WISE) have been especially important for unveiling numerous galactic protostars and their parent star clusters.
=== Brown dwarfs and sub-stellar objects ===
Protostars with masses less than roughly 0.08 M☉ (1.6×1029 kg) never reach temperatures high enough for nuclear fusion of hydrogen to begin. These are known as brown dwarfs. The International Astronomical Union defines brown dwarfs as stars massive enough to fuse deuterium at some point in their lives (13 Jupiter masses (MJ), 2.5 × 1028 kg, or 0.0125 M☉). Objects smaller than 13 MJ are classified as sub-brown dwarfs (but if they orbit around another stellar object they are classified as planets). Both types, deuterium-burning and not, shine dimly and fade away slowly, cooling gradually over hundreds of millions of years.
=== Main sequence stellar mass objects ===
For a more-massive protostar, the core temperature will eventually reach 10 million kelvin, initiating the protonproton chain reaction and allowing hydrogen to fuse, first to deuterium and then to helium. In stars of slightly over 1 M☉ (2.0×1030 kg), the carbonnitrogenoxygen fusion reaction (CNO cycle) contributes a large portion of the energy generation. The onset of nuclear fusion leads relatively quickly to a hydrostatic equilibrium in which energy released by the core maintains a high gas pressure, balancing the weight of the star's matter and preventing further gravitational collapse. The star thus evolves rapidly to a stable state, beginning the main-sequence phase of its evolution.
A new star will sit at a specific point on the main sequence of the HertzsprungRussell diagram, with the main-sequence spectral type depending upon the mass of the star. Small, relatively cold, low-mass red dwarfs fuse hydrogen slowly and will remain on the main sequence for hundreds of billions of years or longer, whereas massive, hot O-type stars will leave the main sequence after just a few million years. A mid-sized yellow dwarf star, like the Sun, will remain on the main sequence for about 10 billion years. The Sun is thought to be in the middle of its main sequence lifespan.
=== Planetary system ===
A star may gain a protoplanetary disk, which furthermore can develop into a planetary system.
== Mature stars ==

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Eventually the star's core exhausts its supply of hydrogen and the star begins to evolve off the main sequence. Without the outward radiation pressure generated by the fusion of hydrogen to counteract the force of gravity, the core contracts until either electron degeneracy pressure becomes sufficient to oppose gravity or the core becomes hot enough (around 100 MK) for helium fusion to begin. Which of these happens first depends upon the star's mass.
=== Low-mass stars ===
What happens after a low-mass star ceases to produce energy through fusion has not been directly observed; the universe is around 13.8 billion years old, which is less time (by several orders of magnitude, in some cases) than it takes for fusion to cease in such stars.
Recent astrophysical models suggest that red dwarfs of 0.1 M☉ may stay on the main sequence for some six to twelve trillion years, gradually increasing in both temperature and luminosity, and take several hundred billion years more to collapse, slowly, into a white dwarf. Such stars will not become red giants as the whole star is a convection zone and it will not develop a degenerate helium core with a shell burning hydrogen. Instead, hydrogen fusion will proceed until almost the whole star is helium.
Slightly more massive stars do expand into red giants, but their helium cores are not massive enough to reach the temperatures required for helium fusion so they never reach the tip of the red-giant branch. When hydrogen shell burning finishes, these stars move directly off the red-giant branch like a post-asymptotic-giant-branch (AGB) star, but at lower luminosity, to become a white dwarf. A star with an initial mass about 0.6 M☉ will be able to reach temperatures high enough to fuse helium, and these "mid-sized" stars go on to further stages of evolution beyond the red-giant branch.
=== Mid-sized stars ===
Stars of roughly 0.610 M☉ become red giants, which are large non-main-sequence stars of stellar classification K or M. Red giants lie along the right edge of the HertzsprungRussell diagram due to their red color and large luminosity. Examples include Aldebaran in the constellation Taurus and Arcturus in the constellation of Boötes.
Mid-sized stars are red giants during two different phases of their post-main-sequence evolution: red-giant-branch stars, with inert cores made of helium and hydrogen-burning shells, and asymptotic-giant-branch stars, with inert cores made of carbon and helium-burning shells inside the hydrogen-burning shells. Between these two phases, stars spend a period on the horizontal branch with a helium-fusing core. Many of these helium-fusing stars cluster towards the cool end of the horizontal branch as K-type giants and are referred to as red clump giants.
==== Subgiant phase ====
When a star exhausts the hydrogen in its core, it leaves the main sequence and begins to fuse hydrogen in a shell outside the core. The core increases in mass as the shell produces more helium. Depending on the mass of the helium core, this continues for several million to one or two billion years, with the star expanding and cooling at a similar or slightly lower luminosity to its main sequence state. Eventually either the core becomes degenerate, in stars around the mass of the sun, or the outer layers cool sufficiently to become opaque, in more massive stars. Either of these changes cause the hydrogen shell to increase in temperature and the luminosity of the star to increase, at which point the star expands onto the red-giant branch.
==== Red-giant-branch phase ====
The expanding outer layers of the star are convective, with the material being mixed by turbulence from near the fusing regions up to the surface of the star. For all but the lowest-mass stars, the fused material has remained deep in the stellar interior prior to this point, so the convecting envelope makes fusion products visible at the star's surface for the first time. At this stage of evolution, the results are subtle, with the largest effects, alterations to the isotopes of hydrogen and helium, being unobservable. The effects of the CNO cycle appear at the surface during the first dredge-up, with lower 12C/13C ratios and altered proportions of carbon and nitrogen. These are detectable with spectroscopy and have been measured for many evolved stars.
The helium core continues to grow on the red-giant branch. It is no longer in thermal equilibrium, either degenerate or above the SchönbergChandrasekhar limit, so it increases in temperature which causes the rate of fusion in the hydrogen shell to increase. The star increases in luminosity towards the tip of the red-giant branch. Red-giant-branch stars with a degenerate helium core all reach the tip with very similar core masses and very similar luminosities, although the more massive of the red giants become hot enough to ignite helium fusion before that point.
==== Horizontal branch ====
In the helium cores of stars in the 0.6 to 2.0 solar mass range, which are largely supported by electron degeneracy pressure, helium fusion will ignite on a timescale of days in a helium flash. In the nondegenerate cores of more massive stars, the ignition of helium fusion occurs relatively slowly with no flash. The nuclear power released during the helium flash is very large, on the order of 108 times the luminosity of the Sun for a few days and 1011 times the luminosity of the Sun (roughly the luminosity of the Milky Way Galaxy) for a few seconds. However, the energy is consumed by the thermal expansion of the initially degenerate core and thus cannot be seen from outside the star. Due to the expansion of the core, the hydrogen fusion in the overlying layers slows and total energy generation decreases. The star contracts, although not all the way to the main sequence, and it migrates to the horizontal branch on the HertzsprungRussell diagram, gradually shrinking in radius and increasing its surface temperature.

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Core helium flash stars evolve to the red end of the horizontal branch but do not migrate to higher temperatures before they gain a degenerate carbon-oxygen core and start helium shell burning. These stars are often observed as a red clump of stars in the colour-magnitude diagram of a cluster, hotter and less luminous than the red giants. Higher-mass stars with larger helium cores move along the horizontal branch to higher temperatures, some becoming unstable pulsating stars in the yellow instability strip (RR Lyrae variables), whereas some become even hotter and can form a blue tail or blue hook to the horizontal branch. The morphology of the horizontal branch depends on parameters such as metallicity, age, and helium content, but the exact details are still being modelled.
==== Asymptotic-giant-branch phase ====
After a star has consumed the helium at the core, hydrogen and helium fusion continues in shells around a hot core of carbon and oxygen. The star follows the asymptotic giant branch on the HertzsprungRussell diagram, paralleling the original red-giant evolution, but with even faster energy generation (which lasts for a shorter time). Although helium is being burnt in a shell, the majority of the energy is produced by hydrogen burning in a shell further from the core of the star. Helium from these hydrogen burning shells drops towards the center of the star and periodically the energy output from the helium shell increases dramatically. This is known as a thermal pulse and they occur towards the end of the asymptotic-giant-branch phase, sometimes even into the post-asymptotic-giant-branch phase. Depending on mass and composition, there may be several to hundreds of thermal pulses.
There is a phase on the ascent of the asymptotic-giant-branch where a deep convective zone forms and can bring carbon from the core to the surface. This is known as the second dredge up, and in some stars there may even be a third dredge up. In this way a carbon star is formed, very cool and strongly reddened stars showing strong carbon lines in their spectra. A process known as hot bottom burning may convert carbon into oxygen and nitrogen before it can be dredged to the surface, and the interaction between these processes determines the observed luminosities and spectra of carbon stars in particular clusters.
Another well known class of asymptotic-giant-branch stars is the Mira variables, which pulsate with well-defined periods of tens to hundreds of days and large amplitudes up to about 10 magnitudes (in the visual, total luminosity changes by a much smaller amount). In more-massive stars the stars become more luminous and the pulsation period is longer, leading to enhanced mass loss, and the stars become heavily obscured at visual wavelengths. These stars can be observed as OH/IR stars, pulsating in the infrared and showing OH maser activity. These stars are clearly oxygen rich, in contrast to the carbon stars, but both must be produced by dredge ups.
==== Post-AGB ====
These mid-range stars ultimately reach the tip of the asymptotic-giant-branch and run out of fuel for shell burning. They are not sufficiently massive to start full-scale carbon fusion, so they contract again, going through a period of post-asymptotic-giant-branch superwind to produce a planetary nebula with an extremely hot central star. The central star then cools to a white dwarf. The expelled gas is relatively rich in heavy elements created within the star and may be particularly oxygen or carbon enriched, depending on the type of the star. The gas builds up in an expanding shell called a circumstellar envelope and cools as it moves away from the star, allowing dust particles and molecules to form. With the high infrared energy input from the central star, ideal conditions are formed in these circumstellar envelopes for maser excitation.
It is possible for thermal pulses to be produced once post-asymptotic-giant-branch evolution has begun, producing a variety of unusual and poorly understood stars known as born-again asymptotic-giant-branch stars. These may result in extreme horizontal-branch stars (subdwarf B stars), hydrogen deficient post-asymptotic-giant-branch stars, variable planetary nebula central stars, and R Coronae Borealis variables.
=== Massive stars ===
In massive stars, the core is already large enough at the onset of the hydrogen burning shell that helium ignition will occur before electron degeneracy pressure has a chance to become prevalent. Thus, when these stars expand and cool, they do not brighten as dramatically as lower-mass stars; however, they were more luminous on the main sequence and they evolve to highly luminous supergiants. Their cores become massive enough that they cannot support themselves by electron degeneracy and will eventually collapse to produce a neutron star or black hole.
==== Supergiant evolution ====
Extremely massive stars (more than approximately 40 M☉), which are very luminous and thus have very rapid stellar winds, lose mass so rapidly due to radiation pressure that they tend to strip off their own envelopes before they can expand to become red supergiants, and thus retain extremely high surface temperatures (and blue-white color) from their main-sequence time onwards. The largest stars of the current generation are about 100150 M☉ because the outer layers would be expelled by the extreme radiation. Although lower-mass stars normally do not burn off their outer layers so rapidly, they can likewise avoid becoming red giants or red supergiants if they are in binary systems close enough so that the companion star strips off the envelope as it expands, or if they rotate rapidly enough so that convection extends all the way from the core to the surface, resulting in the absence of a separate core and envelope due to thorough mixing.

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The core of a massive star, defined as the region depleted of hydrogen, grows hotter and denser as it accretes material from the fusion of hydrogen outside the core. In sufficiently massive stars, the core reaches temperatures and densities high enough to fuse carbon and heavier elements via the alpha process. At the end of helium fusion, the core of a star consists primarily of carbon and oxygen. In stars heavier than about 8 M☉, the carbon ignites and fuses to form neon, sodium, and magnesium. Stars somewhat less massive may partially ignite carbon, but they are unable to fully fuse the carbon before electron degeneracy sets in, and these stars will eventually leave an oxygen-neon-magnesium white dwarf.
The exact mass limit for full carbon burning depends on several factors such as metallicity and the detailed mass lost on the asymptotic giant branch, but is approximately 89 M☉. After carbon burning is complete, the core of these stars reaches about 2.5 M☉ and becomes hot enough for heavier elements to fuse. Before oxygen starts to fuse, neon begins to capture electrons which triggers neon burning. For a range of stars of approximately 8-12 M☉, this process is unstable and creates runaway fusion resulting in an electron capture supernova.
In more massive stars, the fusion of neon proceeds without a runaway deflagration. This is followed in turn by complete oxygen burning and silicon burning, producing a core consisting largely of iron-peak elements. Surrounding the core are shells of lighter elements still undergoing fusion. The timescale for complete fusion of a carbon core to an iron core is so short, just a few hundred years, that the outer layers of the star are unable to react and the appearance of the star is largely unchanged. The iron core grows until it reaches an effective Chandrasekhar mass, higher than the formal Chandrasekhar mass due to various corrections for the relativistic effects, entropy, charge, and the surrounding envelope. The effective Chandrasekhar mass for an iron core varies from about 1.34 M☉ in the least massive red supergiants to more than 1.8 M☉ in more massive stars. Once this mass is reached, electrons begin to be captured into the iron-peak nuclei and the core becomes unable to support itself. The core collapses and the star is destroyed, either in a supernova or direct collapse to a black hole.
==== Supernova ====
When the core of a massive star collapses, it will form a neutron star, or in the case of cores that exceed the TolmanOppenheimerVolkoff limit, a black hole. Through a process that is not completely understood, some of the gravitational potential energy released by this core collapse is converted into a Type Ib, Type Ic, or Type II supernova. It is known that the core collapse produces a massive surge of neutrinos, as observed with supernova SN 1987A. The extremely energetic neutrinos fragment some nuclei; some of their energy is consumed in releasing nucleons, including neutrons, and some of their energy is transformed into heat and kinetic energy, thus augmenting the shock wave started by rebound of some of the infalling material from the collapse of the core. Electron capture in very dense parts of the infalling matter may produce additional neutrons. Because some of the rebounding matter is bombarded by the neutrons, some of its nuclei capture them, creating a spectrum of heavier-than-iron material including the radioactive elements up to (and likely beyond) uranium. Although non-exploding red giants can produce significant quantities of elements heavier than iron using neutrons released in side reactions of earlier nuclear reactions, the abundance of elements heavier than iron (and in particular, of certain isotopes of elements that have multiple stable or long-lived isotopes) produced in such reactions is quite different from that produced in a supernova. Neither abundance alone matches that found in the Solar System, so both supernovae, neutron star mergers and ejection of elements from red giants are required to explain the observed abundance of heavy elements and isotopes thereof.
The energy transferred from collapse of the core to rebounding material not only generates heavy elements, but provides for their acceleration well beyond escape velocity, thus causing a Type Ib, Type Ic, or Type II supernova. Current understanding of this energy transfer is still not satisfactory; although current computer models of Type Ib, Type Ic, and Type II supernovae account for part of the energy transfer, they are not able to account for enough energy transfer to produce the observed ejection of material. However, neutrino oscillations may play an important role in the energy transfer problem as they not only affect the energy available in a particular flavour of neutrinos but also through other general-relativistic effects on neutrinos.
Some evidence gained from analysis of the mass and orbital parameters of binary neutron stars (which require two such supernovae) hints that the collapse of an oxygen-neon-magnesium core may produce a supernova that differs observably (in ways other than size) from a supernova produced by the collapse of an iron core.
The most massive stars that exist today may be completely destroyed by a supernova with an energy greatly exceeding its gravitational binding energy. This rare event, caused by pair-instability, leaves behind no black hole remnant. In the past history of the universe, some stars were even larger than the largest that exists today, and they would immediately collapse into a black hole at the end of their lives, due to photodisintegration.
== Stellar remnants ==
After a star has burned out its fuel supply, its remnants can take one of three forms, depending on the mass during its lifetime.
=== White and black dwarfs ===

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For a star of 1 M☉, the resulting white dwarf is of about 0.6 M☉, compressed into approximately the volume of the Earth. White dwarfs are stable because the inward pull of gravity is balanced by the degeneracy pressure of the star's electrons, a consequence of the Pauli exclusion principle. Electron degeneracy pressure provides a rather soft limit against further compression; therefore, for a given chemical composition, white dwarfs of higher mass have a smaller volume. With no fuel left to burn, the star radiates its remaining heat into space for billions of years.
A white dwarf is very hot when it first forms, more than 100,000 K at the surface and even hotter in its interior. It is so hot that a lot of its energy is lost in the form of neutrinos for the first 10 million years of its existence and will have lost most of its energy after a billion years.
The chemical composition of the white dwarf depends upon its mass. A star that has a mass of about 8-12 solar masses will ignite carbon fusion to form magnesium, neon, and smaller amounts of other elements, resulting in a white dwarf composed chiefly of oxygen, neon, and magnesium, provided that it can lose enough mass to get below the Chandrasekhar limit (see below), and provided that the ignition of carbon is not so violent as to blow the star apart in a supernova. A star of mass on the order of magnitude of the Sun will be unable to ignite carbon fusion, and will produce a white dwarf composed chiefly of carbon and oxygen, and of mass too low to collapse unless matter is added to it later (see below). A star of less than about half the mass of the Sun will be unable to ignite helium fusion (as noted earlier), and will produce a white dwarf composed chiefly of helium.
In the end, all that remains is a cold dark mass sometimes called a black dwarf. However, the universe is not old enough for any black dwarfs to exist yet.
If the white dwarf's mass increases above the Chandrasekhar limit, which is 1.4 M☉ for a white dwarf composed chiefly of carbon, oxygen, neon, and/or magnesium, then electron degeneracy pressure fails due to electron capture and the star collapses. Depending upon the chemical composition and pre-collapse temperature in the center, this will lead either to collapse into a neutron star or runaway ignition of carbon and oxygen. Heavier elements favor continued core collapse, because they require a higher temperature to ignite, because electron capture onto these elements and their fusion products is easier; higher core temperatures favor runaway nuclear reaction, which halts core collapse and leads to a Type Ia supernova. These supernovae may be many times brighter than the Type II supernova marking the death of a massive star, even though the latter has the greater total energy release. This instability to collapse means that no white dwarf more massive than approximately 1.4 M☉ can exist (with a possible minor exception for very rapidly spinning white dwarfs, whose centrifugal force due to rotation partially counteracts the weight of their matter). Mass transfer in a binary system may cause an initially stable white dwarf to surpass the Chandrasekhar limit.
If a white dwarf forms a close binary system with another star, hydrogen from the larger companion may accrete around and onto a white dwarf until it gets hot enough to fuse in a runaway reaction at its surface, although the white dwarf remains below the Chandrasekhar limit. Such an explosion is termed a nova.
=== Neutron stars ===
Ordinarily, atoms are mostly electron clouds by volume, with very compact nuclei at the center (proportionally, if atoms were the size of a football stadium, their nuclei would be the size of dust mites). When a stellar core collapses, the pressure causes electrons and protons to fuse by electron capture. Without electrons, which keep nuclei apart, the neutrons collapse into a dense ball (in some ways like a giant atomic nucleus), with a thin overlying layer of degenerate matter (chiefly iron unless matter of different composition is added later). The neutrons resist further compression by the Pauli exclusion principle, in a way analogous to electron degeneracy pressure, but stronger.
These stars, known as neutron stars, are extremely small—on the order of radius 10 km, no bigger than the size of a large city—and are phenomenally dense. Their period of rotation shortens dramatically as the stars shrink (due to conservation of angular momentum); observed rotational periods of neutron stars range from about 1.5 milliseconds (over 600 revolutions per second) to several seconds. When these rapidly rotating stars' magnetic poles are aligned with the Earth, there is a detectable pulse of radiation each revolution. Such neutron stars are called pulsars, and were the first neutron stars to be discovered. Though electromagnetic radiation detected from pulsars is most often in the form of radio waves, pulsars have also been detected at visible, X-ray, and gamma ray wavelengths.
=== Black holes ===

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If the mass of the stellar remnant is high enough, the neutron degeneracy pressure will be insufficient to prevent collapse below the Schwarzschild radius. The stellar remnant thus becomes a black hole. The mass at which this occurs is not known with certainty, but is currently estimated at between 2 and 3 M☉.
Black holes are predicted by the theory of general relativity. According to classical general relativity, no matter or information can flow from the interior of a black hole to an outside observer, although quantum effects may allow deviations from this strict rule. The existence of black holes in the universe is well supported, both theoretically and by astronomical observation.
Because the core-collapse mechanism of a supernova is, at present, only partially understood, it is still not known whether it is possible for a star to collapse directly to a black hole without producing a visible supernova, or whether some supernovae initially form unstable neutron stars which then collapse into black holes; the exact relation between the initial mass of the star and the final remnant is also not completely certain. Resolution of these uncertainties requires the analysis of more supernovae and supernova remnants.
== Models ==
A stellar evolutionary model is a mathematical model that can be used to compute the evolutionary phases of a star from its formation until it becomes a remnant. The mass and chemical composition of the star are used as the inputs, and the luminosity and surface temperature are the only constraints. The model formulae are based upon the physical understanding of the star, usually under the assumption of hydrostatic equilibrium. Extensive computer calculations are then run to determine the changing state of the star over time, yielding a table of data that can be used to determine the evolutionary track of the star across the HertzsprungRussell diagram, along with other evolving properties. Accurate models can be used to estimate the current age of a star by comparing its physical properties with those of stars along a matching evolutionary track.
== See also ==
== References ==
Hansen, Carl J.; Kawaler, Steven D.; Trimble, Virginia (2004). Stellar interiors: physical principles, structure, and evolution (2nd ed.). Springer-Verlag. ISBN 0-387-20089-4.
Prialnik, Dina (2000). An Introduction to the Theory of Stellar Structure and Evolution. Cambridge University Press. ISBN 0-521-65065-8.
Ryan, Sean G.; Norton, Andrew J. (2010). Stellar Evolution and Nucleosynthesis. Cambridge University Press. ISBN 978-0-521-13320-3.
== Further reading ==
Ekström, S.; Georgy, C.; Eggenberger, P.; Meynet, G.; Mowlavi, N.; Wyttenbach, A.; Granada, A.; Decressin, T.; Hirschi, R.; Frischknecht, U.; Charbonnel, C.; Maeder, A. (2012). "Grids of stellar models with rotation". Astronomy & Astrophysics. 537: A146. arXiv:1110.5049. doi:10.1051/0004-6361/201117751. S2CID 85458919.
Astronomy 606 (Stellar Structure and Evolution) lecture notes, Cole Miller, Department of Astronomy, University of Maryland
Astronomy 162, Unit 2 (The Structure & Evolution of Stars) lecture notes, Richard W. Pogge, Department of Astronomy, Ohio State University
== External links ==
Stellar evolution simulator
Pisa Stellar Models
MESA stellar evolution codes (Modules for Experiments in Stellar Astrophysics)
"The Life of Stars", BBC Radio 4 discussion with Paul Murdin, Janna Levin and Phil Charles (In Our Time, Mar. 27, 2003)
Life cycle of a star [1] [2]

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In astrophysics, stellar nucleosynthesis is the creation of chemical elements by nuclear fusion reactions within stars. Stellar nucleosynthesis has occurred since the original creation of hydrogen, helium and lithium during the Big Bang. As a predictive theory, it yields accurate estimates of the observed abundances of the elements. It explains why the observed abundances of elements change over time and why some elements and their isotopes are much more abundant than others. The theory was initially proposed by Fred Hoyle in 1946, who later refined it in 1954. Further advances were made, especially to nucleosynthesis by neutron capture of the elements heavier than iron, by Margaret and Geoffrey Burbidge, William Alfred Fowler and Fred Hoyle in their famous 1957 B2FH paper, which became one of the most heavily cited papers in astrophysics history.
Stars evolve because of changes in their composition (the abundance of their constituent elements) over their lifespans, first by burning hydrogen (main sequence star), then helium (horizontal branch star), and progressively burning higher elements. However, this does not by itself significantly alter the abundances of elements in the universe as the elements are contained within the star. Later in its life, a low-mass star will slowly eject its atmosphere via stellar wind, forming a planetary nebula, while a highermass star will eject mass via a sudden catastrophic event called a supernova. The term supernova nucleosynthesis is used to describe the creation of elements during the explosion of a massive star or white dwarf.
The advanced sequence of burning fuels is driven by gravitational collapse and its associated heating, resulting in the subsequent burning of carbon, oxygen and silicon. However, most of the nucleosynthesis in the mass range A = 2856 (from silicon to nickel) is actually caused by the upper layers of the star collapsing onto the core, creating a compressional shock wave rebounding outward. The shock front briefly raises temperatures by roughly 50%, thereby causing furious burning for about a second. This final burning in massive stars, called explosive nucleosynthesis or supernova nucleosynthesis, is the final epoch of stellar nucleosynthesis.
A stimulus to the development of the theory of nucleosynthesis was the discovery of variations in the abundances of elements found in the universe. The need for a physical description was already inspired by the relative abundances of the chemical elements in the Solar System. Those abundances, when plotted on a graph as a function of the atomic number of the element, have a jagged sawtooth shape that varies by factors of tens of millions (see history of nucleosynthesis theory). This suggested a natural process that is not random. A second stimulus to understanding the processes of stellar nucleosynthesis occurred during the 20th century, when it was realized that the energy released from nuclear fusion reactions accounted for the longevity of the Sun as a source of heat and light.
== History ==
In 1920, Arthur Eddington, on the basis of the precise measurements of atomic masses by F.W. Aston and a preliminary suggestion by Jean Perrin, proposed that stars obtained their energy from nuclear fusion of hydrogen to form helium and raised the possibility that the heavier elements are produced in stars. This was a preliminary step toward the idea of stellar nucleosynthesis. In 1928 George Gamow derived what is now called the Gamow factor, a quantum-mechanical formula yielding the probability for two contiguous nuclei to overcome the electrostatic Coulomb barrier between them and approach each other closely enough to undergo nuclear reaction due to the strong nuclear force which is effective only at very short distances. In the following decade the Gamow factor was used by Robert d'Escourt Atkinson and Fritz Houtermans and later by Edward Teller and Gamow himself to derive the rate at which nuclear reactions would occur at the high temperatures believed to exist in stellar interiors.
In a 1939 paper entitled "Energy Production in Stars", Hans Bethe analyzed the different possibilities for reactions by which hydrogen is fused into helium. He defined two processes that he believed to be the sources of energy in stars. The first one, the protonproton chain reaction, is the dominant energy source in stars with masses up to about the mass of the Sun. The second process, the carbonnitrogenoxygen cycle, which was also considered by Carl Friedrich von Weizsäcker in 1938, is more important in more massive main-sequence stars. These works concerned the energy generation capable of keeping stars hot. Bethe's two papers did not address the creation of heavier nuclei, however. That theory was begun by Fred Hoyle in 1946 with his argument that a collection of very hot nuclei would assemble thermodynamically into iron. Hoyle followed that in 1954 with a paper describing how advanced fusion stages within massive stars would synthesize the elements from carbon to iron in mass.
Hoyle's theory was extended to other processes, beginning with the publication of the 1957 review paper "Synthesis of the Elements in Stars" by Margaret Burbidge, Geoffrey Burbidge, William Alfred Fowler and Fred Hoyle, more commonly referred to as the B2FH paper. This review paper synthesized information from across fields of nuclear physics, stellar evolution and abundance of the elements to create the foundation of a theory of stellar nucleosynthesis.. In 1957 Alastair G. W. Cameron, working independently showed the OddoHarkins even-odd abundance rule would follow from processes outlined by the B2FH paper. Clayton calculated the first time-dependent models of the s-process in 1961 and of the r-process in 1965, as well as of the burning of silicon into the abundant alpha-particle nuclei and iron-group elements in 1968, and discovered radiogenic chronologies for determining the age of the elements.
== Key reactions ==
The most important reactions in stellar nucleosynthesis:

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Hydrogen fusion:
Deuterium fusion
The protonproton chain
The carbonnitrogenoxygen cycle
Helium fusion:
The triple-alpha process
The alpha process
Fusion of heavier elements:
Lithium burning: a process found most commonly in brown dwarfs
Carbon-burning process
Neon-burning process
Oxygen-burning process
Silicon-burning process
Production of elements heavier than iron:
Neutron capture:
The r-process
The s-process
Proton capture:
The rp-process
The p-process
Photodisintegration
=== Hydrogen fusion ===
Hydrogen fusion (nuclear fusion of four protons to form a helium-4 nucleus) is the dominant process that generates energy in the cores of main-sequence stars. It is also called "hydrogen burning", which should not be confused with the chemical combustion of hydrogen in an oxidizing atmosphere. There are two predominant processes by which stellar hydrogen fusion occurs: the protonproton chain and the carbonnitrogenoxygen (CNO) cycle. Ninety percent of all stars, with the exception of white dwarfs, are fusing hydrogen by these two processes.
In the cores of lower-mass main-sequence stars such as the Sun, the dominant energy production process is the protonproton chain reaction. This creates a helium-4 nucleus through a sequence of reactions that begin with the fusion of two protons to form a deuterium nucleus (one proton plus one neutron) along with an ejected positron and neutrino. In each complete fusion cycle, the protonproton chain reaction releases about 26.2 MeV. Proton-proton chain with a dependence of approximately T4, meaning the reaction cycle is highly sensitive to temperature; a 10% rise of temperature would increase energy production by this method by 46%, hence, this hydrogen fusion process can occur in up to a third of the star's radius and occupy half the star's mass. For stars above 35% of the Sun's mass, the energy flux toward the surface is sufficiently low and energy transfer from the core region remains by radiative heat transfer, rather than by convective heat transfer. As a result, there is little mixing of fresh hydrogen into the core or fusion products outward.
In higher-mass stars, the dominant energy production process is the CNO cycle, which is a catalytic cycle that uses nuclei of carbon, nitrogen and oxygen as intermediaries and in the end produces a helium nucleus as with the protonproton chain. During a complete CNO cycle, 25.0 MeV of energy is released. The difference in energy production of this cycle, compared to the protonproton chain reaction, is accounted for by the energy lost through neutrino emission. CNO cycle is highly sensitive to temperature, with rates proportional to the 16th to 20th power of the temperature; a 10% increase in temperature would result in a 350% increase in energy production. About 90% of the CNO cycle energy generation occurs within the inner 15% of the star's mass, hence it is strongly concentrated at the core. This results in such an intense outward energy flux that convective energy transfer becomes more important than does radiative transfer. As a result, the core region becomes a convection zone, which stirs the hydrogen fusion region and keeps it well mixed with the surrounding proton-rich region. This core convection occurs in stars where the CNO cycle contributes more than 20% of the total energy. As the star ages and the core temperature increases, the region occupied by the convection zone slowly shrinks from 20% of the mass down to the inner 8% of the mass. The Sun produces on the order of 1% of its energy from the CNO cycle.
The type of hydrogen fusion process that dominates in a star is determined by the temperature dependency differences between the two reactions. The protonproton chain reaction starts at temperatures about 4×106 K, making it the dominant fusion mechanism in smaller stars. A self-maintaining CNO chain requires a higher temperature of approximately 1.6×107 K, but thereafter it increases more rapidly in efficiency as the temperature rises, than does the protonproton reaction. Above approximately 1.7×107 K, the CNO cycle becomes the dominant source of energy. This temperature is achieved in the cores of main-sequence stars with at least 1.3 times the mass of the Sun. The Sun itself has a core temperature of about 1.57×107 K. As a main-sequence star ages, the core temperature will rise, resulting in a steadily increasing contribution from its CNO cycle.
=== Helium fusion ===

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Main sequence stars accumulate helium in their cores as a result of hydrogen fusion, but the core does not become hot enough to initiate helium fusion. Helium fusion first begins when a star leaves the red giant branch after accumulating sufficient helium in its core to ignite it. In stars around the mass of the Sun, this begins at the tip of the red giant branch with a helium flash from a degenerate helium core, and the star moves to the horizontal branch where it burns helium in its core. More massive stars ignite helium in their core without a flash and execute a blue loop before reaching the asymptotic giant branch. Such a star initially moves away from the AGB toward bluer colours, then loops back again to what is called the Hayashi track. An important consequence of blue loops is that they give rise to classical Cepheid variables, of central importance in determining distances in the Milky Way and to nearby galaxies. Despite the name, stars on a blue loop from the red giant branch are typically not blue in colour but are rather yellow giants, possibly Cepheid variables. They fuse helium until the core is largely carbon and oxygen. The most massive stars become supergiants when they leave the main sequence and quickly start helium fusion as they become red supergiants. After the helium is exhausted in the core of a star, helium fusion will continue in a shell around the carbonoxygen core.
In all cases, helium is fused to carbon via the triple-alpha process, i.e., three helium nuclei are transformed into carbon via 8Be. This can then form oxygen, neon, and heavier elements via the alpha process. In this way, the alpha process preferentially produces elements with even numbers of protons by the capture of helium nuclei. Elements with odd numbers of protons are formed by other fusion pathways.
== Reaction rate ==
The reaction rate density between species A and B, having number densities nA,B, is given by:
r
=
n
A
n
B
k
r
{\displaystyle r=n_{A}\,n_{B}\,k_{r}}
where kr is the reaction rate constant of each single elementary binary reaction composing the nuclear fusion process;
k
r
=
σ
(
v
)
v
{\displaystyle k_{r}=\langle \sigma (v)\,v\rangle }
where σ(v) is the cross-section at relative velocity v, and averaging is performed over all velocities.
Semi-classically, the cross section is proportional to
π
λ
2
{\textstyle \pi \,\lambda ^{2}}
, where
λ
=
h
/
p
{\textstyle \lambda =h/p}
is the de Broglie wavelength. Thus semi-classically the cross section is proportional to
E
m
=
c
2
{\textstyle {\frac {E}{m}}=c^{2}}
.
However, since the reaction involves quantum tunneling, there is an exponential damping at low energies that depends on Gamow factor EG, given by an Arrhenius-type equation:
σ
(
E
)
=
S
(
E
)
E
e
E
G
E
.
{\displaystyle \sigma (E)={\frac {S(E)}{E}}e^{-{\sqrt {\frac {E_{\text{G}}}{E}}}}.}
Here astrophysical S-factor S(E) depends on the details of the nuclear interaction, and has the dimension of an energy multiplied by a cross section.
One then integrates over all energies to get the total reaction rate, using the MaxwellBoltzmann distribution and the relation:
r
V
=
n
A
n
B
0
(
S
(
E
)
E
e
E
G
E
2
E
π
(
k
T
)
3
e
E
k
T
2
E
m
R
)
d
E
{\displaystyle {\frac {r}{V}}=n_{A}n_{B}\int _{0}^{\infty }{\Bigl (}{\frac {S(E)}{E}}\,e^{-{\sqrt {\frac {E_{\text{G}}}{E}}}}\cdot 2{\sqrt {\frac {E}{\pi (kT)^{3}}}}\,e^{-{\frac {E}{kT}}}\,\cdot {\sqrt {\frac {2E}{m_{\text{R}}}}}{\Bigr )}dE}
where k = 86,17 μeV/K,
m
R
=
m
A
m
B
m
A
+
m
B
{\displaystyle m_{\text{R}}={\frac {m_{A}m_{B}}{m_{A}+m_{B}}}}
is the reduced mass. The integrand equals
S
(
E
)
e
E
G
E
2
2
/
π
(
k
T
)
3
/
2
e
E
k
T
/
m
R
.
{\displaystyle S(E)\,e^{-{\sqrt {\frac {E_{\text{G}}}{E}}}}\cdot 2{\sqrt {2/\pi }}(kT)^{-3/2}\,e^{-{\frac {E}{kT}}}\,/{\sqrt {m_{\text{R}}}}.}
Since this integration of f(E, constant T) has an exponential damping at high energies of the form
e
E
k
T
{\textstyle \sim e^{-{\frac {E}{kT}}}}
and at low energies from the Gamow factor, the integral almost vanishes everywhere except around the peak at E0, called Gamow peak. There:
E
(
E
G
E
+
E
k
T
)
=
0
{\displaystyle -{\frac {\partial }{\partial E}}\left({\sqrt {\frac {E_{\text{G}}}{E}}}+{\frac {E}{kT}}\right)\,=\,0}
Thus:
E
0
=
(
1
2
k
T
E
G
)
2
3
{\displaystyle E_{0}=\left({\frac {1}{2}}kT{\sqrt {E_{\text{G}}}}\right)^{\frac {2}{3}}}
and
E
G
=
E
0
3
2
/
1
2
k
T
{\displaystyle {\sqrt {E_{\text{G}}}}=E_{0}^{\frac {3}{2}}/{\frac {1}{2}}kT}
The exponent can then be approximated around E0 as:
e
(
E
k
T
+
E
G
E
)
e
3
E
0
k
T
e
(
3
(
E
E
0
)
2
4
E
0
k
T
)
=
e
3
E
0
k
T
(
1
+
(
E
E
0
2
E
0
)
2
)
=
e
3
E
0
k
T
(
1
+
(
E
/
E
0
1
)
2
/
4
)
{\displaystyle e^{-({\frac {E}{kT}}+{\sqrt {\frac {E_{\text{G}}}{E}}})}\approx e^{-{\frac {3E_{0}}{kT}}}e^{{\bigl (}-{\frac {3(E-E_{0})^{2}}{4E_{0}kT}}{\bigr )}}=e^{-{\frac {3E_{0}}{kT}}{\bigl (}1+({\frac {E-E_{0}}{2E_{0}}})^{2}{\bigr )}}=e^{-{\frac {3E_{0}}{kT}}{\bigl (}1+(E/E_{0}-1)^{2}/4{\bigr )}}}
And the reaction rate is approximated as:
r
V
n
A
n
B
4
(
2
/
3
)
m
R
E
0
S
(
E
0
)
k
T
e
3
E
0
k
T
{\displaystyle {\frac {r}{V}}\approx n_{A}\,n_{B}\,{\frac {4{\sqrt {(}}2/3)}{\sqrt {m_{\text{R}}}}}\,{\sqrt {E_{0}}}{\frac {S(E_{0})}{kT}}\,e^{-{\frac {3E_{0}}{kT}}}}

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Values of S(E0) are typically 103 103 keV·b, but are damped by a huge factor when involving a beta decay, due to the relation between the intermediate bound state (e.g. diproton) half-life and the beta decay half-life, as in the protonproton chain reaction. Note that typical core temperatures in main-sequence stars (the Sun) give kT of the order of 1 keV:
log
10
k
T
=
16
+
log
10
2.17
{\textstyle \log _{10}kT=-16+\log _{10}2.17}
.
Thus, the limiting reaction in the CNO cycle, proton capture by 147N, has S(E0) ~ S(0) = 3.5 keV·b, while the limiting reaction in the protonproton chain reaction, the creation of deuterium from two protons, has a much lower S(E0) ~ S(0) = 4×1022 keV·b. Incidentally, since the former reaction has a much higher Gamow factor, and due to the relative abundance of elements in typical stars, the two reaction rates are equal at a temperature value that is within the core temperature ranges of main-sequence stars.
== References ==
=== Notes ===
=== Citations ===
== Further reading ==
Bethe, H. A. (January 1939). "Energy Production in Stars". Physical Review. 55 (1): 541547. Bibcode:1939PhRv...55..103B. doi:10.1103/PhysRev.55.103.
Bethe, H. A. (March 1939). "Energy Production in Stars". Physical Review. 55 (5): 434456. Bibcode:1939PhRv...55..434B. doi:10.1103/PhysRev.55.434.
Clayton, Donald D. (1968). Principles of Stellar Evolution and Nucleosynthesis. New York: McGraw-Hill. Bibcode:1968psen.book.....C. LCCN 68-012263. OCLC 299102. A clear physical description of the protonproton chain and of the CNO cycle.
Clayton, Donald D. (2003). Handbook of Isotopes in the Cosmos: Hydrogen to Gallium. Cambridge: Cambridge University Press. ISBN 978-0-521-82381-4. OCLC 249420462.
Hoyle, F. (1954). "On Nuclear Reactions Occurring in Very Hot Stars: Synthesis of Elements from Carbon to Nickel". Astrophysical Journal Supplement. 1: 121146. Bibcode:1954ApJS....1..121H. doi:10.1086/190005.
Iliadis, Christian (2015). Nuclear Physics of Stars (2nd ed.). Weinheim, Germany: Wiley-VCH. Bibcode:2015nps..book.....I. doi:10.1002/9783527692668. ISBN 9783527692668. OCLC 933608179.
Ray, A. (2004). "Stars as Thermonuclear Reactors: Their Fuels and Ashes". arXiv:astro-ph/0405568.
Wallerstein, G.; I. Iben, Jr.; P. Parker; A. M. Boesgaard; G. M. Hale; A. E. Champagne; et al. (1997). "Synthesis of the Elements in Stars: Forty Years of Progress" (PDF). Reviews of Modern Physics. 69 (4): 9951084. Bibcode:1997RvMP...69..995W. doi:10.1103/RevModPhys.69.995. hdl:2152/61093. Archived from the original (PDF) on 2009-03-26. Retrieved 2006-08-04.
Woosley, S. E.; A. Heger; T. A. Weaver (OctoberDecember 2002). "The Evolution and Explosion of Massive Stars" (PDF). Reviews of Modern Physics. 74 (4): 10151071. Bibcode:2002RvMP...74.1015W. doi:10.1103/RevModPhys.74.1015. S2CID 55932331.
== External links ==
"How the Sun Shines", by John N. Bahcall (Nobel Prize site, accessed 6 January 2020)
Nucleosynthesis in NASA's Cosmicopia. Archived on 1999-01-29.

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Stellar vampirism is an astronomical phenomenon in which a star (usually O-type), known as a "vampire star," in a binary system attracts the mass of another. As stars age in binary systems, they can grow past the threshold at which their gravity protects them from their companion. The process of stellar vampirism results in the "vampire star" having an extended life. The "victim" star is left with its core exposed, which mimics the appearance of a much younger star. An example of a star system exhibiting stellar vampirism is HR 6819.
== See also ==
Interacting binary star
== References ==
== External links ==
Media related to Stellar vampirism at Wikimedia Commons

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A supermassive black hole (SMBH or sometimes SBH) is the largest type of black hole, with its mass being on the order of hundreds of thousands, or millions to billions, of times the mass of the Sun (M☉). Black holes are a class of astronomical objects that have undergone gravitational collapse, leaving behind spheroidal regions of space that nothing, not even light, can escape. Observational evidence indicates that almost every large galaxy has a supermassive black hole at its center. For example, the Milky Way galaxy has a supermassive black hole at its center, corresponding to the radio source Sagittarius A*. Accretion of interstellar gas onto supermassive black holes is the process responsible for powering active galactic nuclei (AGNs) and quasars.
Two supermassive black holes have been directly imaged by the Event Horizon Telescope; these are Sagittarius A, at the center of the Milky Way, and the black hole at the center of Messier 87, a giant elliptical galaxy.
== Description ==
Supermassive black holes are classically defined as black holes with a mass above 100,000 (105) solar masses (M☉); some have masses of several billion M☉. Supermassive black holes have physical properties that clearly distinguish them from lower-mass classifications. First, the tidal forces near the event horizon are significantly weaker for supermassive black holes. The tidal force on a body at a black hole's event horizon is inversely proportional to the square of the black hole's mass: a person at the event horizon of a 10 million M☉ black hole experiences about the same tidal force between their head and feet as a person on the surface of the Earth. Unlike with stellar-mass black holes, one would not experience significant tidal force until very deep into the black hole's event horizon.
It is somewhat counterintuitive that the density of an SMBH (defined as the mass of the black hole divided by the volume within its Schwarzschild radius) can be less than the density of water. This is because the Schwarzschild radius (
r
s
{\displaystyle r_{\text{s}}}
) is directly proportional to its mass. Since the volume of a spherical object (such as the event horizon of a non-rotating black hole) is directly proportional to the cube of the radius, the density of a black hole is inversely proportional to the square of the mass, and thus higher mass black holes have a lower average density.
The Schwarzschild radius of the event horizon of a nonrotating and uncharged supermassive black hole of around 1 billion M☉ is comparable to the semi-major axis of the orbit of Uranus, or about 19 AU. Some astronomers refer to black holes of greater than 5 billion M☉ as ultramassive black holes (UMBHs or UBHs), but the term is not broadly used. Possible examples include the black holes at the cores of TON 618, NGC 6166, ESO 444-46 and NGC 4889, which are among the most massive black holes known.
Some studies have suggested that the maximum natural mass that a black hole can reach, while being luminous accretors (featuring an accretion disk), is typically on the order of about 50 billion M☉. However, a 2020 study suggested even larger black holes, dubbed stupendously large black holes (SLABs), with masses greater than 100 billion M☉, could exist based on used models; some studies place the black hole at the core of Phoenix A in this category.

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== History of research ==
The story of how supermassive black holes were found began with the investigation by Maarten Schmidt of the radio source 3C 273 in 1963. Initially this was thought to be a star, but the spectrum proved puzzling. It was determined to be hydrogen emission lines that had been redshifted, indicating the object was moving away from the Earth. Hubble's law showed that the object was located several billion light-years away, and thus must be emitting the energy equivalent of hundreds of galaxies. The rate of light variations of the source dubbed a quasi-stellar object, or quasar, suggested the emitting region had a diameter of one parsec or less. Four such sources had been identified by 1964.
In 1963, Fred Hoyle and W. A. Fowler proposed the existence of hydrogen-burning supermassive stars (SMS) as an explanation for the compact dimensions and high energy output of quasars. These would have a mass of about 105109 M☉. However, Richard Feynman noted stars above a certain critical mass are dynamically unstable and would collapse into a black hole, at least if they were non-rotating. Fowler then proposed that these supermassive stars would undergo a series of collapse and explosion oscillations, thereby explaining the energy output pattern. Appenzeller and Fricke (1972) built models of this behavior, but found that the resulting star would still undergo collapse, concluding that a non-rotating 0.75×106 M☉ SMS "cannot escape collapse to a black hole by burning its hydrogen through the CNO cycle".
Edwin E. Salpeter and Yakov Zeldovich made the proposal in 1964 that matter falling onto a massive compact object would explain the properties of quasars. It would require a mass of around 108 M☉ to match the output of these objects. Donald Lynden-Bell noted in 1969 that the infalling gas would form a flat disk that spirals into the central "Schwarzschild throat". He noted that the relatively low output of nearby galactic cores implied these were old, inactive quasars. Meanwhile, in 1967, Martin Ryle and Malcolm Longair suggested that nearly all sources of extra-galactic radio emission could be explained by a model in which particles are ejected from galaxies at relativistic velocities, meaning they are moving near the speed of light. Martin Ryle, Malcolm Longair, and Peter Scheuer then proposed in 1973 that the compact central nucleus could be the original energy source for these relativistic jets.
Arthur M. Wolfe and Geoffrey Burbidge noted in 1970 that the large velocity dispersion of the stars in the nuclear region of elliptical galaxies could only be explained by a large mass concentration at the nucleus; larger than could be explained by ordinary stars. They showed that the behavior could be explained by a massive black hole with up to 1010 M☉, or a large number of smaller black holes with masses below 103 M☉. Dynamical evidence for a massive dark object was found at the core of the active elliptical galaxy Messier 87 in 1978, initially estimated at 5×109 M☉. Discovery of similar behavior in other galaxies soon followed, including the Andromeda Galaxy in 1984 and the Sombrero Galaxy in 1988.
Donald Lynden-Bell and Martin Rees hypothesized in 1971 that the center of the Milky Way galaxy would contain a massive black hole. Sagittarius A* was discovered and named on February 13 and 15, 1974, by astronomers Bruce Balick and Robert Brown using the Green Bank Interferometer of the National Radio Astronomy Observatory. They discovered a radio source that emits synchrotron radiation; it was found to be dense and immobile because of its gravitation. This was, therefore, the first indication that a supermassive black hole exists in the center of the Milky Way.
The Hubble Space Telescope, launched in 1990, provided the resolution needed to perform more refined observations of galactic nuclei. In 1994 the Faint Object Spectrograph on the Hubble was used to observe Messier 87, finding that ionized gas was orbiting the central part of the nucleus at a velocity of ±500 km/s. The data indicated a concentrated mass of (2.4±0.7)×109 M☉ lay within a 0.25″ span, providing strong evidence of a supermassive black hole.
Using the Very Long Baseline Array to observe Messier 106, Miyoshi et al. (1995) were able to demonstrate that the emission from an H2O maser in this galaxy came from a gaseous disk in the nucleus that orbited a concentrated mass of 3.6×107 M☉, which was constrained to a radius of 0.13 parsecs. Their ground-breaking research noted that a swarm of solar mass black holes within a radius this small would not survive for long without undergoing collisions, making a supermassive black hole the sole viable candidate. Accompanying this observation which provided the first confirmation of supermassive black holes was the discovery of the highly broadened, ionised iron Kα emission line (6.4 keV) from the galaxy MCG-6-30-15. The broadening was due to the gravitational redshift of the light as it escaped from just 3 to 10 Schwarzschild radii from the black hole.
On April 10, 2019, the Event Horizon Telescope Collaboration released the first horizon-scale image of a black hole, in the center of the galaxy Messier 87. In March 2020, astronomers suggested that additional subrings should form the photon ring, proposing a way of better detecting these signatures in the first black hole image. In 2020, the Nobel Prize in Physics was awarded jointly to Andrea Ghez and Reinhard Genzel "for the discovery of a supermassive compact object at the centre of our galaxy". This was considered the first definitive confirmation that Sagittarius A* is indeed a supermassive black hole.
== Formation ==

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The origin of supermassive black holes remains an active field of research. Astrophysicists agree that black holes can grow by accretion of matter and by merging with other black holes. There are several hypotheses for the formation mechanisms and initial masses of the progenitors, or "seeds", of supermassive black holes. Independently of the specific formation channel for the black hole seed, given sufficient mass nearby, it could accrete to become an intermediate-mass black hole and possibly a SMBH if the accretion rate persists.
Distant and early supermassive black holes, such as J03131806, and ULAS J1342+0928, are hard to explain so soon after the Big Bang. Some postulate they might come from direct collapse of dark matter with self-interaction.
=== First stars ===
The early progenitor seeds may be black holes of tens or perhaps hundreds of M☉ that are left behind by the explosions of massive stars and grow by accretion of matter. Another model involves a dense stellar cluster undergoing core collapse as the negative heat capacity of the system drives the velocity dispersion in the core to relativistic speeds.
Before the first stars, large gas clouds could collapse into a "quasi-star", which would in turn collapse into a black hole of around 20 M☉. These stars may have also been formed by dark matter halos drawing in enormous amounts of gas by gravity, which would then produce supermassive stars with tens of thousands of M☉. The "quasi-star" becomes unstable to radial perturbations because of electron-positron pair production in its core and could collapse directly into a black hole without a supernova explosion (which would eject most of its mass, preventing the black hole from growing as fast). A 2018 theory proposes that SMBH seeds were formed in the very early universe each from the collapse of a supermassive star with mass of around 100,000 M☉.
=== Direct-collapse and primordial black holes ===
Large, high-redshift clouds of metal-free gas, when irradiated by a sufficient intense flux of LymanWerner photons, can avoid cooling and fragmenting, thus collapsing as a single object due to self-gravitation. The core of the collapsing object reaches extremely large values of matter density, of the order of about 107 g/cm3, and triggers a general relativistic instability. Thus, the object collapses directly into a black hole, without passing from the intermediate phase of a star, or of a quasi-star. These objects have a typical mass of about 100,000 M☉ and are named direct collapse black holes.
A 2022 computer simulation showed that the first supermassive black holes can arise in rare turbulent clumps of gas, called primordial halos, that were fed by unusually strong streams of cold gas. The key simulation result was that cold flows suppressed star formation in the turbulent halo until the halo's gravity was finally able to overcome the turbulence and formed two direct-collapse black holes of 31,000 M☉ and 40,000 M☉. The birth of the first SMBHs can therefore be a result of standard cosmological structure formation.
Primordial black holes (PBHs) could have been produced directly from external pressure in the first moments after the Big Bang. These black holes would then have more time than any of the above models to accrete, allowing them sufficient time to reach supermassive sizes. Formation of black holes from the deaths of the first stars has been extensively studied and corroborated by observations. The other models for black hole formation listed above are theoretical.
The formation of a supermassive black hole requires a relatively small volume of highly dense matter having small angular momentum. Normally, the process of accretion involves transporting a large initial endowment of angular momentum outwards, and this appears to be the limiting factor in black hole growth. This is a major component of the theory of accretion disks. Gas accretion is both the most efficient and the most conspicuous way in which black holes grow. The majority of the mass growth of supermassive black holes is thought to occur through episodes of rapid gas accretion, which are observable as active galactic nuclei or quasars.
Observations reveal that quasars were much more frequent when the Universe was younger, indicating that supermassive black holes formed and grew early. A major constraining factor for theories of supermassive black hole formation is the observation of distant luminous quasars, which indicate that supermassive black holes of billions of M☉ had already formed when the Universe was less than one billion years old. This suggests that supermassive black holes arose very early in the Universe, inside the first massive galaxies.

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=== Maximum mass limit ===
There is a natural upper limit to how large supermassive black holes can grow. Supermassive black holes in any quasar or active galactic nucleus (AGN) appear to have a theoretical upper limit of physically around 50 billion M☉ for typical parameters, as anything above this slows growth down to a crawl (the slowdown tends to start around 10 billion M☉) and causes the unstable accretion disk surrounding the black hole to coalesce into stars that orbit it. A study concluded that the radius of the innermost stable circular orbit (ISCO) for SMBH masses above this limit exceeds the self-gravity radius, making disc formation no longer possible.
A larger upper limit of around 270 billion M☉ was represented as the absolute maximum mass limit for an accreting SMBH in extreme cases, for example its maximal prograde spin with a dimensionless spin parameter of a = 1, although the maximum limit for a black hole's spin parameter is very slightly lower at a = 0.9982. At masses just below the limit, the disc luminosity of a field galaxy is likely to be below the Eddington limit and not strong enough to trigger the feedback underlying the Msigma relation, so SMBHs close to the limit can evolve above this.
It has been noted that black holes close to this limit are likely to be rather even rarer, as it would require the accretion disc to be almost permanently prograde because the black hole grows and the spin-down effect of retrograde accretion is larger than the spin-up by prograde accretion, due to its ISCO and therefore its lever arm. This would require the hole spin to be permanently correlated with a fixed direction of the potential controlling gas flow, within the black hole's host galaxy, and thus would tend to produce a spin axis and hence AGN jet direction, which is similarly aligned with the galaxy. Current observations do not support this correlation.
The so-called 'chaotic accretion' presumably has to involve multiple small-scale events, essentially random in time and orientation if it is not controlled by a large-scale potential in this way. This would lead the accretion statistically to spin-down, due to retrograde events having larger lever arms than prograde, and occurring almost as often. There are also other interactions with large SMBHs that trend to reduce their spin, including particularly mergers with other black holes, which can statistically decrease the spin. All of these considerations suggested that SMBHs usually cross the critical theoretical mass limit at modest values of their spin parameters, so that 5×1010 M☉ in all but rare cases.
Although modern UMBHs within quasars and galactic nuclei cannot grow beyond around (527)×1010 M☉ through the accretion disk and as well given the current age of the universe, some of these monster black holes in the universe are predicted to still continue to grow up to stupendously large masses of perhaps 1014 M☉ during the collapse of superclusters of galaxies in the extremely far future of the universe.
== Activity and galactic evolution ==
Gravitation from supermassive black holes in the center of many galaxies is thought to power active objects such as Seyfert galaxies and quasars, and the relationship between the mass of the central black hole and the mass of the host galaxy depends upon the galaxy type. An empirical correlation between the size of supermassive black holes and the stellar velocity dispersion
σ
{\displaystyle \sigma }
of a galaxy bulge is called the Msigma relation.
An AGN is now considered to be a galactic core hosting a massive black hole that is accreting matter and displays a sufficiently strong luminosity. The nuclear region of the Milky Way, for example, lacks sufficient luminosity to satisfy this condition. The unified model of AGN is the concept that the large range of observed properties of the AGN taxonomy can be explained using just a small number of physical parameters. For the initial model, these values consisted of the angle of the accretion disk's torus to the line of sight and the luminosity of the source. AGN can be divided into two main groups: a radiative mode AGN in which most of the output is in the form of electromagnetic radiation through an optically thick accretion disk, and a jet mode in which relativistic jets emerge perpendicular to the disk.
=== Mergers and recoiled SMBHs ===
The interaction of a pair of SMBH-hosting galaxies can lead to merger events. Dynamical friction on the hosted SMBH objects causes them to sink toward the center of the merged mass, eventually forming a pair with a separation of under a kiloparsec. The interaction of this pair with surrounding stars and gas will then gradually bring the SMBH together as a gravitationally bound binary system with a separation of ten parsecs or less. Once the pair draw as close as 0.001 parsecs, gravitational radiation will cause them to merge. By the time this happens, the resulting galaxy will have long since relaxed from the merger event, with the initial starburst activity and AGN having faded away.

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The gravitational waves from this coalescence can give the resulting SMBH a velocity boost of up to several thousand km/s, propelling it away from the galactic center and possibly even ejecting it from the galaxy. This phenomenon is called a gravitational recoil. The other possible way to eject a black hole is the classical slingshot scenario, also called slingshot recoil. In this scenario first a long-lived binary black hole forms through a merger of two galaxies. A third SMBH is introduced in a second merger and sinks into the center of the galaxy. Due to the three-body interaction one of the SMBHs, usually the lightest, is ejected. Due to conservation of linear momentum the other two SMBHs are propelled in the opposite direction as a binary. All SMBHs can be ejected in this scenario. An ejected black hole is called a runaway black hole.
There are different ways to detect recoiling black holes. Often a displacement of a quasar/AGN from the center of a galaxy or a spectroscopic binary nature of a quasar/AGN is seen as evidence for a recoiled black hole.
Candidate recoiling black holes include NGC 3718, SDSS1133, 3C 186, E1821+643 and SDSSJ0927+2943. Candidate runaway black holes are HE04502958, CID-42 and objects around RCP 28. Runaway supermassive black holes may trigger star formation in their wakes. A linear feature near the dwarf galaxy RCP 28 was interpreted as the star-forming wake of a candidate runaway black hole. Later it was however found that this feature is likely a bulge-less edge-on galaxy. A study using JWST spectroscopy did however find more evidence for this object being produced by a runaway black hole.
=== Hawking radiation ===
Hawking radiation is black-body radiation that is predicted to be released by black holes, due to quantum effects near the event horizon. This radiation reduces the mass and energy of black holes, causing them to shrink and ultimately vanish. If black holes evaporate via Hawking radiation, a non-rotating and uncharged stupendously large black hole with a mass of 1×1011 M☉ will evaporate in around 2.1×10100 years. Black holes formed during the predicted collapse of superclusters of galaxies in the far future with 1×1014 M☉ would evaporate over a timescale of up to 2.1×10109 years.
== Evidence ==
=== Doppler measurements ===
Some of the best evidence for the presence of black holes is provided by the Doppler effect whereby light from nearby orbiting matter is red-shifted when receding and blue-shifted when advancing. For matter very close to a black hole the orbital speed must be comparable with the speed of light, so receding matter will appear very faint compared with advancing matter, which means that systems with intrinsically symmetric discs and rings will acquire a highly asymmetric visual appearance. This effect has been allowed for in modern computer-generated images such as the example presented here, based on a plausible model for the supermassive black hole in Sgr A* at the center of the Milky Way. However, the resolution provided by presently available telescope technology is still insufficient to confirm such predictions directly.
What already have been observed directly in many systems are the lower non-relativistic velocities of matter orbiting further out from what are presumed to be black holes. Direct Doppler measures of water masers surrounding the nuclei of nearby galaxies have revealed a very fast Keplerian motion, only possible with a high concentration of matter in the center. Currently, the only known objects that can pack enough matter in such a small space are black holes, or things that will evolve into black holes within astrophysically short timescales. For active galaxies farther away, the width of broad spectral lines can be used to probe the gas orbiting near the event horizon. The technique of reverberation mapping uses variability of these lines to measure the mass and perhaps the spin of the black hole that powers active galaxies.
=== In the Milky Way ===
Evidence indicates that the Milky Way galaxy has a supermassive black hole at its center, 26,000 light-years from the Solar System, in a region called Sagittarius A* because:
The star S2 follows an elliptical orbit with a period of 15.2 years and a pericenter (closest distance) of 17 light-hours (1.8×1013 m or 120 AU) from the center of the central object.
From the motion of star S2, the object's mass can be estimated as 4.0 million M☉, or about 7.96×1036 kg.
The radius of the central object must be less than 17 light-hours, because otherwise S2 would collide with it. Observations of the star S14 indicate that the radius is no more than 6.25 light-hours, about the diameter of Uranus' orbit.
No known astronomical object other than a black hole can contain 4.0 million M☉ in this volume of space.
Infrared observations of bright flare activity near Sagittarius A* show orbital motion of plasma with a period of 45±15 min at a separation of six to ten times the gravitational radius of the candidate SMBH. This emission is consistent with a circularized orbit of a polarized "hot spot" on an accretion disk in a strong magnetic field. The radiating matter is orbiting at 30% of the speed of light just outside the innermost stable circular orbit.
On January 5, 2015, NASA reported observing an X-ray flare 400 times brighter than usual, a record-breaker, from Sagittarius A*. The unusual event may have been caused by the breaking apart of an asteroid falling into the black hole or by the entanglement of magnetic field lines within gas flowing into Sagittarius A*, according to astronomers.
=== Outside the Milky Way ===

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Unambiguous dynamical evidence for supermassive black holes exists only for a handful of galaxies; these include the Milky Way, the Local Group galaxies M31 and M32, and a few galaxies beyond the Local Group, such as NGC 4395. In these galaxies, the root mean square (or rms) velocities of the stars or gas rises proportionally to 1/r near the center, indicating a central point mass. In all other galaxies observed to date, the rms velocities are flat, or even falling, toward the center, making it impossible to state with certainty that a supermassive black hole is present.
Nevertheless, it is commonly accepted that the center of nearly every galaxy contains a supermassive black hole. The reason for this assumption is the Msigma relation, a tight (low scatter) relation between the mass of the hole in the 10 or so galaxies with secure detections, and the velocity dispersion of the stars in the bulges of those galaxies. This correlation, although based on just a handful of galaxies, suggests to many astronomers a strong connection between the formation of the black hole and the galaxy itself.
On March 28, 2011, a supermassive black hole was seen tearing a mid-size star apart. That is the only likely explanation of the observations that day of sudden X-ray radiation and the follow-up broad-band observations. The source was previously an inactive galactic nucleus, and from study of the outburst the galactic nucleus is estimated to be a SMBH with mass of the order of a million M☉. This rare event is assumed to be a relativistic outflow (material being emitted in a jet at a significant fraction of the speed of light) from a star tidally disrupted by the SMBH. A significant fraction of a solar mass of material is expected to have accreted onto the SMBH. Subsequent long-term observation will allow this assumption to be confirmed if the emission from the jet decays at the expected rate for mass accretion onto a SMBH.
== Individual studies ==
The nearby Andromeda Galaxy, 2.5 million light-years away, contains a 1.4+0.650.45×108 (140 million) M☉ central black hole, significantly larger than the Milky Way's. The largest supermassive black hole in the Milky Way's vicinity appears to be that of Messier 87 (i.e., M87*), at a mass of (6.5±0.7)×109 (c. 6.5 billion) M☉ at a distance of 48.92 million light-years. The supergiant elliptical galaxy NGC 4889, at a distance of 336 million light-years away in the Coma Berenices constellation, contains a black hole measured to be 2.1+3.51.3×1010 (21 billion) M☉.
Masses of black holes in quasars can be estimated via indirect methods that are subject to substantial uncertainty. The quasar TON 618 is an example of an object with an extremely large black hole, estimated at 4.07×1010 (40.7 billion) M☉. Its redshift is 2.219. Other examples of quasars with large estimated black hole masses are the hyperluminous quasar APM 08279+5255, with an estimated mass of 1×1010 (10 billion) M☉, and the quasar SMSS J215728.21-360215.1, with a mass of (3.4±0.6)×1010 (34 billion) M☉, or nearly 10,000 times the mass of the black hole at the Milky Way's Galactic Center.
Some galaxies, such as the galaxy 4C +37.11, appear to have two supermassive black holes at their centers, forming a binary system. If they collided, the event would create strong gravitational waves. Binary supermassive black holes are believed to be a common consequence of galactic mergers. The binary pair in OJ 287, 3.5 billion light-years away, contains the most massive black hole in a pair, with a mass estimated at 18.348 billion M☉. In 2011, a super-massive black hole was discovered in the dwarf galaxy Henize 2-10, which has no bulge. The precise implications for this discovery on black hole formation are unknown, but may indicate that black holes formed before bulges.

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In 2012, astronomers reported an unusually large mass of approximately 17 billion M☉ for the black hole in the compact, lenticular galaxy NGC 1277, which lies 220 million light-years away in the constellation Perseus. The putative black hole has approximately 59 percent of the mass of the bulge of this lenticular galaxy (14 percent of the total stellar mass of the galaxy). Another study reached a very different conclusion: this black hole is not particularly overmassive, estimated at between 2 and 5 billion M☉ with 5 billion M☉ being the most likely value. On February 28, 2013, astronomers reported on the use of the NuSTAR satellite to accurately measure the spin of a supermassive black hole for the first time, in NGC 1365, reporting that the event horizon was spinning at almost the speed of light.
In September 2014, data from different X-ray telescopes have shown that the extremely small, dense, ultracompact dwarf galaxy M60-UCD1 hosts a 20 million solar mass black hole at its center, accounting for more than 10% of the total mass of the galaxy. The discovery is quite surprising, since the black hole is five times more massive than the Milky Way's black hole despite the galaxy being less than five-thousandths the mass of the Milky Way.
Some galaxies lack any supermassive black holes in their centers. Although most galaxies with no supermassive black holes are very small, dwarf galaxies, one discovery remains mysterious: The supergiant elliptical cD galaxy A2261-BCG has not been found to contain an active supermassive black hole of at least 1010 M☉, despite the galaxy being one of the largest galaxies known; over six times the size and one thousand times the mass of the Milky Way. Despite that, several studies gave very large mass values for a possible central black hole inside A2261-BGC, such as about as large as 6.5+10.94.1×1010 M☉ or as low as (611)×109 M☉. Since a supermassive black hole will only be visible while it is accreting, a supermassive black hole can be nearly invisible, except in its effects on stellar orbits. This implies that either A2261-BGC has a central black hole that is accreting at a low level or has a mass rather below 1010 M☉.
In December 2017, astronomers reported the detection of the most distant quasar known by this time, ULAS J1342+0928, containing the most distant supermassive black hole, at a reported redshift of z = 7.54, surpassing the redshift of 7 for the previously known most distant quasar ULAS J1120+0641.
In February 2020, astronomers reported the discovery of the Ophiuchus Supercluster eruption, the most energetic event in the Universe ever detected since the Big Bang. It occurred in the Ophiuchus Cluster in the galaxy NeVe 1, caused by the accretion of nearly 270 million M☉ of material by its central 7 billion M☉ supermassive black hole. The eruption lasted for about 100 million years and released 5.7 million times more energy than the most powerful gamma-ray burst known. The eruption released shock waves and jets of high-energy particles that punched the intracluster medium, creating a cavity about 1.5 million light-years wide ten times the Milky Way's diameter.
In February 2021, astronomers released, for the first time, a very high-resolution image of 25,000 active supermassive black holes, covering four percent of the Northern celestial hemisphere, based on ultra-low radio wavelengths, as detected by the Low-Frequency Array (LOFAR) in Europe.
In August 2025, a SMBH in little red dot CAPERS-LRD-z9 was reported whose canonical mass was estimated to be 3.8+27.83.35×107 (38 million) M☉. This represents a confirmed massive black hole very early in the history of the universe (redshift of 9.288, only 500 million years after the big bang).
== See also ==
== Notes ==
== References ==
== Further reading ==
Fulvio Melia (2003). The Edge of Infinity. Supermassive Black Holes in the Universe. Cambridge University Press. ISBN 978-0-521-81405-8. OL 22546388M.
Carr, Bernard; Kühnel, Florian (2022). "Primordial black holes as dark matter candidates". SciPost Physics Lecture Notes 48. arXiv:2110.02821. doi:10.21468/SciPostPhysLectNotes.48. S2CID 238407875.
Chakraborty, Amlan; Chanda, Prolay K.; Pandey, Kanhaiya Lal; Das, Subinoy (2022). "Formation and Abundance of Late-forming Primordial Black Holes as Dark Matter". The Astrophysical Journal. 932 (2): 119. arXiv:2204.09628. Bibcode:2022ApJ...932..119C. doi:10.3847/1538-4357/ac6ddd. S2CID 248266315.
Ferrarese, Laura & Merritt, David (2002). "Supermassive Black Holes". Physics World. 15 (1): 4146. arXiv:astro-ph/0206222. Bibcode:2002astro.ph..6222F. doi:10.1088/2058-7058/15/6/43. S2CID 5266031.
Krolik, Julian (1999). Active Galactic Nuclei. Princeton University Press. ISBN 978-0-691-01151-6. OL 361705M.
Merritt, David (2013). Dynamics and Evolution of Galactic Nuclei. Princeton University Press. ISBN 978-0-691-12101-7.
Dotan, Calanit; Rossi, Elena M.; Shaviv, Nir J. (2011). "A lower limit on the halo mass to form supermassive black holes". Monthly Notices of the Royal Astronomical Society. 417 (4): 30353046. arXiv:1107.3562. Bibcode:2011MNRAS.417.3035D. doi:10.1111/j.1365-2966.2011.19461.x. S2CID 54854781.
Argüelles, Carlos R.; Díaz, Manuel I.; Krut, Andreas; Yunis, Rafael (2021). "On the formation and stability of fermionic dark matter haloes in a cosmological framework". Monthly Notices of the Royal Astronomical Society. 502 (3): 42274246. arXiv:2012.11709. doi:10.1093/mnras/staa3986.
Fiacconi, Davide; Rossi, Elena M. (2017). "Light or heavy supermassive black hole seeds: The role of internal rotation in the fate of supermassive stars". Monthly Notices of the Royal Astronomical Society. 464 (2): 22592269. arXiv:1604.03936. doi:10.1093/mnras/stw2505.
Davelaar, Jordy; Bronzwaer, Thomas; Kok, Daniel; Younsi, Ziri; Mościbrodzka, Monika; Falcke, Heino (2018). "Observing supermassive black holes in virtual reality". Computational Astrophysics and Cosmology. 5 (1) 1. arXiv:1811.08369. Bibcode:2018ComAC...5....1D. doi:10.1186/s40668-018-0023-7.
== External links ==
Black Holes: Gravity's Relentless Pull Interactive multimedia Web site about the physics and astronomy of black holes from the Space Telescope Science Institute
Images of supermassive black holes
NASA images of supermassive black holes
The black hole at the heart of the Milky Way
ESO video clip of stars orbiting a galactic black hole
Star Orbiting Massive Milky Way Centre Approaches to within 17 Light-Hours ESO, October 21, 2002
Images, Animations, and New Results from the UCLA Galactic Center Group
Washington Post article on Supermassive black holes
Video (2:46) Simulation of stars orbiting Milky Way's central massive black hole
Video (2:13) Simulation reveals supermassive black holes (NASA, October 2, 2018)
From Super to Ultra: Just How Big Can Black Holes Get? Archived June 17, 2019, at the Wayback Machine
September 2020, Paul Sutter 29 (September 29, 2020). "Black holes so big we don't know how they form could be hiding in the universe". Space.com. Retrieved February 6, 2021.{{cite web}}: CS1 maint: numeric names: authors list (link)
"Testing general relativity with a supermassive black hole".
"Wandering Black Holes | Center for Astrophysics".
"Supermassive stars might be born in the chaos around supermassive black holes". May 10, 2021.

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The tidal force or tide-generating force is the difference in gravitational attraction between different points in a gravitational field. It causes different parts of bodies to be pulled unevenly, those bodies as a result being stretched towards the attraction.
It is the differential force of gravity, the net between gravitational forces, the derivative of gravitational potential, the gradient of gravitational fields. Therefore tidal forces are a residual force, a secondary effect of gravity, highlighting its spatial elements, making the closer near-side more attracted than the more distant far-side.
This produces a range of tidal phenomena, such as ocean tides. Earth's tides are mainly produced by the relative close gravitational field of the Moon
and to a lesser extent by the stronger, but further away gravitational field of the Sun. The ocean on the side of Earth facing the Moon is being pulled by the gravity of the Moon away from Earth's crust, while on the other side of Earth there the crust is being pulled away from the ocean, resulting in Earth being stretched, bulging on both sides, and having opposite high-tides. Tidal forces viewed from Earth, that is from a rotating reference frame, appear as centripetal and centrifugal forces, but are not caused by the rotation.
Further tidal phenomena include solid-earth tides, tidal locking, breaking apart of celestial bodies and formation of ring systems within the Roche limit, and in extreme cases, spaghettification of objects. Tidal forces have also been shown to be fundamentally related to gravitational waves.
In celestial mechanics, the expression tidal force can refer to a situation in which a body or material (for example, tidal water) is mainly under the gravitational influence of a second body (for example, the Earth), but is also perturbed by the gravitational effects of a third body (for example, the Moon). The perturbing force is sometimes in such cases called a tidal force (for example, the perturbing force on the Moon): it is the difference between the force exerted by the third body on the second and the force exerted by the third body on the first.
== Explanation ==
When a body (body 1) is acted on by the gravity of another body (body 2), the field can vary significantly on body 1 between the side of the body facing body 2 and the side facing away from body 2. Figure 2 shows the differential force of gravity on a spherical body (body 1) exerted by another body (body 2).
These tidal forces cause strains on both bodies and may distort them or even, in extreme cases, break one or the other apart. The Roche limit is the distance from a planet at which tidal effects would cause an object to disintegrate because the differential force of gravity from the planet overcomes the attraction of the parts of the object for one another. These strains would not occur if the gravitational field were uniform, because a uniform field only causes the entire body to accelerate together in the same direction and at the same rate.
== Size and distance ==
The relationship of an astronomical body's size, to its distance from another body, strongly influences the magnitude of tidal force. The tidal force acting on an astronomical body, such as the Earth, is directly proportional to the diameter of the Earth and inversely proportional to the cube of the distance from another body producing a gravitational attraction, such as the Moon or the Sun. Tidal action on bath tubs, swimming pools, lakes, and other small bodies of water is negligible.
Figure 3 is a graph showing how gravitational force declines with distance. In this graph, the attractive force decreases in proportion to the square of the distance (Y = 1/X2), while the slope (Y = 2/X3) is inversely proportional to the cube of the distance.
The tidal force corresponds to the difference in Y between two points on the graph, with one point on the near side of the body, and the other point on the far side. The tidal force becomes larger, when the two points are either farther apart, or when they are more to the left on the graph, meaning closer to the attracting body.
For example, even though the Sun has a stronger overall gravitational pull on Earth, the Moon creates a larger tidal bulge because the Moon is closer. This difference is due to the way gravity weakens with distance: the Moon's closer proximity creates a steeper decline in its gravitational pull as you move across Earth (compared to the Sun's very gradual decline from its vast distance). This steeper gradient in the Moon's pull results in a larger difference in force between the near and far sides of Earth, which is what creates the bigger tidal bulge.
Gravitational attraction is inversely proportional to the square of the distance from the source. The attraction will be stronger on the side of a body facing the source, and weaker on the side away from the source. The tidal force is proportional to the difference.
=== Sun, Earth, and Moon ===
The Sun is about 20 million times the Moon's mass, and acts on the Earth over a distance about 400 times larger than that of the Moon. Because of the cubic dependence on distance, this results in the solar tidal force on the Earth being about half that of the lunar tidal force.
== Effects ==

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In the case of an infinitesimally small elastic sphere, the effect of a tidal force is to distort the shape of the body without any change in volume. The sphere becomes an ellipsoid with two bulges, pointing towards and away from the other body. Larger objects distort into an ovoid, and are slightly compressed, which is what happens to the Earth's oceans under the action of the Moon. All parts of the Earth are subject to the Moon's gravitational forces, causing the water in the oceans to redistribute, forming bulges on the sides near the Moon and far from the Moon.
When a body rotates while subject to tidal forces, internal friction results in the gradual dissipation of its rotational kinetic energy as heat. In the case for the Earth, and Earth's Moon, the loss of rotational kinetic energy results in a gain of about 2 milliseconds per century. If the body is close enough to its primary, this can result in a rotation which is tidally locked to the orbital motion, as in the case of the Earth's moon. Tidal heating produces dramatic volcanic effects on Jupiter's moon Io. Stresses caused by tidal forces also cause a regular monthly pattern of moonquakes on Earth's Moon.
Tidal forces contribute to ocean currents, which moderate global temperatures by transporting heat energy toward the poles. It has been suggested that variations in tidal forces correlate with cool periods in the global temperature record at 6- to 10-year intervals, and that harmonic beat variations in tidal forcing may contribute to millennial climate changes. No strong link to millennial climate changes has been found to date.
Tidal effects become particularly pronounced near small bodies of high mass, such as neutron stars or black holes, where they are responsible for the "spaghettification" of infalling matter. Tidal forces create the oceanic tide of Earth's oceans, where the attracting bodies are the Moon and, to a lesser extent, the Sun. Tidal forces are also responsible for tidal locking, tidal acceleration, and tidal heating. Tides may also induce seismicity.
By generating conducting fluids within the interior of the Earth, tidal forces also affect the Earth's magnetic field.
== Formulation ==
For a given (externally generated) gravitational field, the tidal acceleration at a point with respect to a body is obtained by vector subtraction of the gravitational acceleration at the center of the body (due to the given externally generated field) from the gravitational acceleration (due to the same field) at the given point. Correspondingly, the term tidal force is used to describe the forces due to tidal acceleration. Note that for these purposes the only gravitational field considered is the external one; the gravitational field of the body (as shown in the graphic) is not relevant. (In other words, the comparison is with the conditions at the given point as they would be if there were no externally generated field acting unequally at the given point and at the center of the reference body. The externally generated field is usually that produced by a perturbing third body, often the Sun or the Moon in the frequent example-cases of points on or above the Earth's surface in a geocentric reference frame.)
Tidal acceleration does not require rotation or orbiting bodies; for example, the body may be freefalling in a straight line under the influence of a gravitational field while still being influenced by (changing) tidal acceleration.
By Newton's law of universal gravitation and laws of motion, a body of mass m at distance R from the center of a sphere of mass M feels a force
F
g
{\textstyle {\vec {F}}_{g}}
,
F
g
=
r
^
G
M
m
R
2
{\displaystyle {\vec {F}}_{g}=-{\hat {r}}~G~{\frac {Mm}{R^{2}}}}
equivalent to an acceleration
a
g
{\textstyle {\vec {a}}_{g}}
,
a
g
=
r
^
G
M
R
2
{\displaystyle {\vec {a}}_{g}=-{\hat {r}}~G~{\frac {M}{R^{2}}}}
where
r
^
{\textstyle {\hat {r}}}
is a unit vector pointing from the body M to the body m (here, acceleration from m towards M has negative sign).
Consider now the acceleration due to the sphere of mass M experienced by a particle in the vicinity of the body of mass m. With R as the distance from the center of M to the center of m, let ∆r be the (relatively small) distance of the particle from the center of the body of mass m. For simplicity, distances are first considered only in the direction pointing towards or away from the sphere of mass M. If the body of mass m is itself a sphere of radius ∆r, then the new particle considered may be located on its surface, at a distance (R ± ∆r) from the centre of the sphere of mass M, and ∆r may be taken as positive where the particle's distance from M is greater than R. Leaving aside whatever gravitational acceleration may be experienced by the particle towards m on account of m's own mass, we have the acceleration on the particle due to gravitational force towards M as:
a
g
=
r
^
G
M
(
R
±
Δ
r
)
2
{\displaystyle {\vec {a}}_{g}=-{\hat {r}}~G~{\frac {M}{(R\pm \Delta r)^{2}}}}
Pulling out the R2 term from the denominator gives:
a
g
=
r
^
G
M
R
2
1
(
1
±
Δ
r
R
)
2
{\displaystyle {\vec {a}}_{g}=-{\hat {r}}~G~{\frac {M}{R^{2}}}~{\frac {1}{\left(1\pm {\frac {\Delta r}{R}}\right)^{2}}}}
The Maclaurin series of
1
/
(
1
±
x
)
2
{\textstyle 1/(1\pm x)^{2}}
is
1
2
x
+
3
x
2
{\textstyle 1\mp 2x+3x^{2}\mp \cdots }
which gives a series expansion of:
a
g
=
r
^
G
M
R
2
±
r
^
G
2
M
R
2
Δ
r
R
+
{\displaystyle {\vec {a}}_{g}=-{\hat {r}}~G~{\frac {M}{R^{2}}}\pm {\hat {r}}~G~{\frac {2M}{R^{2}}}~{\frac {\Delta r}{R}}+\cdots }

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The first term is the gravitational acceleration due to M at the center of the reference body
m
{\textstyle m}
, i.e., at the point where
Δ
r
{\textstyle \Delta r}
is zero. This term does not affect the observed acceleration of particles on the surface of m because with respect to M, m (and everything on its surface) is in free fall. When the force on the far particle is subtracted from the force on the near particle, this first term cancels, as do all other even-order terms. The remaining (residual) terms represent the difference mentioned above and are tidal force (acceleration) terms. When ∆r is small compared to R, the terms after the first residual term are very small and can be neglected, giving the approximate tidal acceleration
a
t
,
axial
{\textstyle {\vec {a}}_{t,{\text{axial}}}}
for the distances ∆r considered, along the axis joining the centers of m and M:
a
t
,
axial
±
r
^
2
Δ
r
G
M
R
3
{\displaystyle {\vec {a}}_{t,{\text{axial}}}\approx \pm {\hat {r}}~2\Delta r~G~{\frac {M}{R^{3}}}}
When calculated in this way for the case where ∆r is a distance along the axis joining the centers of m and M,
a
t
{\textstyle {\vec {a}}_{t}}
is directed outwards from to the center of m (where ∆r is zero).
Tidal accelerations can also be calculated away from the axis connecting the bodies m and M, requiring a vector calculation. In the plane perpendicular to that axis, the tidal acceleration is directed inwards (towards the center where ∆r is zero), and its magnitude is
1
2
|
a
t
,
axial
|
{\textstyle {\frac {1}{2}}\left|{\vec {a}}_{t,{\text{axial}}}\right|}
in linear approximation as in Figure 2.
The tidal accelerations at the surfaces of planets in the Solar System are generally very small. For example, the lunar tidal acceleration at the Earth's surface along the MoonEarth axis is about 1.1×107 g, while the solar tidal acceleration at the Earth's surface along the SunEarth axis is about 0.52×107 g, where g is the gravitational acceleration at the Earth's surface. Hence the tide-raising force (acceleration) due to the Sun is about 45% of that due to the Moon. The solar tidal acceleration at the Earth's surface was first given by Newton in the Principia.
== See also ==
Amphidromic point
Disrupted planet
Galactic tide
Tidal resonance
Tidal stripping
Tidal tensor
Spacetime curvature
== References ==
== External links ==
Analysis and Prediction of Tides: GeoTide
Gravitational Tides by J. Christopher Mihos of Case Western Reserve University
Audio: Cain/Gay Astronomy Cast Tidal Forces July 2007.
Gray, Meghan; Merrifield, Michael. "Tidal Forces". Sixty Symbols. Brady Haran for the University of Nottingham.
Pau Amaro Seoane. "Stellar collisions: Tidal disruption of a star by a massive black hole". Retrieved 2018-12-28.
Myths about Gravity and Tides by Mikolaj Sawicki of John A. Logan College and the University of Colorado.
Tidal Misconceptions by Donald E. Simanek
Tides and centrifugal force by Paolo Sirtoli

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The universe comprises all of existence: all forms of matter and energy, and the structures they form, from sub-atomic particles to entire galactic filaments. Since the early 20th century, the field of cosmology establishes that space and time emerged together at the Big Bang 13.787±0.020 billion years ago and that the universe has been expanding since then. The observable portion of the universe is approximately 93 billion light-years in diameter at present. The total size of the universe is not known.
Some of the earliest cosmological models of the universe were geocentric, placing Earth at the center. During the Scientific Revolution, astronomical observations led to a heliocentric model. Further observational improvements led to the realization that the Sun is one of a few hundred billion stars in the Milky Way, which is one of a few hundred billion galaxies in the observable universe. At the largest scale, galaxies are distributed uniformly and the same in all directions. At smaller scales, galaxies are distributed in clusters and superclusters, which form immense filaments and voids in space, creating a vast foam-like structure. Discoveries in the early 20th century, including general relativity, led to the modern view of an expanding, isotropic, homogeneous universe. Evidence accumulated supporting the Big Bang theory: an initial hot fireball cooled and becoming less dense as the universe expanded, allowing the first subatomic particles and simple atoms to form. Giant clouds of hydrogen and helium were gradually drawn to the places where matter was most dense, forming the first galaxies, stars, and eventually, everything else.
From studying the effects of gravity on both matter and light, it has been discovered that the universe contains much more matter than is accounted for by visible objects; stars, galaxies, nebulae and interstellar gas. This unseen matter is known as dark matter. In the widely accepted ΛCDM cosmological model, dark matter accounts for about 25.8%±1.1% of the mass and energy in the universe while about 69.2%±1.2% is dark energy, a mysterious form of energy responsible for the acceleration of the expansion of the universe. Ordinary ('baryonic') matter therefore composes only 4.84%±0.1% of the universe. Stars, planets, and visible gas clouds only form about 6% of this ordinary matter.
There are many competing hypotheses about the ultimate fate of the universe and about what, if anything, preceded the Big Bang.
== Definition ==
The physical universe has been defined as "The totality of all space and time; all that is, has been, and will be." The universe contains all energy and matter, including therefore planets, moons, stars, galaxies, and the contents of intergalactic space.
Some philosophers and scientists support the inclusion of ideas and abstract concepts—such as mathematics and logic—in the definition of the universe. The word universe may also refer to concepts such as the cosmos, the world, and nature.
== Etymology ==
The word universe derives from the Old French word univers, which in turn derives from the Latin word universus, meaning 'combined into one'. The Latin word 'universum' was used by Cicero and later Latin authors in many of the same senses as the modern English word is used.
=== Synonyms ===
A term for universe among the ancient Greek philosophers from Pythagoras onwards was τὸ πᾶν (tò pân) 'the all', defined as all matter and all space, and τὸ ὅλον (tò hólon) 'all things', which did not necessarily include the void. Another synonym was ὁ κόσμος (ho kósmos) meaning 'the world, the cosmos'. Synonyms are also found in Latin authors (totum, mundus, natura) and survive in modern languages, e.g., the German words Das All, Weltall, and Natur for universe. The same synonyms are found in English, such as everything (as in the theory of everything), the cosmos (as in cosmology), the world (as in the many-worlds interpretation), and nature (as in natural laws or natural philosophy).
== Chronology and the Big Bang ==
The prevailing model for the evolution of the universe is the Big Bang theory. In the Big Bang model, the earliest state of the universe was an extremely hot and dense but the universe cooled during subsequent expansion. The model is based on general relativity and on symmetry assumptions such as the homogeneity and isotropy of space. A version of the model with a cosmological constant (Lambda) and cold dark matter, known as the Lambda-CDM model, provides an excellent account of most observations of the universe.

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Much of very earliest time is not understood. An intense period of expansion called cosmic inflation is postulated to explain many astronomical observations and set the initial conditions for the Lambda-CDM model.
Within the first fraction of a second of the universe's existence, it was extremely dense, and the high energy meant all the particles of the Standard model were in equilibrium. As the universe cooled due to expansion, the state of the universe went through phase transitions analogous to water freezing. Various types of elementary particles associated stably producing a plasma of electrons, protons, and neutrons, with very energetic photons preventing them from binding until about one minute after the Big Bang.
During the next few minutes, some protons and neutrons combined to form atomic nuclei through nuclear fusion. This process, known as Big Bang nucleosynthesis, lasted for about 15 minutes, produced helium, with small amounts of deuterium (a form of hydrogen) and traces of lithium. No other nuclei formed in significant amounts during this time. All of the neutrons that did not fuse decayed in to protons and electrons.
After nucleosynthesis ended, the universe was still far too hot for matter to form neutral atoms, so it contained a hot, dense, optically opaque plasma of negatively charged electrons, neutral neutrinos and positive nuclei. After about 377,000 years, the universe had cooled enough that electrons and nuclei could form the first stable atoms. This is known as recombination for historical reasons; electrons and nuclei were combining for the first time. Unlike plasma, neutral atoms are transparent to many wavelengths of light, so for the first time, the universe also became transparent. The photons released ("decoupled") when these atoms formed can still be seen today; they form the cosmic microwave background (CMB).
As the universe expanded, the energy density of electromagnetic radiation decreased more quickly than that of matter because the energy of each photon decreased as it is cosmologically redshifted. At around 47,000 years, the energy density of matter became larger than that of photons and neutrinos, and began to dominate the large scale behavior of the universe. This marked the end of the radiation-dominated era and the start of the matter-dominated era.
In the earliest stages of the universe, tiny fluctuations within the universe's density led to concentrations of dark matter gradually forming. Ordinary matter, attracted to these by gravity, formed large gas clouds and eventually, stars and galaxies, where the dark matter was most dense, and voids where it was least dense. After around 100300 million years, the first stars formed, known as Population III stars. These were probably very massive, luminous, non metallic and short-lived. They were responsible for the gradual reionization of the universe between about 200500 million years and 1 billion years, and also for seeding the universe with elements heavier than helium, through stellar nucleosynthesis.
The universe contains a mysterious energy—possibly a scalar field—called dark energy, the density of which does not change over time. After about 9.8 billion years, the universe had expanded sufficiently so that the density of matter was less than the density of dark energy, marking the beginning of the present dark-energy-dominated era. In this era, the expansion of the universe is accelerating due to dark energy.
== Physical properties ==
Of the four fundamental interactions, gravitation is the dominant at astronomical length scales. Gravity's effects are cumulative; by contrast, the effects of positive and negative charges tend to cancel one another, making electromagnetism relatively insignificant on astronomical length scales. The remaining two interactions, the weak and strong nuclear forces, decline very rapidly with distance; their effects are confined mainly to sub-atomic length scales.
=== Size and regions ===
Due to the finite speed of light, there is a limit (known as the particle horizon) to how far light can travel over the age of the universe.
The spatial region from which we can receive light is called the observable universe. The proper distance (measured at a fixed time) between Earth and the edge of the observable universe is 46 billion light-years (14 billion parsecs), making the diameter of the observable universe about 93 billion light-years (28 billion parsecs). Although the distance traveled by light from the edge of the observable universe is close to the age of the universe times the speed of light, 13.8 billion light-years (4.2×10^9 pc), the proper distance is larger because the edge of the observable universe and the Earth have since moved further apart.
For comparison, the Milky Way is roughly 87,400 light-years in diameter, and the nearest sister galaxy to the Milky Way, the Andromeda Galaxy, is located roughly 2.5 million light-years away.
Because humans cannot observe space beyond the edge of the observable universe, it is unknown whether the size of the universe in its totality is finite or infinite.
=== Age and expansion ===

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Assuming that the Lambda-CDM model is correct, the measurements of the parameters using a variety of techniques by numerous experiments yield a best value of the age of the universe at 13.799 ± 0.021 billion years, as of 2015.
Over time, the universe and its contents have evolved. For example, the relative population of quasars and galaxies has changed and the universe has expanded. This expansion is inferred from the observation that the light from distant galaxies has been redshifted, which implies that the galaxies are receding from us. Analyses of Type Ia supernovae indicate that the expansion is accelerating.
The more matter there is in the universe, the stronger the mutual gravitational pull of the matter. If the universe were too dense then it would re-collapse into a black hole. However, if the universe contained too little matter then it would expand too quickly for astronomical structures, like galaxies or planets, to form. Since the Big Bang, the universe has expanded monotonically. The massenergy density of the universe, equivalent to about 5 protons per cubic meter, allowed it to expand for the last 13.8 billion years, giving time to form the universe as observed today.
There are dynamical forces acting on the particles in the universe which affect the expansion rate. Before 1998, it was expected that the expansion rate would be decreasing as time went on due to the influence of gravitational interactions in the universe; and thus there is an additional observable quantity in the universe called the deceleration parameter, which most cosmologists expected to be positive and related to the matter density of the universe. In 1998, the deceleration parameter was measured by two different groups to be negative, approximately 0.55, which technically implies that the second derivative of the cosmic scale factor
a
¨
{\displaystyle {\ddot {a}}}
has been positive in the last 56 billion years.
=== Spacetime ===
Modern physics regards events as being organized into spacetime. This idea originated with the special theory of relativity, which predicts that if one observer sees two events happening in different places at the same time, a second observer who is moving relative to the first will see those events happening at different times. The two observers will disagree on the time
T
{\displaystyle T}
between the events, and they will disagree about the distance
D
{\displaystyle D}
separating the events, but they will agree on the speed of light
c
{\displaystyle c}
, and they will measure the same value for the combination
c
2
T
2
D
2
{\displaystyle c^{2}T^{2}-D^{2}}
. The square root of the absolute value of this quantity is called the interval between the two events. The interval expresses how widely separated events are, not just in space or in time, but in the combined setting of spacetime.
The special theory of relativity describes a flat spacetime. Its successor, the general theory of relativity, explains gravity as curvature of spacetime arising due to its energy content. A curved path like an orbit is not the result of a force deflecting a body from an ideal straight-line path, but rather the body's attempt to fall freely through a background that is itself curved by the presence of other masses. A remark by John Archibald Wheeler that has become proverbial among physicists summarizes the theory: "Spacetime tells matter how to move; matter tells spacetime how to curve", and therefore there is no point in considering one without the other. The Newtonian theory of gravity is a good approximation to the predictions of general relativity when gravitational effects are weak and objects are moving slowly compared to the speed of light.
The relation between matter distribution and spacetime curvature is given by the Einstein field equations, which require tensor calculus to express. The universe appears to be a smooth spacetime continuum consisting of three spatial dimensions and one temporal (time) dimension. Therefore, an event in the spacetime of the physical universe can be identified by a set of four coordinates: (x, y, z, t).
=== Shape ===
Cosmologists often work with space-like slices of spacetime that are surfaces of constant time in comoving coordinates. The geometry of these spatial slices is set by the density parameter, Omega (Ω), defined as the average matter density of the universe divided by a critical value. This selects one of three possible geometries depending on whether Ω is equal to, less than, or greater than 1. These are called, respectively, the flat, open and closed universes.
Observations, including the Cosmic Background Explorer (COBE), Wilkinson Microwave Anisotropy Probe (WMAP), and Planck maps of the CMB, suggest that the universe is infinite in extent with a finite age, as described by the FriedmannLemaîtreRobertsonWalker (FLRW) models. These FLRW models thus support inflationary models and the standard model of cosmology, describing a flat, homogeneous universe presently dominated by dark matter and dark energy.
=== Support of life ===
The fine-tuned universe hypothesis is the proposition that the conditions that allow the existence of observable life in the universe can only occur when certain universal fundamental physical constants lie within a very narrow range of values. According to this hypothesis, if any of several fundamental constants were only slightly different, the universe would have been unlikely to be conducive to the establishment and development of matter, astronomical structures, elemental diversity, or life as it is understood. Whether this is true, and whether that question is even logically meaningful to ask, are subjects of much debate. The proposition is discussed among philosophers, scientists, theologians, and proponents of creationism.
== Composition ==

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The massenergy density of the universe is 68% dark energy, 27% dark matter, and 5% ordinary matter. Other contents are neutrinos (less than 0.3%) and electromagnetic radiation (about 0.005%).
The universe has 10 billion times more matter than antimatter. In the very early universe matter and antimatter annihilated each other leaving a high density of photons. In the Standard Model of particle physics, equal amounts antimatter and matter should have been created. The cause of this observed baryon asymmetry is not known.
The distribution of matter throughout the universe is highly variable. The average density is about 1 proton per 200 litres. Vast volumes of the universe are voids of exceptionally low density. The interstellar medium far from stars but within a galaxy has density of a few protons per litre.
The proportions of all types of matter and energy have changed over the history of the universe. The total amount of electromagnetic radiation generated within the universe has decreased by 1/2 in the past 2 billion years. Today, ordinary matter, which includes atoms, stars, galaxies, and life, accounts for only 4.9% of the contents of the universe. The present overall density of this type of matter is very low, roughly 4.5 × 1031 grams per cubic centimeter, corresponding to a density of the order of only one proton for every four cubic meters of volume. The nature of both dark energy and dark matter is unknown. Dark matter, a mysterious form of matter that has not yet been identified, accounts for 26.8% of the cosmic contents. Dark energy, which is the energy of empty space and is causing the expansion of the universe to accelerate, accounts for the remaining 68.3% of the contents.
Matter, dark matter, and dark energy are distributed homogeneously throughout the universe over length scales longer than 300 million light-years (ly) or so. However, over shorter length-scales, matter tends to clump hierarchically; many atoms are condensed into stars, most stars into galaxies, most galaxies into clusters, superclusters and, finally, large-scale galactic filaments. The observable universe contains as many as an estimated 2 trillion galaxies and, overall, as many as an estimated 1024 stars more stars (and earth-like planets) than all the grains of beach sand on planet Earth; but less than the total number of atoms estimated in the universe as 1082; and the estimated total number of stars in an inflationary universe (observed and unobserved), as 10100. Typical galaxies range from dwarfs with as few as ten million (107) stars up to giants with one trillion (1012) stars. Between the larger structures are voids, which are typically 10150 Mpc (33 million490 million ly) in diameter. The Milky Way is in the Local Group of galaxies, which in turn is in the Laniakea Supercluster. This supercluster spans over 500 million light-years, while the Local Group spans over 10 million light-years. The universe also has vast regions of relative emptiness; the largest known void measures 1.8 billion ly (550 Mpc) across.
The observable universe is isotropic on scales significantly larger than superclusters, meaning that the statistical properties of the universe are the same in all directions as observed from Earth. The universe is bathed in highly isotropic microwave radiation that corresponds to a thermal equilibrium blackbody spectrum of roughly 2.72548 kelvins. The hypothesis that the large-scale universe is homogeneous and isotropic is known as the cosmological principle. A universe that is both homogeneous and isotropic looks the same from all vantage points and has no center.
=== Dark energy ===
An explanation for why the expansion of the universe is accelerating remains elusive. It is often attributed to the gravitational influence of "dark energy", an unknown form of energy that is hypothesized to permeate space. On a massenergy equivalence basis, the density of dark energy (~ 7 × 1030 g/cm3) is much less than the density of ordinary matter or dark matter within galaxies. However, in the present dark-energy era, it dominates the massenergy of the universe because it is uniform across space.
Two proposed forms for dark energy are the cosmological constant, a constant energy density filling space homogeneously, and scalar fields such as quintessence or moduli, dynamic quantities whose energy density can vary in time and space while still permeating them enough to cause the observed rate of expansion. Contributions from scalar fields that are constant in space are usually also included in the cosmological constant. The cosmological constant can be formulated to be equivalent to vacuum energy.
=== Dark matter ===
Dark matter is a hypothetical kind of matter that is invisible to the entire electromagnetic spectrum, but which accounts for most of the matter in the universe. The existence and properties of dark matter are inferred from its gravitational effects on visible matter, radiation, and the large-scale structure of the universe. Other than neutrinos, a form of hot dark matter, dark matter has not been detected directly, making it one of the greatest mysteries in modern astrophysics. Dark matter neither emits nor absorbs light or any other electromagnetic radiation at any significant level. Dark matter is estimated to constitute 26.8% of the total massenergy and 84.5% of the total matter in the universe.
=== Ordinary matter ===

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The remaining 4.9% of the massenergy of the universe is ordinary matter, that is, atoms, ions, electrons and the objects they form. This matter includes stars, which produce nearly all of the light we see from galaxies, as well as interstellar gas in the interstellar and intergalactic media, planets, and all the objects from everyday life that we can bump into, touch or squeeze. The great majority of ordinary matter in the universe is unseen, since visible stars and gas inside galaxies and clusters account for less than 10 percent of the ordinary matter contribution to the massenergy density of the universe.
Ordinary matter commonly exists in four states (or phases): solid, liquid, gas, and plasma. However, advances in experimental techniques have revealed other previously theoretical phases, such as BoseEinstein condensates and fermionic condensates. Ordinary matter is composed of two types of elementary particles: quarks and leptons. For example, the proton is formed of two up quarks and one down quark; the neutron is formed of two down quarks and one up quark; and the electron is a kind of lepton. An atom consists of an atomic nucleus, made up of protons and neutrons (both of which are baryons), and electrons that orbit the nucleus.
Soon after the Big Bang, primordial protons and neutrons formed from the quarkgluon plasma of the early universe as it cooled below two trillion degrees. A few minutes later, in a process known as Big Bang nucleosynthesis, nuclei formed from the primordial protons and neutrons. This nucleosynthesis formed lighter elements, those with small atomic numbers up to lithium and beryllium, but the abundance of heavier elements dropped off sharply with increasing atomic number. Some boron may have been formed at this time, but the next heavier element, carbon, was not formed in significant amounts. Big Bang nucleosynthesis shut down after about 20 minutes due to the rapid drop in temperature and density of the expanding universe. Subsequent formation of heavier elements resulted from stellar nucleosynthesis and supernova nucleosynthesis.
=== Particles ===
Ordinary matter and the forces that act on matter can be described in terms of elementary particles. These particles are sometimes regarded as fundamental because they have no known substructure. In most contemporary models they are thought of as points in space. All elementary particles are described by quantum mechanics and exhibit waveparticle duality: their behavior has both particle-like and wave-like aspects manifest under different circumstances.
Of central importance is the Standard Model, a theory that is concerned with electromagnetic interactions and the weak and strong nuclear interactions. The Standard Model is supported by the experimental confirmation of the existence of particles that compose matter: quarks and leptons, and their corresponding "antimatter" duals, as well as the force particles that mediate interactions: the photon, the W and Z bosons, and the gluon. The Standard Model predicted the existence of the recently discovered Higgs boson, a particle that is a manifestation of a field within the universe that can endow particles with mass. Because of its success in explaining a wide variety of experimental results, the Standard Model is sometimes regarded as a "theory of almost everything". The Standard Model does not, however, accommodate gravity. A true forceparticle "theory of everything" has not been attained.
==== Hadrons ====
A hadron is a composite particle made of quarks held together by the strong force. Hadrons are categorized into two families: baryons (such as protons and neutrons) made of three quarks, and mesons (such as pions) made of one quark and one antiquark. Of the hadrons, protons are stable, and neutrons bound within atomic nuclei are stable. Other hadrons are unstable under ordinary conditions and are thus insignificant constituents of the modern universe.
From approximately 106 seconds after the Big Bang, during a period known as the hadron epoch, the temperature of the universe had fallen sufficiently to allow quarks to bind together into hadrons, and the mass of the universe was dominated by hadrons. Initially, the temperature was high enough to allow the formation of hadronanti-hadron pairs, which kept matter and antimatter in thermal equilibrium. However, as the temperature of the universe continued to fall, hadronanti-hadron pairs were no longer produced. Most of the hadrons and anti-hadrons were then eliminated in particleantiparticle annihilation reactions, leaving a small residual of hadrons by the time the universe was about one second old.
==== Leptons ====

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A lepton is an elementary, half-integer spin particle that does not undergo strong interactions but is subject to the Pauli exclusion principle; no two leptons of the same species can be in exactly the same state at the same time. Two main classes of leptons exist: charged leptons (also known as the electron-like leptons), and neutral leptons (better known as neutrinos). Electrons are stable and the most common charged lepton in the universe, whereas muons and taus are unstable particles that quickly decay after being produced in high energy collisions, such as those involving cosmic rays or carried out in particle accelerators. Charged leptons can combine with other particles to form various composite particles such as atoms and positronium. The electron governs nearly all of chemistry, as it is found in atoms and is directly tied to all chemical properties. Neutrinos rarely interact with anything, and are consequently rarely observed. Neutrinos stream throughout the universe but rarely interact with normal matter.
The lepton epoch was the period in the evolution of the early universe in which the leptons dominated the mass of the universe. It started roughly 1 second after the Big Bang, after the majority of hadrons and anti-hadrons annihilated each other at the end of the hadron epoch. During the lepton epoch, the temperature of the universe was still high enough to create leptonanti-lepton pairs, so leptons and anti-leptons were in thermal equilibrium. Approximately 10 seconds after the Big Bang, the temperature of the universe had fallen to the point where leptonanti-lepton pairs were no longer created. Most leptons and anti-leptons were then eliminated in annihilation reactions, leaving a small residue of leptons. The mass of the universe was then dominated by photons as it entered the following photon epoch.
==== Photons ====
A photon is the quantum of light and all other forms of electromagnetic radiation. It is the carrier for the electromagnetic force. The effects of this force are easily observable at the microscopic and at the macroscopic level because the photon has zero rest mass; this allows long distance interactions.
The photon epoch started after most leptons and anti-leptons were annihilated at the end of the lepton epoch, about 10 seconds after the Big Bang. Atomic nuclei were created in the process of nucleosynthesis which occurred during the first few minutes of the photon epoch. For the remainder of the photon epoch the universe contained a hot dense plasma of nuclei, electrons and photons. About 380,000 years after the Big Bang, the temperature of the universe fell to the point where nuclei could combine with electrons to create neutral atoms. As a result, photons no longer interacted frequently with matter and the universe became transparent. The highly redshifted photons from this period form the cosmic microwave background. Tiny variations in the temperature of the CMB correspond to variations in the density of the universe that were the early "seeds" from which all subsequent structure formation took place.
== Habitability ==
The frequency of life in the universe has been a frequent point of investigation in astronomy and astrobiology, being the issue of the Drake equation and the different views on it, from identifying the Fermi paradox, the situation of not having found any signs of extraterrestrial life, to arguments for a biophysical cosmology, a view of life being inherent to the physical cosmology of the universe.
== Cosmological models ==
=== Model of the universe based on general relativity ===
General relativity is the geometric theory of gravitation formulated by Albert Einstein in 1915 and remains the standard description of gravity in modern physics. It extends special relativity and Newton's law of universal gravitation by describing gravity as a manifestation of the curvature of space and time (spacetime). In this framework, the curvature of spacetime is determined by the energy and momentum of matter and radiation.
This relationship is expressed through the Einstein field equations, which link the distribution of matter and energy to the geometry of spacetime. The resulting geometry governs the motion of matter, so that solutions of these equations describe how the universe evolves over time.
Under the cosmological principle, which assumes that the universe is homogeneous and isotropic on large scales, the field equations admit a class of solutions described by the metric tensor known as the FriedmannLemaîtreRobertsonWalker metric. In this description, the universe is characterized by two quantities: a scale factor, which describes how its overall size changes with time, and a curvature index, which specifies its spatial geometry. The curvature can be flat, positively curved, or negatively curved.
The evolution of the scale factor depends on both the spatial curvature and the cosmological constant, which represents the energy density of empty space and may be associated with dark energy. The relation governing this evolution is known as the Friedmann equation, introduced by Alexander Friedmann.
The curvature determines the global geometry of space. A positively curved universe has a finite volume and can be visualized as a three-dimensional sphere. A flat or negatively curved universe is spatially infinite. Although this may seem counterintuitive, models with flat or negative curvature allow an infinite universe to emerge from an initial state in which the scale factor vanishes, consistent with the cosmological principle. Analogies include an infinite plane (flat) or other geometries such as a torus.
The ultimate fate of the universe depends on both the curvature and the cosmological constant. A sufficiently dense universe with positive curvature would eventually recollapse in a Big Crunch, possibly followed by a Big Bounce. In contrast, a flat or negatively curved universe would expand indefinitely, approaching a Big Freeze and eventual heat death of the universe. Observations indicate that the expansion of the universe is accelerating, raising the possibility of a Big Rip. Current data suggest that the universe is close to flat, with a density near the critical value separating recollapse from eternal expansion.
=== Multiverse hypotheses ===

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Some speculative theories have proposed that our universe is but one of a set of disconnected universes, collectively denoted as the multiverse. An easily visualized metaphor of these concepts is a group of separate soap bubbles, in which observers living on one soap bubble cannot interact with those on other soap bubbles, even in principle. According to one common terminology, each "soap bubble" of spacetime is denoted as a universe, whereas humans' particular spacetime is denoted as the universe, just as humans call Earth's moon the Moon. The entire collection of these separate spacetimes is denoted as the multiverse.
Max Tegmark and Brian Greene have proposed different classification schemes for multiverse ideas. In Tegmark's scheme multiverses might result from the immense size of the spacetime, from cosmological processes that produce spacetime bubbles, from quantum mechanical unitarity, or because we live in a mathematical construct. If space is infinite, or sufficiently large and uniform, identical instances of the history of Earth's entire Hubble volume occur every so often, simply by chance. Tegmark calculated that our nearest so-called doppelgänger is 1010115 metres away from us (a double exponential function larger than a googolplex). The physical basis of these ideas have been challenged.
== Historical conceptions ==
Historically, there have been many ideas of the cosmos (cosmologies) and its origin (cosmogonies). Theories of an impersonal universe governed by physical laws were first proposed by the Greeks and Indians. Ancient Chinese philosophy encompassed the notion of the universe including both all of space and all of time. Over the centuries, improvements in astronomical observations and theories of motion and gravitation led to ever more accurate descriptions of the universe. The modern era of cosmology began with Albert Einstein's 1915 general theory of relativity, which made it possible to quantitatively predict the origin, evolution, and conclusion of the universe as a whole. Most modern, accepted theories of cosmology are based on general relativity and, more specifically, the predicted Big Bang.
=== Mythologies ===
Many cultures have stories describing the origin of the world and universe. Cultures generally regard these stories as having some truth. There are however many differing beliefs in how these stories apply amongst those believing in a supernatural origin, ranging from a god directly creating the universe as it is now to a god just setting the "wheels in motion" (for example via mechanisms such as the big bang and evolution).
Ethnologists and anthropologists who study myths have developed various classification schemes for the various themes that appear in creation stories. For example, in one type of story, the world is born from a world egg; such stories include the Finnish epic poem Kalevala, the Chinese story of Pangu or the Indian Brahmanda Purana. In related stories, the universe is created by a single entity emanating or producing something by him- or herself, as in the Tibetan Buddhism concept of Adi-Buddha, the ancient Greek story of Gaia (Mother Earth), the Aztec goddess Coatlicue myth, the ancient Egyptian god Atum story, and the Judeo-Christian Genesis creation narrative in which the Abrahamic God created the universe. In another type of story, the universe is created from the union of male and female deities, as in the Māori story of Rangi and Papa. In other stories, the universe is created by crafting it from pre-existing materials, such as the corpse of a dead god—as from Tiamat in the Babylonian epic Enuma Elish or from the giant Ymir in Norse mythology—or from chaotic materials, as in Izanagi and Izanami in Japanese mythology. In other stories, the universe emanates from fundamental principles, such as Brahman and Prakrti, and the creation myth of the Serers.
=== Philosophical models ===

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The pre-Socratic Greek philosophers and Indian philosophers developed some of the earliest philosophical concepts of the universe. The earliest Greek philosophers noted that appearances can be deceiving, and sought to understand the underlying reality behind the appearances. In particular, they noted the ability of matter to change forms (e.g., ice to water to steam) and several philosophers proposed that all the physical materials in the world are different forms of a single primordial material, or arche. The first to do so was Thales, who proposed this material to be water. Thales' student, Anaximander, proposed that everything came from the limitless apeiron. Anaximenes proposed the primordial material to be air on account of its perceived attractive and repulsive qualities that cause the arche to condense or dissociate into different forms. Anaxagoras proposed the principle of Nous (Mind), while Heraclitus proposed fire (and spoke of logos). Empedocles proposed the elements to be earth, water, air and fire. His four-element model became very popular. Like Pythagoras, Plato believed that all things were composed of number, with Empedocles' elements taking the form of the Platonic solids. Democritus, and later philosophers—most notably Leucippus—proposed that the universe is composed of indivisible atoms moving through a void (vacuum), although Aristotle did not believe that to be feasible because air, like water, offers resistance to motion. Air will immediately rush in to fill a void, and moreover, without resistance, it would do so indefinitely fast.
Although Heraclitus argued for eternal change, his contemporary Parmenides emphasized changelessness. Parmenides' poem On Nature has been read as saying that all change is an illusion, that the true underlying reality is eternally unchanging and of a single nature, or at least that the essential feature of each thing that exists must exist eternally, without origin, change, or end. His student Zeno of Elea challenged everyday ideas about motion with several famous paradoxes. Aristotle responded to these paradoxes by developing the notion of a potential countable infinity, as well as the infinitely divisible continuum.
The Indian philosopher Kanada, founder of the Vaisheshika school, developed a notion of atomism and proposed that light and heat were varieties of the same substance. In the 5th century AD, the Buddhist atomist philosopher Dignāga proposed atoms to be point-sized, durationless, and made of energy. They denied the existence of substantial matter and proposed that movement consisted of momentary flashes of a stream of energy.
The notion of temporal finitism was inspired by the doctrine of creation shared by the three Abrahamic religions: Judaism, Christianity and Islam. The Christian philosopher, John Philoponus, presented the philosophical arguments against the ancient Greek notion of an infinite past and future. Philoponus' arguments against an infinite past were used by the early Muslim philosopher, Al-Kindi (Alkindus); the Jewish philosopher, Saadia Gaon (Saadia ben Joseph); and the Muslim theologian, Al-Ghazali (Algazel).
Pantheism is the philosophical religious belief that the universe itself is identical to divinity and a supreme being or entity. The physical universe is thus understood as an all-encompassing, immanent deity. The term 'pantheist' designates one who holds both that everything constitutes a unity and that this unity is divine, consisting of an all-encompassing, manifested god or goddess.
=== Astronomical concepts ===
The earliest written records of identifiable predecessors to modern astronomy come from Ancient Egypt and Mesopotamia from around 3000 to 1200 BCE. Babylonian astronomers of the 7th century BCE viewed the world as a flat disk surrounded by the ocean.
Later Greek philosophers, observing the motions of the heavenly bodies, were concerned with developing models of the universe based more profoundly on empirical evidence. Some of the earliest cosmological models of the universe were developed by ancient Greek and Indian philosophers and were geocentric, placing Earth at the center. The first coherent model was proposed by Eudoxus of Cnidos, a student of Plato who followed Plato's idea that heavenly motions had to be circular. In order to account for the known complications of the planets' motions, particularly retrograde movement, Eudoxus' model included 27 different celestial spheres: four for each of the planets visible to the naked eye, three each for the Sun and the Moon, and one for the stars. All of these spheres were centered on the Earth, which remained motionless while they rotated eternally. Aristotle elaborated upon this model, increasing the number of spheres to 55 in order to account for further details of planetary motion. For Aristotle, normal matter was entirely contained within the terrestrial sphere, and it obeyed fundamentally different rules from heavenly material.
The post-Aristotle treatise De Mundo (of uncertain authorship and date) stated, "Five elements, situated in spheres in five regions, the less being in each case surrounded by the greater—namely, earth surrounded by water, water by air, air by fire, and fire by ether—make up the whole universe". This model was also refined by Callippus and after concentric spheres were abandoned, it was brought into nearly perfect agreement with astronomical observations by Ptolemy. The success of such a model is largely due to the mathematical fact that any function (such as the position of a planet) can be decomposed into a set of circular functions (the Fourier modes). Other Greek scientists, such as the Pythagorean philosopher Philolaus, postulated (according to Stobaeus' account) that at the center of the universe was a "central fire" around which the Earth, Sun, Moon and planets revolved in uniform circular motion.
The Greek astronomer Aristarchus of Samos was the first known individual to propose a heliocentric model of the universe. Though the original text has been lost, a reference in Archimedes' book The Sand Reckoner describes Aristarchus's heliocentric model. Archimedes wrote:

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You, King Gelon, are aware the universe is the name given by most astronomers to the sphere the center of which is the center of the Earth, while its radius is equal to the straight line between the center of the Sun and the center of the Earth. This is the common account as you have heard from astronomers. But Aristarchus has brought out a book consisting of certain hypotheses, wherein it appears, as a consequence of the assumptions made, that the universe is many times greater than the universe just mentioned. His hypotheses are that the fixed stars and the Sun remain unmoved, that the Earth revolves about the Sun on the circumference of a circle, the Sun lying in the middle of the orbit, and that the sphere of fixed stars, situated about the same center as the Sun, is so great that the circle in which he supposes the Earth to revolve bears such a proportion to the distance of the fixed stars as the center of the sphere bears to its surface.
Aristarchus thus believed the stars to be very far away, and saw this as the reason why stellar parallax had not been observed, that is, the stars had not been observed to move relative each other as the Earth moved around the Sun. The stars are in fact much farther away than the distance that was generally assumed in ancient times, which is why stellar parallax is only detectable with precision instruments. The geocentric model, consistent with planetary parallax, was assumed to be the explanation for the unobservability of stellar parallax.
The only other astronomer from antiquity known by name who supported Aristarchus's heliocentric model was Seleucus of Seleucia, a Hellenistic astronomer who lived a century after Aristarchus. According to Plutarch, Seleucus was the first to prove the heliocentric system through reasoning, but it is not known what arguments he used. Seleucus' arguments for a heliocentric cosmology were probably related to the phenomenon of tides. According to Strabo (1.1.9), Seleucus was the first to state that the tides are due to the attraction of the Moon, and that the height of the tides depends on the Moon's position relative to the Sun. Alternatively, he may have proved heliocentricity by determining the constants of a geometric model for it, and by developing methods to compute planetary positions using this model, similar to Nicolaus Copernicus in the 16th century. During the Middle Ages, heliocentric models were also proposed by the Persian astronomers Albumasar and Al-Sijzi.
The Aristotelian model was accepted in the Western world for roughly two millennia, until Copernicus revived Aristarchus's perspective that the astronomical data could be explained more plausibly if the Earth rotated on its axis and if the Sun were placed at the center of the universe.
In the center rests the Sun. For who would place this lamp of a very beautiful temple in another or better place than this wherefrom it can illuminate everything at the same time?
As noted by Copernicus, the notion that the Earth rotates is very old, dating at least to Philolaus (c.450 BC), Heraclides Ponticus (c.350 BC) and Ecphantus the Pythagorean. Roughly a century before Copernicus, the Christian scholar Nicholas of Cusa also proposed that the Earth rotates on its axis in his book, On Learned Ignorance (1440). Al-Sijzi also proposed that the Earth rotates on its axis. Empirical evidence for the Earth's rotation on its axis, using the phenomenon of comets, was given by Tusi (12011274) and Ali Qushji (14031474).
This cosmology was accepted by Isaac Newton, Christiaan Huygens and later scientists. Newton demonstrated that the same laws of motion and gravity apply to earthly and to celestial matter, making Aristotle's division between the two obsolete. Edmund Halley (1720) and Jean-Philippe de Chéseaux (1744) noted independently that the assumption of an infinite space filled uniformly with stars would lead to the prediction that the nighttime sky would be as bright as the Sun itself; this became known as Olbers' paradox in the 19th century. Newton believed that an infinite space uniformly filled with matter would cause infinite forces and instabilities causing the matter to be crushed inwards under its own gravity. This instability was clarified in 1902 by the Jeans instability criterion. One solution to these paradoxes is the Charlier universe, in which the matter is arranged hierarchically (systems of orbiting bodies that are themselves orbiting in a larger system, ad infinitum) in a fractal way such that the universe has a negligibly small overall density; such a cosmological model had also been proposed earlier in 1761 by Johann Heinrich Lambert.
=== Deep space astronomy ===
During the 18th century, Immanuel Kant speculated that nebulae could be entire galaxies separate from the Milky Way, and in 1850, Alexander von Humboldt called these separate galaxies Weltinseln, or "world islands", a term that later developed into "island universes". In 1919, when the Hooker Telescope was completed, the prevailing view was that the universe consisted entirely of the Milky Way Galaxy. Using the Hooker Telescope, Edwin Hubble identified Cepheid variables in several spiral nebulae and in 19221923 proved conclusively that Andromeda Nebula and Triangulum among others, were entire galaxies outside our own, thus proving that the universe consists of a multitude of galaxies. With this Hubble formulated the Hubble constant, which allowed for the first time a calculation of the age of the universe and size of the Observable Universe, which became increasingly precise with better meassurements, starting at 2 billion years and 280 million light-years, until 2006 when data of the Hubble Space Telescope allowed a very accurate calculation of the age of the universe and size of the Observable Universe.
The modern era of physical cosmology began in 1917, when Albert Einstein first applied his general theory of relativity to model the structure and dynamics of the universe. The discoveries of this era, and the questions that remain unanswered, are outlined in the sections above.
== See also ==
== References ==
Footnotes

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Citations
=== Bibliography ===
Van Der Waerden, B. L. (June 1987). "The Heliocentric System in Greek, Persian and Hindu Astronomy". Annals of the New York Academy of Sciences. 500 (1): 525545. Bibcode:1987NYASA.500..525V. doi:10.1111/j.1749-6632.1987.tb37224.x. ISSN 0077-8923. S2CID 222087224.
Landau LD, Lifshitz EM (1975). The classical theory of fields. Course of theoretical physics. Vol. 2 (4th rev. English ed.). Oxford; New York: Pergamon Press. pp. 358397. ISBN 978-0-08-018176-9.
Liddell, Henry George & Scott, Robert (1994). A Greek-English lexicon. Oxford: Clarendon Pr. ISBN 978-0-19-864214-5.
Misner, Charles W.; Thorne, Kip S.; Wheeler, John Archibald; Kip; Wheeler; J.A. (2008). Gravitation (27. printing ed.). New York, NY: Freeman. pp. 703816. ISBN 978-0-7167-0344-0.
Raine, Derek; Thomas, Edwin G. (2001). An introduction to the science of cosmology. Series in astronomy and astrophysics. Bristol: Institute of Physics Publ. ISBN 978-0-7503-0405-4.
Rindler, Wolfgang (1986). Essential relativity: special, general, and cosmological. Texts and monographs in physics. New York Heidelberg: Springer. pp. 193244. ISBN 978-0-387-10090-6.
Rees, Martin J.; DK Publishing, Inc; Smithsonian Institution, eds. (2012). Universe (Rev. ed.). New York: DK Pub. ISBN 978-0-7566-9841-6. OCLC 809932784.
== External links ==
NASA/IPAC Extragalactic Database (NED) / (NED-Distances).
There are about 1082 atoms in the observable universe LiveScience, July 2021.
This is why we will never know everything about our universe Forbes, May 2019.

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A variable star is a star whose brightness as seen from Earth (its apparent magnitude) changes systematically with time. This variation may be caused by a change in emitted light or by something partly blocking the light, so variable stars are classified as either:
Intrinsic variables, whose inherent luminosity changes; for example, because the star swells and shrinks.
Extrinsic variables, whose apparent changes in brightness are due to changes in the amount of their light that can reach Earth; for example, because the star has an orbiting companion that sometimes eclipses it.
Depending on the type of star system, this variation can include cyclical, irregular, fluctuating, or transient behavior. Changes can occur on time scales that range from under an hour to multiple years. Many, possibly most, stars exhibit at least some oscillation in luminosity: the energy output of the Sun, for example, varies by about 0.1% over an 11-year solar cycle. At the opposite extreme, a supernova event can briefly outshine an entire galaxy. Of the 58,200 variable stars that have been catalogued as of 2023, the most common type are pulsating variables with just under 30,000, followed by eclipsing variables with over 10,000.
Variable stars have been observed since the dawn of human history. The first documented periodic variable was the eclipsing binary Algol. The periodic variable Omicron Ceti, later named Mira, was discovered in the 17th century, followed by Chi Cygni then R Hydrae. By 1786, ten had been documented. Variable star discovery increased rapidly with the advent of photographic plates. When Cepheid variables were shown to have a period-luminosity relationship in 1912, this allowed them to be used for distance measurement. As a result, it was demonstrated that spiral nebulae are galaxies outside the Milky Way. Variable stars now form several methods for the cosmic distance ladder that is used to determine the scale of the visible universe. The periods of eclipsing binaries allowed for a more precise determination of the mass and radii of their component stars, which proved especially useful for modelling stellar evolution.
== Discovery ==
An ancient Egyptian calendar of lucky and unlucky days composed some 3,200 years ago may be the oldest preserved historical document of the discovery of a variable star, the eclipsing binary Algol, but the validity of this claim has been questioned. Aboriginal Australians are also known to have observed the variability of Betelgeuse and Antares, incorporating these brightness changes into narratives that are passed down through oral tradition. Pre-telescope observations of novae and supernovae events were recorded by Babylonian, Chinese, and Arab astronomers, among others.
Of the modern astronomers in the telescope era, the first periodic variable star was identified in 1638 when Johannes Holwarda noticed that Omicron Ceti (later named Mira) pulsated in a cycle taking 11 months; the star had previously been described as a nova by David Fabricius in 1596. This discovery, combined with supernovae observed in 1572 and 1604, proved that the starry sky was not eternally invariable as Aristotle and other ancient philosophers had taught. In this way, the discovery of variable stars contributed to the astronomical revolution of the sixteenth and early seventeenth centuries.
The second variable star to be described was the eclipsing variable Algol, by Geminiano Montanari in 1669; John Goodricke gave the correct explanation of its variability in 1784. Chi Cygni was identified in 1686 by G. Kirch, then R Hydrae in 1704 by G. D. Maraldi. Eta Aquilae, the first Cepheid variable to be discovered, was spotted by Edward Pigott in 1784. By 1786, ten variable stars were known. John Goodricke himself discovered Delta Cephei and Beta Lyrae. Since 1850, the number of known variable stars has increased rapidly, especially when it became possible to identify variable stars by means of photography. In 1885, Harvard College Observatory began a program of repeatedly photographing the entire sky for the purpose of discovering variable stars.
In 1912 Henrietta Swan Leavitt discovered a relationship between the brightness of Cepheid variables and their periodicity. Edwin Hubble used this result in 1924 when he discovered a Cepheid variable in what was then termed the Andromeda Nebula. The resulting distance estimate demonstrated that this nebula was an "island universe", located well outside the Milky Way galaxy. This ended the Great Debate about the nature of spiral nebulae. In 1930, astrophysicist Cecilia Payne published the book The Stars of High Luminosity, in which she made numerous observations of variable stars, paying particular attention to Cepheid variables. Her analyses and observations of variable stars, carried out with her husband, Sergei Gaposchkin, laid the basis for all subsequent work on the subject.
The 2008 edition of the General Catalogue of Variable Stars lists more than 46,000 variable stars in the Milky Way, as well as 10,000 in other galaxies, and over 10,000 'suspected' variables. Amateur astronomers have long played a significant role in variable star observation, with perhaps the oldest such organization being the Variable Star Section of the British Astronomical Association, founded in 1890.
== Detecting variability ==
The most common kinds of variability involve changes in brightness, but other types of variability also occur, in particular changes in the spectrum and polarization. By combining light curve data with observed spectral changes, astronomers are often able to explain why a particular star is variable.
=== Variable star observations ===

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Variable stars are generally analysed using photometry, spectrophotometry, spectroscopy, and polarimetry. Measurements of their changes in brightness can be plotted to produce light curves. For regular variables, the period of variation and its amplitude can be very well established; for many variable stars, though, these quantities may vary slowly over time, or even from one period to the next. Peak brightnesses in the light curve are known as maxima, while troughs are known as minima.
Amateur astronomers can do useful scientific study of variable stars by visually comparing the star with other stars within the same telescopic field of view of which the magnitudes are known and constant. By estimating the variable's magnitude and noting the time of observation a visual lightcurve can be constructed. Organizations like the American Association of Variable Star Observers and the British Astronomical Association collect such observations from participants around the world and share the data with the scientific community.
From the light curve the following data are derived:
are the brightness variations periodical, semiperiodical, irregular, or unique?
what is the period of the brightness fluctuations?
what is the shape of the light curve (symmetrical or not, angular or smoothly varying, does each cycle have only one or more than one minima, etcetera)?
From the spectrum the following data are derived:
what kind of star is it: what is its temperature, its luminosity class (dwarf star, giant star, supergiant, etc.)?
is it a single star, or a binary? (the combined spectrum of a binary star may show elements from the spectra of each of the member stars)
does the spectrum change with time? (for example, the star may turn hotter and cooler periodically)
changes in brightness may depend strongly on the part of the spectrum that is observed (for example, large variations in visible light but hardly any changes in the infrared)
if the wavelengths of spectral lines are shifted this points to movements (for example, a periodical swelling and shrinking of the star, or its rotation, or an expanding gas shell) (Doppler effect)
strong magnetic fields on the star betray themselves in the spectrum
abnormal emission or absorption lines may be indication of a hot stellar atmosphere, or gas clouds surrounding the star.
In very few cases it is possible to make pictures of a stellar disk. These may show darker spots on its surface. One such technique is Doppler imaging, which can use the shift of spectral lines to measure velocity, then use it to determine the location of a spot across the surface of a rapidly rotating star.
=== Interpretation of observations ===
Combining light curves with spectral data often gives a clue as to the changes that occur in a variable star. For example, evidence for a pulsating star is found in its shifting spectrum because its surface periodically moves toward and away from us, with the same frequency as its changing brightness.
About two-thirds of all variable stars appear to be pulsating. In the 1930s astronomer Arthur Stanley Eddington showed that the mathematical equations that describe the interior of a star may lead to instabilities that cause a star to pulsate. This mechanism was known as the Eddington valve, but is now more commonly called the Kappamechanism. The most common type of instability is related to oscillations in the degree of ionization in outer, convective layers of the star. Most stars have two layers where hydrogen and helium ionization occurs, respectively. These are referred to as partial ionization zones. The location of these layers determine the pulsational properties of the star. The pulsation of cepheids is known to be driven by oscillations in the ionization of helium (from He++ to He+ and back to He++).
When the star is in the swelling phase, the partial ionization zone expands, causing it to cool. Because of the decreasing temperature the degree of ionization also decreases. This makes the plasma more transparent, and thus makes it easier for the star to radiate its energy. This in turn makes the star start to contract. As the gas is thereby compressed, it is heated and the degree of ionization again increases. This makes the gas more opaque, and radiation temporarily becomes captured in the gas. This heats the gas further, leading it to expand once again. Thus a cycle of expansion and compression (swelling and shrinking) is maintained.
In many cases, a predictive mathematical model can be constructed of the variable behavior. Typically an assumption is made of a constant period of variability. The model can then be used to construct an O-C diagram, which is a plot of the observed (O) behavior minus the computed (C) behavior model over a period of time, or folded over multiple cycles. If the model produces a good fit, this diagram can be used to detect a change in period, apsidal rotation, the effect of the Applegate mechanism, random period changes, or the interaction of a binary system with a third body.
== Nomenclature ==
In a given constellation, the first variable stars discovered were designated with letters R through Z, e.g. R Andromedae. This system of nomenclature was developed by Friedrich W. Argelander, who gave the first previously unnamed variable in a constellation the letter R, the first letter not used by Bayer. Letters RR through RZ, SS through SZ, up to ZZ are used for the next discoveries, e.g. RR Lyrae. Later discoveries used letters AA through AZ, BB through BZ, and up to QQ through QZ (with J omitted to avoid confusion with I). Once those 334 combinations are exhausted, variables are numbered in order of discovery, starting with the prefixed V335 onwards.
== Classification ==
Variable stars may be either intrinsic or extrinsic.

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Intrinsic variable stars
The variability is being caused by changes in the physical properties of the stars themselves. This category can be divided into four subgroups:
Pulsating variables, stars whose radius alternately expands and contracts as part of their natural evolutionary aging processes.
Eruptive variables, stars who experience eruptions on their surfaces like flares or mass ejections.
Cataclysmic or explosive variables, stars that undergo a cataclysmic change in their properties like novae and supernovae.
X-ray variables, close binary systems with a hot mass-accreting compact object.
Extrinsic variable stars
The variability is caused by external viewing perspectives like rotation or eclipses. There are two subgroups:
Eclipsing binaries, double stars or planetary systems where, as seen from Earth's vantage point the stars occasionally eclipse one another as they orbit, or the planet eclipses its star.
Rotating variables, stars whose variability is caused by phenomena related to their rotation. Examples are stars with extreme "sunspots" which affect the apparent brightness or stars that have fast rotation speeds causing them to become ellipsoidal in shape.
These subgroups themselves are further divided into specific types of variable stars that are usually named after their prototype. For example, dwarf novae are designated U Gem stars after the first recognized star in the class, U Geminorum.
The population of stars in the Milky Way galaxy is divided into two groups based on their age, chemical abundances, and motion through the galaxy. Population I stars are limited to the flat plane of the galactic system, known as thin disk stars. These originate in open clusters and often display high abundances of elements produced by stellar fusion processes their metallicity. The Population II stars are more often distributed in the thick disk, the galactic halo, globular clusters, and galactic bulge. These are much older stars that show lower abundances of elements more massive than helium. In some cases the classification system of variable stars and their behavior is determined by their population membership.
== Intrinsic variable stars ==
Examples of types within these divisions are given below.
=== Pulsating variable stars ===
Pulsating stars swell and shrink, affecting their brightness and spectrum. Pulsations are generally split into: radial, where the entire star expands and shrinks as a whole; and non-radial, where one part of the star expands while another part shrinks.
Depending on the type of pulsation and its location within the star, there is a natural or fundamental frequency which determines the period of the star. Stars may also pulsate in a harmonic or overtone which is a higher frequency, corresponding to a shorter period. Pulsating variable stars sometimes have a single well-defined period, but often they pulsate simultaneously with multiple frequencies and complex analysis is required to determine the separate interfering periods. In some cases, the pulsations do not have a defined frequency, causing a random variation, referred to as stochastic. The study of stellar interiors using their pulsations is known as asteroseismology.
The expansion phase of a pulsation is caused by the blocking of the internal energy flow by material with a high opacity, but this must occur at a particular depth of the star to create visible pulsations. If the expansion occurs below a convective zone then no variation will be visible at the surface. If the expansion occurs too close to the surface the restoring force will be too weak to create a pulsation. The restoring force to create the contraction phase of a pulsation can be pressure if the pulsation occurs in a non-degenerate layer deep inside a star, and this is called an acoustic or pressure mode of pulsation, abbreviated to p-mode. In other cases, the restoring force is gravity and this is called a g-mode. Pulsating variable stars typically pulsate in only one of these modes.
==== Cepheids and cepheid-like variables ====
The HertzsprungRussell diagram is a scatter plot of stars showing the relationship between the absolute magnitude and the spectral class (luminosity vs. effective temperature). Most ordinary stars like the Sun occupy a band called the main sequence that runs from lower right to upper left on this diagram. Several kinds of these pulsating stars occupy a box called the Cepheid instability strip that crosses the main sequence in the region of A- and F-class stars, then proceeds vertically and to the right on the HR diagram, finally crossing the track for supergiants. These stars swell and shrink very regularly, caused by the star's own mass resonance, generally by the fundamental frequency. The Eddington valve mechanism for pulsating variables is believed to account for cepheid-like pulsations.
The pulsational instability of Cepheid variables correlates with variations in the spectral class, effective temperature, and surface radial velocity of the star. Each of the subgroups on the instability strip has a fixed relationship between period and absolute magnitude, as well as a relation between period and mean density of the star. The period-luminosity relationship makes these high luminosity Cepheids very useful for determining distances to galaxies within the Local Group and beyond.
The Cepheids are named only for Delta Cephei, while a completely separate class of variables is named after Beta Cephei.
Classical Cepheid variables
Type I cepheids, also called Classical Cepheids or Delta Cephei variables, are evolved population I (young, massive, and luminous) yellow supergiants which undergo pulsations with very regular periods on the range of 1100 days. They are relatively rare stars with hydrogen-burning progenitors that had 4 to 20 solar masses and temperatures above a B5 class. Their radial pulsations are driven by the high opacity of ionized helium and hydrogen in their outer layers. Because of their high luminosity, Classical Cepheids can be viewed in nearby galaxies outside the Milky Way. On September 10, 1784, Edward Pigott detected the variability of Eta Aquilae, the first known representative of the class of Cepheid variables. However, the namesake for classical Cepheids is the star Delta Cephei, discovered to be variable by John Goodricke a few months later.
Type II Cepheids

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Type II Cepheids (historically termed W Virginis stars) have extremely regular light pulsations and a luminosity relation much like the δ Cephei variables, so initially they were confused with the latter category. Type II Cepheids are uncommon stars that belong to the older Population II category, compared to the younger type I Cepheids. The Type II have somewhat lower metallicity, much lower mass of around 0.50.6 M☉, somewhat lower luminosity, and a slightly offset period versus luminosity relationship, so it is always important to know which type of star is being observed. They can be identified based on the shape of their light curve. Type II Cepheids are further sub-divided based on their pulsation periods as BL Her stars for periods of 1 to 4 days, W Vir stars for 4 to 20 days, and RV Tau stars for longer periods of up to 100 days. These three subtypes correspond to consecutive states of stellar evolution after the star has exhausted the helium at its core.
RV Tauri variables
These are yellow supergiant stars (actually low mass post-AGB stars at the most luminous stage of their lives) which have alternating deep and shallow minima. This double-peaked variation typically has periods of 30150 days and amplitudes of up to 3 magnitudes. Superimposed on this variation, there may be long-term variations over periods of several years. Their spectra are of type F or G at maximum light and type K or M at minimum brightness. They lie near the instability strip, forming a higher luminosity extension of the type II Cepheids, while being cooler than type I Cepheids. Their pulsations are caused by the same basic mechanisms related to helium opacity, but they are at a very different stage of their lives.
RR Lyrae variables
These relatively common variable stars are somewhat similar to Cepheids, but are not as luminous and have shorter periods. They are older than type I Cepheids, belonging to Population II, but of lower mass than type II Cepheids. Due to their common occurrence in globular clusters, they are occasionally referred to as cluster-type Cepheids. They also have a well established period-luminosity relationship in the infrared K-band, and so are also useful as distance indicators. As standard candles, they can be detected out to 1 Mpc, which lies within the local group of galaxies. These are low mass giants having an A- or F-type spectrum, and are currently on the horizontal branch. They are radially pulsating and vary by about 0.22 in visual magnitude (20% to over 500% change in luminosity) over a period of several hours to a day or more. The category is divided into Bailey subtypes 'a', 'b', and 'c', depending on the shape of the light curve.
Delta Scuti variables
Delta Scuti (δ Sct) variables are similar to Cepheids but much fainter and with much shorter periods. They were once known as Dwarf Cepheids. Delta Scuti variables display both radial and non-radial pulsations modes. They often show many superimposed periods, which combine to form a complex light curve. Their spectral type is usually late A- and early F-type stars, and they lie on or near the main sequence on the H-R diagram. When metallicity is solar, they have masses ranging from about 1.6 times the Sun for slower periods up to 2.4 at higher pulsation rates. With rotation rates of 40 to 250 km/s, Delta Scuti stars show small amplitudes of 0.010.03 magnitude with multiple pulsation modes, including many non-radial. For slower rotation rates under 30 km/s, the amplitude is 0.200.30 magnitude or more, and they are often radial pulsators. Stars with Delta Scuti-like variations and an amplitude greater than 0.3 magnitude are known as AI Vel-type variables, after their prototype, AI Velorum.
SX Phoenicis variables
These stars are metal-poor, population II analogues of δ Scuti variables and are mainly found in globular clusters. They exhibit fluctuations in their brightness in the order of 0.7 magnitude (about 100% change in luminosity) or so with short periods of 1 to 3 hours. They have masses in the range of 1.01.3 solar. Within a cluster, they are referred to as pulsating blue stragglers, presumably being formed from the merger of two ordinary stars in a close binary system. SX Phe variables are slow rotators and most pulsation modes are radial.
Rapidly oscillating Ap variables
The roAp variables are rapidly rotating, strongly magnetic, chemically peculiar stars of spectral type A or occasionally F0, known as Ap stars. Their pulsatation behavior is much like those of Delta Scuti or Gamma Doradus variables found on the main sequence. They have extremely rapid variations with periods of a few minutes and amplitudes of a few thousandths of a magnitude. Unlike Delta Scuti stars, roAp stars pulsate with either a single high frequency or with multiple high frequencies that are closely spaced. However, the isolated high frequencies of roAp stars have also been observed in stars that are not chemically peculiar, and some Delta Scuti stars show pulsation in the roAp range. Thus the distinction is unclear.
==== Long period variables ====
The long period variables are cool evolved stars that pulsate with periods in the range of weeks to several years. All giant stars cooler than spectral type K5 are variable because of radial pulsations. Many variables of this class show longer period secondary variations that run for several hundred to several thousand days. This may change the brightness by up to several magnitudes although it is often much smaller, with the more rapid primary variations superimposed. The reasons for this type of secondary variation are not clearly understood, being variously ascribed to pulsations, binarity, and stellar rotation.
Mira variables

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Mira variables are aging red giant stars nearing the end of their active life on asymptotic giant branch (AGB). They have radial pulsation periods that can range from under 100 to over 2,000 days, although most are in the 200 to 450 day range. They fade and brighten over a range of 8 magnitudes, a thousand fold change in luminosity. Mira itself, also known as Omicron Ceti (ο Cet), varies in brightness from almost 2nd magnitude to as faint as 10th magnitude with a period of roughly 332 days. The very large visual amplitudes are mainly due to the shifting of energy output between visual and infra-red as the temperature of the star changes. In a few cases, Mira variables show dramatic period changes over a period of decades, thought to be related to the thermal pulsing cycle of the most advanced AGB stars.
Semiregular variables
These are long-period variables with shorter periods and smaller amplitudes than Miras, and their light curves are less regular. Types SRa and SRb are red giants, with the latter type displaying a less regular periodicity. The visual amplitude is typically less than 2.5 magnitudes. They are believed to be precursors of Mira variables, but are longer lived and thus more common. The types SRc and SRd consist mostly of red supergiants and yellow supergiants, respectively.
Semiregular variables may show a definite period on occasion, but more often show less well-defined variations that can sometimes be resolved into multiple periods. A well-known example of a semiregular variable is Betelgeuse, which varies in brightness by half a magnitude with overlapping periods of 1.10 and 5.75 years. At least some of the semi-regular variables are very closely related to Mira variables, possibly the only difference being pulsating in a different harmonic.
Slow irregular variables
These are red giants or supergiants with little or no detectable periodicity. Some are poorly studied semiregular variables, often with multiple periods, but others may simply be chaotic. These variables are classified as type Lb or Lc, depending on whether they are cool giants or cool supergiants, respectively. A prominent example of a slow irregular variable is Antares, which is classified as an Lc type with a brightness that ranges from 0.88 to 1.16 in visual magnitude.
==== Beta Cephei variables ====
Beta Cephei (β Cep) variables (sometimes called Beta Canis Majoris variables, especially in Europe) undergo short period pulsations in the order of 0.10.6 days with an amplitude of 0.010.3 magnitudes (1% to 30% change in luminosity). They are at their brightest during minimum contraction. Many stars of this kind exhibits multiple pulsation periods.
==== Slowly pulsating B-type stars ====
Slowly pulsating B (SPB) stars are hot main-sequence stars slightly less luminous than the Beta Cephei stars, with longer periods and larger amplitudes. They have masses in the range of 2.57 M☉, and non-radial pulsation periods from 0.5 to 3 days. Many are rapid rotators, which can cause them to appear cooler and, in some cases, lie outside instability strip.
==== Very rapidly pulsating hot (subdwarf B) stars ====
The prototype of this rare class is V361 Hydrae, a 15th magnitude subdwarf B star. They pulsate with periods of a few minutes and may simultaneous pulsate with multiple periods. They have amplitudes of a few hundredths of a magnitude and are given the GCVS acronym RPHS. They are p-mode pulsators.
==== PV Telescopii variables ====
Stars in this rare class are chemically peculiar type B (Bp) supergiants with a period of 0.11 day and an amplitude of 0.1 magnitude on average. Their spectra are peculiar by having weak hydrogen but extra strong carbon and helium lines, making this a type of extreme helium star. The prototype for this category of variable is PV Telescopii, which undergoes small but complex luminosity variations and radial velocity fluctuations.
==== Alpha Cygni variables ====
Alpha Cygni (α Cyg) variables are nonradially pulsating supergiants of spectral classes B to A. Their periods range from several days to several weeks, and their amplitudes of variation are typically of the order of 0.1 magnitudes. The light changes, which often seem irregular, may be caused by the superposition of many oscillations with close periods. The progenitors of these stars have at least 14 solar masses. At least for the brighter members, these variables appear to have returned to the blue supergiant region of the HR diagram after losing considerable mass as red supergiants. Deneb, in the constellation of Cygnus is the prototype of this class.
==== Gamma Doradus variables ====
Gamma Doradus (γ Dor) variables are non-radially pulsating main-sequence stars of spectral classes F to late A, with luminosity classes of IV-V or V. Their periods are 0.3 to 3 days and their amplitudes typically of the order of 0.1 magnitudes or less. This variable type occupies a narrow range near the low-luminosity part of the instability strip, which partially overlaps the range of Delta Scuti variables. The physical properties of Gamma Doradus variables are similar to long-period Delta Scuti variables. Their slow period and low amplitudes makes Gamma Doradus variables difficult to discover from the ground; most have been spotted by space missions.
==== Solar-like oscillations ====
The Sun oscillates with very low amplitude in a large number of modes having periods around 5 minutes. The study of these oscillations is known as helioseismology. Oscillations in the Sun are driven stochastically by convection in its outer layers. The term solar-like oscillations is used to describe oscillations in other stars that are excited in the same way and the study of these oscillations is one of the main areas of active research in the field of asteroseismology. Stars with surface convection layers that can produce solar-like oscillations are generally cooler than the right edge of the instability strip, which includes the lower main sequence along with subgiants and red giants. However, solar-like oscillations can also be excited by stellar pulsations, such as by Cepheids.

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==== Fast yellow pulsating supergiants ====
A fast yellow pulsating supergiant (FYPS) is a luminous yellow supergiant with pulsations shorter than a day. They are thought to have evolved beyond a red supergiant phase, but the mechanism for the pulsations is unknown. The class was named in 2020 through analysis of TESS observations.
==== Pulsating white dwarfs ====
These non-radially pulsating stars have short periods of hundreds to thousands of seconds with tiny fluctuations of 0.001 to 0.2 magnitudes. Known types of pulsating white dwarf (or pre-white dwarf) include the DAV, or ZZ Ceti, stars, with hydrogen-dominated atmospheres and the spectral type DA; DBV, or V777 Her, stars, with helium-dominated atmospheres and the spectral type DB; and GW Vir stars, with atmospheres dominated by helium, carbon, and oxygen. GW Vir stars may be subdivided into DOV and PNNV stars.
==== BLAP variables ====
A Blue Large-Amplitude Pulsator (BLAP) is a very rare class of radially-pulsating star characterized by changes of 0.2 to 0.4 magnitudes with typical periods of 7 to 75 minutes. They are thought to be the small helium core of a red giant that has had the remainder of its atmosphere stripped away by a binary companion. It has been hypothesized that they are the long-sought surviving companions of Type Ia supernovae. Alternatively, they may form from the merger of two low-mass white dwarfs. BLAP are effectively pre-white dwarf bodies with an effective temperature between 20,000 and 35,000 K. Most of these objects are in the medium or late stage of helium fusion.
=== Eruptive variable stars ===
Eruptive variable stars show unpredictable brightness variations caused by material being lost from the star, or in some cases being accreted to it. Despite the name, these are distinguished from cataclysmic variables because the eruptions are due to non-thermonuclear processes.
==== Young stellar object ====
Protostars are young objects that have not yet completed the process of contraction from a gas nebula to a veritable star. During this phase, the object is deeply embedded in an optically thick envelope, so that the variability induced by the rapid accretion process is primarily visible in the infrared. Once the object has expelled most of this nascent cocoon of gas and dust, it stabilizes in mass and becomes a premain-sequence star that is contracting toward the main sequence. The luminosity of this object is derived from gravitational contraction. These objects often exhibit irregular brightness variations in association with strong magnetic fields.
Orion variables
Orion variables are young, hot premain-sequence stars usually embedded in nebulosity. They have irregular periods with amplitudes of several magnitudes. These irregular variables are so-named because many were first located in the Orion Nebula. A well-known subtype of Orion variables are the T Tauri variables. Variability of T Tauri stars is due to spots on the stellar surface and gas-dust clumps, orbiting in the circumstellar disks. This class of variables are subdivided into classical and weak-line T Tauri. The former display a typical emission line spectra, while the latter do not show strong emission lines and lack a strong stellar wind or accretion disk. The third class, Herbig Ae/Be stars, are the more massive form. The fourth are the RW Aurigae irregular variables that have similar properties but lack nearby nebulosity. These last irregular variables do display emission lines, providing evidence for circumstellar shells.
Herbig Ae/Be stars
Variability of more massive (28 solar mass) Herbig Ae/Be stars is thought to be due to gas-dust clumps, orbiting in the circumstellar disks. They can also occur due to cold spots on the photosphere or pulsations when crossing the instability strip. The optical variations are typically up to a magnitude in amplitude and occur on time scales of days to weeks. A particularly extreme example is UX Orionis, which is the prototype of "UXORs"; these protostars vary by 2 to 3 magnitudes.
FU Orionis variables
A small fraction of young stellar objects are eruptive. The two primary types are dubbed FUors and EXors, after their prototype stars, FU Orionis and EX Lupi. (There are also intermediate types and Fu Ori-like YSOs.) The two types differ in the amplitude and time scales of their outbursts. FUors reside in reflection nebulae and show sharp increases in their luminosity in the order of 56 magnitudes followed by a very slow decline. FU Orionis variables are of spectral type F or G and are possibly an evolutionary phase in the life of T Tauri stars. EXors exhibit flares like a FUor, but their duration is much shorter. They can exhibit brief flashes up to 5 magnitudes. Its possible these are the next stage in evolution following the FUor phase.
==== Giants and supergiants ====
Large, more luminous stars with lower surface gravity lose their matter relatively easily. Mass loss rates are greater in higher luminosity stars, with the stellar wind being propelled by radiation pressure, and in cool, low mass giants, by radiation pressure on dust grains and by pulsations. For this reason variability due to eruptions and mass loss is more common among giants and supergiants.
Luminous blue variables

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Also known as the S Doradus variables, luminous blue variables (LBV) are among the most luminous stars known. Examples include the hypergiants η Carinae and P Cygni. They have permanent high mass loss, but at intervals of years internal pulsations cause the star to exceed its Eddington limit and the mass loss increases significantly. Visual brightness increases although the overall luminosity is largely unchanged. Giant eruptions observed in a few LBVs do increase the luminosity, so much so that they have been tagged supernova impostors, and may be a different type of event.
This category of variables are sub-divided into two classes. Classical LBVs have evolved from stars with at least 50 times the mass of the Sun. The high mass of these stars prevent them from becoming red supergiants. The second class are less luminous LBVs with initial masses in the range of around 2540 M☉. These can become red supergiants and many may already have done so. A distinguishing feature of all LBVs is a higher luminosity to mass ratio compared to non-LBVs in the same region of the H-R diagram. They occupy a separate LBV/S Dor instability strip, which is distinct from the Cepheid instability strip.
Yellow hypergiants
These massive evolved stars are unstable due to their high luminosity and position above the instability strip, and they exhibit slow but sometimes large photometric and spectroscopic changes due to high mass loss and occasional larger eruptions, combined with secular variation on an observable timescale. One of the best studied examples is Rho Cassiopeiae.
R Coronae Borealis variables
While classed as eruptive variables, these stars do not undergo periodic increases in brightness. Instead they spend most of their time undergoing small amplitude, semi-regular changes in luminosity, probably due to pulsations. At irregular intervals, they suddenly decline by 19 magnitudes (2.5 to 4000 times dimmer) before recovering to their initial brightness over months to years. They are carbon dust-producing stars belonging to a category of carbon-rich, hydrogen deficient supergiants. R Coronae Borealis (R CrB) is the prototype star. This dust production is the cause of the large declines in brightness. Two scenarios have been proposed for the formation of an R CrB star: either the merger of a carbon-oxygen white dwarf with a helium white dwarf, or the central stellar remnant from a planetary nebula undergoes helium flash, becoming a supergiant.
DY Persei variables are considered a subclass of cool R CrB variables. They are carbon-rich stars on the asymptotic giant branch that display both pulsational and irregular patterns of variability. Their dust declines are shallower and more symmetric than typical R CrB variables. This may indicate the two types have different dust production methods.
==== WolfRayet variables ====
Classic population I WolfRayet (WR) stars are massive hot stars that sometimes show variability, probably due to several different causes including binary interactions and rotating gas clumps around the star. While evolving they underwent intense mass loss, leaving behind a hot helium core with little hydrogen in the outer layers. They exhibit broad emission line spectra with helium, nitrogen, carbon and oxygen lines. Variations in some WR stars appear to be stochastic while others show multiple periods.
==== Gamma Cassiopeiae variables ====
Gamma Cassiopeiae (γ Cas) variables are non-supergiant fast-rotating B class emission line-type stars that fluctuate irregularly by up to 1.5 magnitudes (4 fold change in luminosity). This is caused by the ejection of matter at their equatorial regions due to the rapid rotational velocity. Gamma Cas variables are a source of bright X-ray emission, which may be due to gas accretion onto a white dwarf companion.
==== Flare stars ====
Flare stars are defined by the observation of a flare event, which is a brief but dramatic increase in stellar luminosity. In main-sequence stars major eruptive variability is uncommon. Flare activity is more likely among young stars that are spinning rapidly. The frequency of flares is more common and their prominence is more apparent among UV Ceti variables, which are very faint main-sequence stars with stronger magnetic fields. They increase in brightness by several magnitudes in just a few seconds, and then fade back to normal brightness in half an hour or less. Several nearby red dwarfs are flare stars, including Proxima Centauri and Wolf 359.
A superflare is a class of energetic, short duration flare that has been observed on Sun-like stars. It has a typical energy of at least ~1033 erg, which is greater than the strongest observed solar flare: the 1859 Carrington Event with an estimated energy of ~5×1032 erg. The Kepler space telescope light curves showed over 2,000 superflares on 250 G-type dwarfs. The occurrence rate is higher on younger, faster rotating stars.
==== RS Canum Venaticorum variables ====
These are detached binary systems with at least one of the components having a highly active chromosphere, including huge sunspots and flares, believed to be enhanced by the close companion. The former is usually an evolved star, while the latter is a lower mass star, either main-sequence or a subdwarf. Tidal forces between the stars has locked their rotation period to the orbital period, giving them a high rotation rate of a few days. They display emission lines from the chromosphere and X-ray output from the corona. Variability scales ranges from days, close to the orbital period and sometimes also with eclipses, to years as sunspot activity varies.
=== Cataclysmic or explosive variable stars ===
These variables display outbursts from thermonuclear bursts at the surface or near the core. The category also includes nova-like objects that display outbursts like a nova from a rapid release of energy, or because their spectrum resembles that of a nova at minimum light.
==== Supernovae ====

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Supernovae are the most dramatic type of cataclysmic variable, being some of the most energetic events in the universe. A supernova can briefly emit as much energy as an entire galaxy, brightening by more than 20 magnitudes (over one hundred million times brighter). The supernova explosion is caused by a white dwarf or a star core reaching a certain mass/density limit, the Chandrasekhar limit, causing the object to collapse in a fraction of a second. This collapse "bounces" and causes the star to explode and emit this enormous energy quantity. The outer layers of these stars are blown away at speeds of many thousands of kilometers per second.
The expelled matter may form nebulae called supernova remnants. A well-known example of such a nebula is the Crab Nebula, left over from a supernova that was observed in China and elsewhere in 1054. The progenitor object may either disintegrate completely in the explosion, or, in the case of a massive star, the core can become a neutron star (generally a pulsar) or a black hole.
Supernovae can result from the death of an extremely massive star, many times heavier than the Sun. At the end of the life of this massive star, a non-fusible iron core is formed from fusion ashes. The mass of this iron core is pushed towards the Chandrasekhar limit until it is surpassed and therefore collapses. One of the most studied supernovae of this type is SN 1987A in the Large Magellanic Cloud.
A supernova may also result from mass transfer onto a white dwarf from a star companion in a double star system. The Chandrasekhar limit is surpassed from the infalling matter. The absolute luminosity of this latter type is related to properties of its light curve, so that these supernovae can be used to establish the distance to other galaxies.
==== Luminous red nova ====
Luminous red novae are stellar explosions caused by the merger of two stars. They are not related to classical novae. For a brief period prior to the merger event the two components share a common envelope, which is followed by a mass ejection event that expels the envelope. They have a characteristic red appearance and a lengthy plateau phase following the initial outburst. The luminosity of these transient events lies between those of novae and supernovae, and their evolution lasts from several weeks to months. The galactic rate of these events is 0.2 per year.
==== Novae ====
Classical novae are the result of dramatic explosions, but unlike supernovae these events do not result in the destruction of the progenitor star. They form in close binary systems, with one component being a white dwarf accreting matter from the other ordinary star component, and may recur over periods of decades to centuries or millennia. Novae ignite from the sudden onset of runaway thermonuclear fusion at the base of the accreted matter, which under certain high pressure conditions (degenerate matter) accelerates explosively. They are categorised by their speed class, which range from very fast to very slow, depending on the time for the nova to decrease by 2 or 3 visual magnitudes from peak brightness. Several naked eye novae have been recorded, V1500 Cygni being the brightest in the recent history, reaching 2nd magnitude in 1975.
Recurrent novae are defined as having undergone more than one such event in recorded history. These tend to occur on higher mass white dwarfs and have smaller ejecta mass. M31N 2008-12a, a recurrent nova in the Andromeda Galaxy, erupts as often as every 12 months. It has an estimated mass close to the Chandrasekhar limit, and thus is a Type Ia supernova progenitor candidate.
==== Dwarf novae ====
Dwarf novae are double stars involving a white dwarf in which matter transfer between the component gives rise to regular outbursts. They are dimmer and repeat more often than "classical" novae. There are three types of dwarf nova:
U Geminorum stars, which have outbursts lasting roughly 520 days followed by quiet periods of typically a few hundred days. During an outburst they brighten typically by 26 magnitudes. These stars are also known as SS Cygni variables after the variable in Cygnus which produces among the brightest and most frequent displays of this variable type.
Z Camelopardalis stars, in which occasional plateaux of brightness called standstills are seen, part way between maximum and minimum brightness.
SU Ursae Majoris stars, which undergo both frequent small outbursts, and rarer but larger superoutbursts. These binary systems usually have orbital periods of under 2.5 hours.
==== Z Andromedae variables ====
These symbiotic binary systems are composed of a red giant and a compact star (typically a white dwarf) enveloped in a cloud of gas and dust. They undergo nova-like outbursts with amplitudes of 13 magnitudes, and are caused by accretion rates greater than is needed to maintain stable fusion. The prototype for this class is Z Andromedae.
==== AM CVn variables ====
AM CVn variables are symbiotic binaries where a white dwarf is accreting helium-rich material from either another white dwarf, a helium star, or an evolved main-sequence star. They can undergo complex variations, or at times no variations, with ultrashort periods. The orbital periods of these systems are in the range of 565 minutes, with those between 2244 minutes showing outburst behavior that increases the brightness by 34 magnitudes. The last is due to instabilities in the accretion disk.
=== Variable X-ray sources ===
These optically variable binary systems are sources of intense X-ray emission that do not belong to one of the other variable star categories. One of the components is an accreting compact object: either a white dwarf, neutron star, or stellar mass black hole. A notable example of such a variable X-ray source is Cygnus X-1.
==== DQ Herculis variables ====

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DQ Herculis systems are interacting binaries in which a low-mass star transfers mass to a highly magnetic white dwarf. The white dwarf spin period is significantly shorter than the binary orbital period and can sometimes be detected as a photometric periodicity. An accretion disk usually forms around the white dwarf, but its innermost regions are magnetically truncated by the white dwarf. Once captured by the white dwarf's magnetic field, the material from the inner disk travels along the magnetic field lines until it accretes. In extreme cases, the white dwarf's magnetism prevents the formation of an accretion disk.
==== AM Herculis variables ====
In these cataclysmic variables, the white dwarf's magnetic field is so strong that it synchronizes the white dwarf's spin period with the binary orbital period. Instead of forming an accretion disk, the accretion flow is channeled along the white dwarf's magnetic field lines until it impacts the white dwarf near a magnetic pole. Cyclotron radiation beamed from the accretion region can cause orbital variations of several magnitudes. BY Cam-type systems are known as asynchronous polars due to a slight (12%) difference between the rotation period and the orbital period. This asynchronity is believed to be caused by flare activity on the accreting white dwarf.
==== X-ray binaries ====
High mass X-ray binaries consist of a Be star or a supergiant in a relatively close orbit with a neutron star companion. Mass is being transferred to the accreting compact object from the donor star, which results in X-ray emission. In the case of a Be star, a gaseous disk orbiting the star at the equator is responsible for the optical variability, while the interaction of the companion is truncating the disk.
== Extrinsic variable stars ==
There are two main groups of extrinsic variables: rotating stars and eclipsing stars.
=== Rotating variable stars ===
Stars with sizeable sunspots may show significant variations in brightness as they rotate, and brighter areas of the surface are brought into view. Bright spots also occur at the magnetic poles of magnetic stars. Stars with ellipsoidal shapes may also show changes in brightness as they present varying areas of their surfaces to the observer.
==== Non-spherical stars ====
Rotating stars can vary in brightness due to their shape.
Ellipsoidal variables
These are very close binaries, the components of which are non-spherical due to their tidal interaction. As the stars rotate the area of their surface presented towards the observer changes and this in turn affects their brightness as seen from Earth. In 1920, Pi5 Orionis became the first system where this effect was clearly detected. The light curves of these systems are often quasi-sinusoidal in shape. A comparison with the radial velocity curve will often suffice to determine if the system is ellipsoidal. A further clue to an ellipsoidal variable is a rounding of the light curve at maximum. The reflection-effect, where each component illuminates the facing hemisphere of the nearby companion, is a further complication to orbit and shape analysis.
==== Stellar spots ====
For a magnetically active star, the surface is not uniformly bright, but has darker and brighter areas (like the sun's solar spots). The star's chromosphere too may vary in brightness. As the star rotates, brightness variations of a few tenths of magnitudes are observed.
FK Comae Berenices variables
These stars rotate extremely rapidly for an evolved star (~100 km/s at the equator); hence they are ellipsoidal in shape. They are (apparently) single giant stars with spectral types G and K and show strong chromospheric emission lines. Examples of this rare class are FK Com, V1794 Cygni and YY Mensae. A possible explanation for the rapid rotation of FK Comae stars is that they are the result of the merger of a (contact) binary.
BY Draconis variable stars
BY Draconis stars are a common type of variable with spectral class F, G, K or M that vary by less than 0.5 magnitudes (70% change in luminosity) with periods of a few days. The stellar magnetic field creates an inhomogeneous pattern of dark star spots and bright faculae across the surface, which are carried into and out of the line of sight by the star's rotation. These stars are typically young and rapidly rotating; they show strong emission lines in their spectrum. As the star ages, the interaction of the magnetic field with the stellar wind drags down the rotation rate, lowering the activity level.
Many stars in the spectral range of F to M-class, including the Sun, display various levels of surface activity that is driven by their magnetic dynamo. The activity can be concentrated in latitude ranges and the amplitude can vary over time based on one or more stellar cycles. For example, the Sun has a single activity cycle lasting about 11 years, with the Sun turning slightly more blue during peak activity. A long period of chromospheric inactivity on an otherwise active star is termed a Maunder minimum. This rare event happened to the Sun during the 17th century, but, as of 2012, has not been definitely identified on another star.
==== Magnetic fields ====
These variables have a magnetic field but lack significant chromospheric activity.
Alpha2 Canum Venaticorum variables
Alpha2 Canum Venaticorum (α2 CVn or ACV) variables are magnetic chemically peculiar stars of spectral class B0F0 that show fluctuations of 0.01 to 0.1 magnitudes (1% to 10%) due to differences of elemental abundances as inhomogeneously distributed across the stellar surface. I.e. they have "chemical spots". They also display spectral and magnetic field variability as they slowly rotate. The cause of the inhomogeneous energy distribution on these stars is thought to be enhanced line blanketing as chemical spectral lines are made more intense by the Zeeman effect. This results in added heating of some layers of the atmosphere as the UV flux is converted to the visual band through backwarming. This class of variable is named after the first Ap star to show rotationally-modulated photometric variability, Alpha2 Canum Venaticorum.
SX Arietis variables

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These stars are high temperature analogs of α2 CVn variables, consisting of magnetic chemically peculiar Bp stars with effective temperatures above 10,000 K. They exhibit brightness fluctuations of some 0.1 magnitude caused by chemical spots, with a cyclic period matching the rotation rate.
Optically variable pulsars
Few pulsars have been detected in visible light. These neutron stars change in brightness as they rotate. Because of the rapid rotation, brightness variations are extremely fast, from milliseconds to a few seconds. The first and the best known example is the Crab Pulsar. The exact cause of this pulsed emission is unclear, but it may be related to synchrotron radiation of electrons in the outer magnetosphere.
=== Eclipsing binaries ===
Extrinsic variables have variations in their brightness, as seen by terrestrial observers, due to some external source. One of the most common reasons for this is the presence of a binary companion star, so that the two together form a binary star. When seen from certain angles, one star may eclipse the other, causing a reduction in brightness. One of the most famous eclipsing binaries, and the first to be discovered, is Algol, or Beta Persei (β Per).
Detached, double-lined eclipsing binaries are a useful tool for testing the validity of stellar evolution models. By examining the spectral types of the components and their combined light curve, the masses and radii of both stars can be precisely determined. Under the assumption that both stars formed at the same time, the model can then be used to extrapolate their history and see if it matches the current radii of the components.
==== Algol variables ====
Algol variables undergo eclipses with one or two minima separated by periods of nearly constant light. The prototype of this class is Algol in the constellation Perseus. Most systems with Algol-type light curves are detached binaries. However, some definitions of Algol variables apply to semi-detached binary systems, where one of the components has filled its Roche lobe and is transferring mass to the companion star. These are dubbed classical Algol systems, with Algol itself being one such semi-detached system.
==== Double Periodic variables ====
Double periodic variables (DPVs) are Algol-like, consisting of a semidetached binary system where the primary has at least seven times the mass of the Sun and the secondary, now with 13 times the mass of the Sun, is overflowing its Roche lobe. The primary component is orbited by a massive, optically-thick accretion disk. The system shows a long period of photometric variation that is about 35 times the orbital period. The smaller donor star is tidally locked to the orbital period, and this rapid rotation may be driving a magnetic dynamo. This in turn may be causing the longer period variation by modulating the mass transfer rate. An example of a DPV is V393 Scorpii.
==== Beta Lyrae variables ====
Beta Lyrae (β Lyr) variables are close eclipsing binaries, named after the prototype star Beta Lyrae, or Sheliak. The gravitational interaction of the components causes at least one member to form an ellipsoidal shape, resulting in a light curve that varies continually even outside the eclipse. In the Beta Lyrae system, one of the components is overflowing its Roche lobe, creating a mass exchange. This flow of material is adding features to the light curve. Many Beta Lyrae-type variables are also double periodic variables, including Beta Lyrae itself.
==== W Serpentis variables ====
W Serpentis is the prototype of a class of semi-detached binaries including a giant or supergiant transferring material to a massive more compact star. The latter star has an optically-thick accretion disk, and the mass transfer rate is higher than in Algol variables. They are characterised, and distinguished from the similar β Lyr systems, by strong UV emission from accretions hotspots on a disc of material. The light curve can be noisy and the orbital period is often variable.
==== W Ursae Majoris variables ====
The stars in the W UMa group of eclipsing variables show periods of less than a day. The components are so closely situated to each other that their surfaces are almost in contact with each other. They are termed over-contact eclipsing binaries, and they share a common envelope. As a result, the spectral type does not change during an orbit. Their orbit is circular and the components are in synchronous rotation with the orbital period.
=== Planetary transits ===
Stars with planets show brightness variations if their planets pass between Earth and the star. For the Sun, this occurs with the planets inferior to the Earth, namely Mercury and Venus. With exoplanets, these variations are much smaller than those seen with stellar companions, but are detectable using photometric observations with a sufficiently high signal-to-noise ratio. Examples include HD 209458, WASP-43, and all of the planets and planet candidates detected by the Kepler and TESS space-based missions.
== See also ==
Guest star
Irregular variable
List of transiting exoplanets
List of variable stars
== References ==
== Further reading ==
Eddington, A.S.; Plakidis, S. (1929). "Irregularities of Period of Long Period Variable Stars". Monthly Notices of the Royal Astronomical Society. 90 (1). London, UK: 6571. doi:10.1093/mnras/90.1.65. Retrieved February 17, 2023.
== External links ==
The American Association of Variable Star Observers
GCVS Variability Types
Society for Popular Astronomy Variable Star Section

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In general relativity, a white hole is a hypothetical region of spacetime and singularity that cannot be entered from the outside, although energy, matter, light and information can escape from it. In this sense, it is the opposite of a black hole, from which energy, matter, light and information cannot escape. White holes appear in the theory of eternal black holes. In addition to a black hole region in the future, such a solution of the Einstein field equations has a white hole region in its past. This region does not exist for black holes that have formed through gravitational collapse, however, nor are there any observed physical processes through which a white hole could be formed.
Supermassive black holes (SMBHs) are theoretically predicted to be at the center of every galaxy and may be essential for their formation. Stephen Hawking and others have proposed that these supermassive black holes could spawn supermassive white holes.
== Overview ==
Like black holes, white holes have properties such as mass, charge, and angular momentum. They attract matter like any other mass, but objects falling towards a white hole would never actually reach the white hole's event horizon (though in the case of the maximally extended Schwarzschild solution, discussed below, the white hole event horizon in the past becomes a black hole event horizon in the future, so any object falling towards it will eventually reach the black hole horizon). Imagine a gravitational field, without a surface. Acceleration due to gravity is the greatest on the surface of any body. But since black holes lack a surface, acceleration due to gravity increases exponentially, but never reaches a final value as there is no considered surface in a singularity.
In quantum mechanics, the black hole emits Hawking radiation and so it can come to thermal equilibrium with a gas of radiation (not compulsory). Because a thermal-equilibrium state is time-reversal-invariant, Stephen Hawking argued that the time reversal of a black hole in thermal equilibrium results in a white hole in thermal equilibrium (each absorbing and emitting energy to equivalent degrees). Consequently, this may imply that black holes and white holes are reciprocal in structure, wherein the Hawking radiation from an ordinary black hole is identified with a white hole's emission of energy and matter. Hawking's semi-classical argument is reproduced in a quantum mechanical AdS/CFT treatment, where a black hole in anti-de Sitter space is described by a thermal gas in a gauge theory, whose time reversal is the same as itself.
== History ==

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In the 1930s, physicists Robert Oppenheimer and Hartland Snyder introduced the idea of white holes as a solution to Einstein's equations of general relativity. These equations, the foundation of modern physics, describe the curvature of spacetime due to massive objects. Whereas black holes are born from the collapse of stars, white holes represent the theoretical birth of space, time, and potentially even universes. At the center, space and time do not end into a singularity, but continue across a short transition region where the Einstein equations are violated by quantum effects. From this region, space and time emerge with the structure of a white hole interior, a possibility already suggested by John Lighton Synge.
The possibility of the existence of white holes was put forward by cosmologist Igor Novikov in 1964, developed by Nikolai Kardashev. White holes are predicted as part of a solution to the Einstein field equations known as the maximally extended version of the Schwarzschild metric describing an eternal black hole with no charge and no rotation. Here, "maximally extended" implies that spacetime should not have any "edges". For any possible trajectory of a free-falling particle (following a geodesic) in spacetime, it should be possible to continue this path arbitrarily far into the particle's future, unless the trajectory hits a gravitational singularity like the one at the center of the black hole's interior. In order to satisfy this requirement, it turns out that in addition to the black hole interior region that particles enter when they fall through the event horizon from the outside, there must be a separate white hole interior region, which allows us to extrapolate the trajectories of particles that an outside observer sees rising up away from the event horizon. For an observer outside using Schwarzschild coordinates, infalling particles take an infinite time to reach the black hole horizon infinitely far in the future, while outgoing particles that pass the observer have been traveling outward for an infinite time since crossing the white hole horizon infinitely far in the past (however, the particles or other objects experience only a finite proper time between crossing the horizon and passing the outside observer). The black hole/white hole appears "eternal" from the perspective of an outside observer, in the sense that particles traveling outward from the white hole interior region can pass the observer at any time, and particles traveling inward, which will eventually reach the black hole interior region can also pass the observer at any time.
Just as there are two separate interior regions of the maximally extended spacetime, there are also two separate exterior regions, sometimes called two different "universes", with the second universe allowing us to extrapolate some possible particle trajectories in the two interior regions. This means that the interior black-hole region can contain a mix of particles that fell in from either universe (and thus an observer who fell in from one universe might be able to see light that fell in from the other one), and likewise particles from the interior white-hole region can escape into either universe. All four regions can be seen in a spacetime diagram that uses KruskalSzekeres coordinates (see figure).
In this spacetime, it is possible to come up with coordinate systems such that if one picks a hypersurface of constant time (a set of points that all have the same time coordinate, such that every point on the surface has a space-like separation, giving what is called a 'space-like surface') and draw an "embedding diagram" depicting the curvature of space at that time, the embedding diagram will look like a tube connecting the two exterior regions, known as an "Einstein-Rosen bridge" or Schwarzschild wormhole. Depending on where the space-like hypersurface is chosen, the Einstein-Rosen bridge can either connect two black hole event horizons in each universe (with points in the interior of the bridge being part of the black hole region of the spacetime), or two white hole event horizons in each universe (with points in the interior of the bridge being part of the white hole region). It is impossible to use the bridge to cross from one universe to the other, however, because it is impossible to enter a white hole event horizon from the outside, and anyone entering a black hole horizon from either universe will inevitably hit the black hole singularity.
Note that the maximally extended Schwarzschild metric describes an idealized black hole/white hole that exists eternally from the perspective of external observers; a more realistic black hole that forms at some particular time from a collapsing star would require a different metric. When the infalling stellar matter is added to a diagram of a black hole's history, it removes the part of the diagram corresponding to the white hole interior region. But because the equations of general relativity are time-reversible they exhibit Time reversal symmetry general relativity must also allow the time-reverse of this type of "realistic" black hole that forms from collapsing matter. The time-reversed case would be a white hole that has existed since the beginning of the universe, and that emits matter until it finally "explodes" and disappears. Despite the fact that such objects are permitted theoretically, they are not taken as seriously as black holes by physicists, since there would be no processes that would naturally lead to their formation; they could exist only if they were built into the initial conditions of the Big Bang. Additionally, it is predicted that such a white hole would be highly "unstable" in the sense that if any small amount of matter fell towards the horizon from the outside, this would prevent the white hole's explosion as seen by distant observers, with the matter emitted from the singularity never able to escape the white hole's gravitational radius.

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title: "White hole"
chunk: 3/4
source: "https://en.wikipedia.org/wiki/White_hole"
category: "reference"
tags: "science, encyclopedia"
date_saved: "2026-05-05T13:33:53.430075+00:00"
instance: "kb-cron"
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== Properties ==
Depending on the type of black hole solution considered, there are several types of white holes. In the case of the Schwarzschild black hole mentioned above, a geodesic coming out of a white hole comes from the "gravitational singularity" it contains. In the case of a black hole possessing an electric charge (Reissner-Nordström black hole) or an angular momentum (Kerr black hole), then the white hole happens to be the "exit door" of a black hole existing in another universe. Such a black hole white hole configuration is called a wormhole. In both cases, however, it is not possible to reach the region "in" the white hole, so the behavior of it and, in particular, what may come out of it is completely impossible to predict. In this sense, a white hole is a configuration according to which the evolution of the universe cannot be predicted, because it is not deterministic. A "bare singularity" is another example of a non-deterministic configuration, but does not have the status of a white hole, however, because there is no region inaccessible from a given region. In its basic conception, the Big Bang can be seen as a naked singularity in outer space, but does not correspond to a white hole.
== Physical relevance ==
In its mode of formation, a black hole comes from a residue of a massive star whose core contracts until it turns into a black hole. Such a configuration is not static: it starts with a massive and extended body which contracts to give a black hole. The black hole therefore does not exist for all eternity, and there is no corresponding white hole.
To be able to exist, a white hole must either arise from a physical process leading to its formation, or be present from the creation of the universe. None of these solutions appear satisfactory: there is no known astrophysical process that can lead to the formation of such a configuration, and imposing it from the creation of the universe amounts to assuming a very specific set of initial conditions which has no concrete motivation.
In view of the enormous quantities radiated by quasars, whose luminosity makes it possible to observe them from several billion light-years away, it had been assumed that they were the seat of exotic physical phenomena such as a white hole, or a phenomenon of continuous creation of matter (see the article on the steady state theory). These ideas are now abandoned, the observed properties of quasars being very well explained by those of an accretion disk in the center of which is a supermassive black hole.
== Big Bang/Supermassive white hole ==
A view of black holes first proposed in the late 1980s might be interpreted as shedding some light on the nature of classical white holes. Some researchers have proposed that when a black hole forms, a Big Bang may occur at the core/singularity, which would create a new universe that expands outside of the parent universe.
The EinsteinCartanSciamaKibble theory of gravity extends general relativity by removing a constraint of the symmetry of the affine connection and regarding its antisymmetric part, the torsion tensor, as a dynamical variable. Torsion naturally accounts for the quantum-mechanical, intrinsic angular momentum (spin) of matter. According to general relativity, the gravitational collapse of a sufficiently compact mass forms a singular black hole. In the EinsteinCartan theory, however, the minimal coupling between torsion and Dirac spinors generates a repulsive spinspin interaction that is significant in fermionic matter at extremely high densities. Such an interaction prevents the formation of a gravitational singularity. Instead, the collapsing matter on the other side of the event horizon reaches an enormous but finite density and rebounds, forming a regular EinsteinRosen bridge. The other side of the bridge becomes a new, growing baby universe. For observers in the baby universe, the parent universe appears as the only white hole. Accordingly, the observable universe is the EinsteinRosen interior of a black hole existing as one of possibly many inside a larger universe. The Big Bang was a nonsingular Big Bounce at which the observable universe had a finite, minimum scale factor.
Shockwave cosmology, proposed by Joel Smoller and Blake Temple in 2003, has the "big bang" as an explosion inside a black hole, producing the expanding volume of space and matter that includes the observable universe. This black hole eventually becomes a white hole as the matter density reduces with the expansion. A related theory gives an alternative to dark energy.
A 2012 paper argues that the Big Bang itself is a white hole. It further suggests that the emergence of a white hole, which was named a "Small Bang", is spontaneous—all the matter is ejected at a single pulse. Thus, unlike black holes, white holes cannot be continuously observed; rather, their effects can be detected only around the event itself. The paper even proposed identifying a new group of gamma-ray bursts with white holes.
=== Various hypotheses ===
Unlike black holes for which there is a well-studied physical process (i.e. gravitational collapse, which gives rise to black holes when a star somewhat more massive than the sun exhausts its nuclear "fuel"), there is no clear analogous process that leads reliably to the production of white holes. Some hypotheses have been put forward:

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