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| title | chunk | source | category | tags | date_saved | instance |
|---|---|---|---|---|---|---|
| Cosmic distance ladder | 2/7 | https://en.wikipedia.org/wiki/Cosmic_distance_ladder | reference | science, encyclopedia | 2026-05-05T13:32:00.949192+00:00 | kb-cron |
=== Problems === Two problems exist for any class of standard candle. The principal one is calibration, that is the determination of exactly what the absolute magnitude of the candle is. This includes defining the class well enough that members can be recognized, and finding enough members of that class with well-known distances to allow their true absolute magnitude to be determined with enough accuracy. The second problem lies in recognizing members of the class, and not mistakenly using a standard candle calibration on an object which does not belong to the class. At extreme distances, which is where one most wishes to use a distance indicator, this recognition problem can be quite serious. A significant issue with standard candles is the recurring question of how standard they are. For example, all observations seem to indicate that Type Ia supernovae that are of known distance have the same brightness, corrected by the shape of the light curve. The basis for this closeness in brightness is discussed below; however, the possibility exists that the distant Type Ia supernovae have different properties than nearby Type Ia supernovae. The use of Type Ia supernovae is crucial in determining the correct cosmological model. If indeed the properties of Type Ia supernovae are different at large distances, i.e. if the extrapolation of their calibration to arbitrary distances is not valid, ignoring this variation can dangerously bias the reconstruction of the cosmological parameters, in particular the reconstruction of the matter density parameter. That this is not merely a philosophical issue can be seen from the history of distance measurements using Cepheid variables. In the 1950s, Walter Baade discovered that the nearby Cepheid variables used to calibrate the standard candle were of a different type than the ones used to measure distances to nearby galaxies. The nearby Cepheid variables were population I stars with much higher metal content than the distant population II stars. As a result, the population II stars were actually much brighter than believed, and when corrected, this had the effect of doubling the estimates of distances to the globular clusters, the nearby galaxies, and the diameter of the Milky Way. Most recently kilonovae have been proposed as another type of standard candle. "Since kilonovae explosions are spherical, astronomers could compare the apparent size of a supernova explosion with its actual size as seen by the gas motion, and thus measure the rate of cosmic expansion at different distances."
== Standard siren == Gravitational waves originating from the inspiral phase of compact binary systems, such as neutron stars or black holes, have the useful property that energy emitted as gravitational radiation comes exclusively from the orbital energy of the pair, and the resultant shrinking of their orbits is directly observable as an increase in the frequency of the emitted gravitational waves. To leading order, the rate of change of frequency
f
{\displaystyle f}
is given by
d
f
d
t
=
96
π
8
/
3
(
G
M
)
5
3
f
11
3
5
c
5
,
{\displaystyle {\frac {df}{dt}}={\frac {96\pi ^{8/3}(G{\mathcal {M}})^{\frac {5}{3}}f^{\frac {11}{3}}}{5\,c^{5}}},}
where
G
{\displaystyle G}
is the gravitational constant,
c
{\displaystyle c}
is the speed of light, and
M
{\displaystyle {\mathcal {M}}}
is a single (therefore computable) number called the chirp mass of the system, a combination of the masses
(
m
1
,
m
2
)
{\displaystyle (m_{1},m_{2})}
of the two objects
M
=
(
m
1
m
2
)
3
/
5
(
m
1
+
m
2
)
1
/
5
.
{\displaystyle {\mathcal {M}}={\frac {(m_{1}m_{2})^{3/5}}{(m_{1}+m_{2})^{1/5}}}.}