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Einstein@Home has carried out many analysis runs using data from the LIGO instruments. Since its first search run in 2005, the sensitivity of the LIGO detectors has been improved in a series of steps and upgrades. This is continuing with the current Advanced LIGO detectors. At the same time, Einstein@Home search algorithms have also improved. Together these have increased the search sensitivity by several orders of magnitude. Einstein@Home's first analysis used data from the "third science run" (S3) of LIGO. Processing of the S3 data set was conducted between 22 February 2005 and 2 August 2005. This analysis employed 60 segments from the LIGO Hanford 4-km detector, totaling ten hours of data each. Each 10-hour segment was analyzed for CW signals by the volunteers' computers using a matched-filtering technique. When all matched-filtering results were returned, the results from different segments were then combined in a "post-processing step" on Einstein@Home servers via a coincidence scheme to further enhance search sensitivity. Results were published on the Einstein@Home webpages. Work on the S4 data set (LIGO's fourth science run) was started via interlacing with the S3 calculations and finished in July 2006. This analysis used 10 segments of 30 hours each from the LIGO Hanford 4-km detector and 7 segments of 30 hours each from the LIGO Livingston 4-km detector. Besides the S4 data being more sensitive, a more sensitive coincidence combination scheme was also applied in the post-processing. The results of this search have led to the first scientific publication of Einstein@Home in Physical Review D. Einstein@Home gained considerable attention in the international volunteer computing community when an optimized application for the S4 data set analysis was developed and released in March 2006 by project volunteer Akos Fekete, a Hungarian programmer. Fekete improved the official S4 application and introduced SSE, 3DNow! and SSE3 optimizations into the code improving performance by up to 800%. Fekete was recognized for his efforts and was afterward officially involved with the Einstein@Home team in the development of the new S5 application. As of late July 2006, this new official application had become widely distributed among Einstein@Home users. The app created a large surge in the project's total performance and productivity, as measured by floating point speed (or FLOPS), which over time has increased by approximately 50% compared to non-optimized S4 applications. The first Einstein@Home analysis of the early LIGO S5 data set, where the instruments initially reached their design sensitivity, began on 15 June 2006. This search used 22 segments of 30 hours each from the LIGO Hanford 4-km detector and six segments of 30 hours from the LIGO Livingston 4-km detector. This analysis run (code name "S5R1"), employing the search methodology as Einstein@Home, was very similar to the previous S4 analysis. However, the search results were more sensitive due to the use of more data of better quality compared to S4. Over large parts of the search parameter space, these results, which also appeared in Physical Review D, are the most exhaustive published to date. The second Einstein@Home search of LIGO S5 data (code name "S5R3") constituted a further major improvement regarding search sensitivity. As opposed to previous searches, the ensuing results were already combined on the volunteers' computers via a Hough transform technique. This method matched-filtered results from 84 data segments of 25 hours each, parameters from which came from both 4-km LIGO Hanford and Livingston instruments. On 7 May 2010, a new Einstein@Home search (code name "S5GC1"), which uses a significantly improved search method, launched. This program analyzed 205 data segments of 25 hours each, using data from both 4-km LIGO Hanford and Livingston instruments. It employed a technique which exploited global parameter-space correlations to efficiently combine the matched-filtering results from the different segments. Results from an Einstein@Home all-sky search for continuous gravitational waves in LIGO S5 data were published on 13 February 2013. In the most sensitive frequency band of the search (a half-Hertz band at 152.5 Hertz), the presence of periodic gravitational waves with strain amplitude larger than 7.6×1025 could be excluded at 90% confidence. Overall, the search was 3 times as sensitive as previous Einstein@Home searches in LIGO S5 data. Details of the two-stage follow-up procedure for signal candidates used in this study were published on 25 June 2014. A search for high-frequency (1249 Hertz to 1499 Hertz) continuous gravitational waves in LIGO S5 data by Einstein@Home, published on 26 September 2016, was the only such search in LIGO data. No signal candidates were identified. The search excluded neutron stars with spin frequencies between 625 Hertz and 770 Hertz and with ellipticities greater than 2.8×107 closer than 100 parsec to Earth. Data from LIGO 6th science run (S6) were analyzed by Einstein@Home and the results were published on 18 November 2016. No signal was found and the search set the most stringent upper limits for an all-sky search for continuous gravitational waves at the time of publication. In the most sensitive frequency band between 170.5 Hertz and 171 Hertz there were (with 90% confidence) no continuous gravitational waves with a strain amplitude of more than 5.5×1025 detected. At frequencies of 230 Hertz, the search results exclude neutron stars with ellipticities greater than 106 within 100 parsecs of Earth. Einstein@Home conducted a directed search for continuous gravitational waves from the central object in the supernova remnant Cassiopeia A. It used data from the LIGO S6 run and searched over a range of frequencies from 50 Hertz to 1000 Hertz, because the spin frequency of the central object is unknown. No signal was found. The upper limits on gravitational-wave emission from Cassiopeia A were the most stringent at the time of publication, about a factor two lower than previous upper limits. On 28 December 2016 results from a follow-up of the all-sky search for continuous gravitational waves in LIGO S6 data were published. Out of a total of 3.8 × 1010 signal candidates from the earlier search, the 16 million most promising were analyzed using a four-stage hierarchical process. No candidate was found to be consistent with an astrophysical source of continuous gravitational waves. In the frequency band between 170.5 Hertz and 171 Hertz the upper limit (90% confidence) on the strain amplitude was 4.3×1025, a factor 1.3 lower than in the previous search. Searches for continuous gravitational waves are limited by the available computing power. Within the project, research on improving the sensitivity of the searches with new methods is conducted. In late 2017 two publications were published, describing improved methods of candidate clustering in the hierarchical searches and new "veto" methods that distinguish between astrophysical continuous gravitational waves and detector artifacts mimicking them. Both these new methods were employed in the first Einstein@Home all-sky search for continuous gravitational waves in Advanced LIGO data from the first observing run (O1), the results of which were published on 8 December 2017. The first part of the search investigated the lower end of the LIGO frequency band between 20 Hertz and 100 Hertz. No signals were found. The most stringent upper limit (90% confidence) on the gravitational-wave strain amplitude set by the search was 1.8×1025 at a frequency of 100 Hertz.