Millisecond pulsar

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This diagram shows the steps astronomers say are needed to create a pulsar with a superfast spin. 1. A massive supergiant star and a "normal" Sun-like star orbit each other. 2. The massive star explodes, leaving a pulsar that eventually slows down, turns off, and becomes a cooling neutron star. 3. The Sun-like star eventually expands, spilling material on to the neutron star. This "accretion" speeds up the neutron star's spin. 4. Accretion ends, the neutron star is "recycled" into a millisecond pulsar. But in a densely packed globular cluster (2b)... The lowest mass stars are ejected, the remaining normal stars evolve, and the "recycling" scenario (3-4) takes place, creating many millisecond pulsars. Millisecond Pulsar.jpg
This diagram shows the steps astronomers say are needed to create a pulsar with a superfast spin. 1. A massive supergiant star and a "normal" Sun-like star orbit each other. 2. The massive star explodes, leaving a pulsar that eventually slows down, turns off, and becomes a cooling neutron star. 3. The Sun-like star eventually expands, spilling material on to the neutron star. This "accretion" speeds up the neutron star's spin. 4. Accretion ends, the neutron star is "recycled" into a millisecond pulsar. But in a densely packed globular cluster (2b)... The lowest mass stars are ejected, the remaining normal stars evolve, and the "recycling" scenario (3-4) takes place, creating many millisecond pulsars.

A millisecond pulsar (MSP) is a pulsar with a rotational period less than about 10 milliseconds. Millisecond pulsars have been detected in radio, X-ray, and gamma ray portions of the electromagnetic spectrum. The leading hypothesis for the origin of millisecond pulsars is that they are old, rapidly rotating neutron stars that have been spun up or "recycled" through accretion of matter from a companion star in a close binary system. [1] [2] For this reason, millisecond pulsars are sometimes called recycled pulsars.

Contents

Origins

Millisecond pulsars are thought to be related to low-mass X-ray binary systems. It is thought that the X-rays in these systems are emitted by the accretion disk of a neutron star produced by the outer layers of a companion star that has overflowed its Roche lobe. The transfer of angular momentum from this accretion event can increase the rotation rate of the pulsar to hundreds of times per second, as is observed in millisecond pulsars.

There has been recent evidence that the standard evolutionary model fails to explain the evolution of all millisecond pulsars, especially young millisecond pulsars with relatively high magnetic fields, e.g. PSR B1937+21. Bülent Kiziltan and S. E. Thorsett (UCSC) showed that different millisecond pulsars must form by at least two distinct processes. [3] But the nature of the other process remains a mystery. [4]

Many millisecond pulsars are found in globular clusters. This is consistent with the spin-up hypothesis of their formation, as the extremely high stellar density of these clusters implies a much higher likelihood of a pulsar having (or capturing) a giant companion star. Currently there are approximately 130 millisecond pulsars known in globular clusters. [5] The globular cluster Terzan 5 contains 37 of these, followed by 47 Tucanae with 22 and M28 and M15 with 8 pulsars each.

Pulsar rotational speed limits

The stellar grouping Terzan 5 The star cluster Terzan 5.jpg
The stellar grouping Terzan 5

The first millisecond pulsar, PSR B1937+21, was discovered in 1982 by Backer et al. [6] Spinning roughly 641 times per second, it remains the second fastest-spinning millisecond pulsar of the approximately 200 that have been discovered. [7] Pulsar PSR J1748-2446ad, discovered in 2004, is the fastest-spinning pulsar known, as of 2023, spinning 716 times per second. [8] [9]

Current models of neutron star structure and evolution predict that pulsars would break apart if they spun at a rate of c. 1500 rotations per second or more, [10] [11] and that at a rate of above about 1000 rotations per second they would lose energy by gravitational radiation faster than the accretion process would accelerate them. [12]

In early 2007 data from the Rossi X-ray Timing Explorer and INTEGRAL spacecraft discovered a neutron star XTE J1739-285 rotating at 1122 Hz. [13] The result is not statistically significant, with a significance level of only 3 sigma. While it is an interesting candidate for further observations, current results are inconclusive. Still, it is believed that gravitational radiation plays a role in slowing the rate of rotation. One X-ray pulsar that spins at 599 revolutions per second, IGR J00291+5934, is a prime candidate for helping detect such waves in the future (most such X-ray pulsars only spin at around 300 rotations per second).

Millisecond pulsars, which can be timed with high precision, have a stability comparable to atomic-clock-based time standards when averaged over decades. [14] [15] This also makes them very sensitive probes of their environments. For example, anything placed in orbit around them causes periodic Doppler shifts in their pulses' arrival times on Earth, which can then be analyzed to reveal the presence of the companion and, with enough data, provide precise measurements of the orbit and the object's mass. The technique is so sensitive that even objects as small as asteroids can be detected if they happen to orbit a millisecond pulsar. The first confirmed exoplanets, discovered several years before the first detections of exoplanets around "normal" solar-like stars, were found in orbit around a millisecond pulsar, PSR B1257+12. These planets remained, for many years, the only Earth-mass objects known outside of the Solar System. One of them, PSR B1257+12 b, has an even smaller mass, just under twice that of the Moon, and is still today the smallest-mass object known beyond the Solar System. [16]

Gravitational wave detection using pulsar timing

Gravitational waves are an important prediction from Einstein's general theory of relativity and result from the bulk motion of matter, fluctuations during the early universe and the dynamics of space-time itself. Pulsars are rapidly rotating, highly magnetized neutron stars formed during the supernova explosions of massive stars. They act as highly accurate clocks with a wealth of physical applications ranging from celestial mechanics, neutron star seismology, tests of strong-field gravity and Galactic astronomy.

The proposal to use pulsars as gravitational wave detectors was originally made by Sazhin [17] and Detweiler [18] in the late 1970s. The idea is to treat the solar system barycenter and a distant pulsar as opposite ends of an imaginary arm in space. The pulsar acts as the reference clock at one end of the arm sending out regular signals which are monitored by an observer on the Earth. The effect of a passing gravitational wave would be to perturb the local space-time metric and cause a change in the observed rotational frequency of the pulsar.

Plot of correlation between pulsars observed by NANOGrav (2023) vs angular separation between pulsars, compared with a theoretical model (dashed purple) and if there were no gravitational wave background (solid green) Correlation vs angular separation between pulsars.svg
Plot of correlation between pulsars observed by NANOGrav (2023) vs angular separation between pulsars, compared with a theoretical model (dashed purple) and if there were no gravitational wave background (solid green)

Hellings and Downs [21] extended this idea in 1983 to an array of pulsars and found that a stochastic background of gravitational waves would produce a quadrupolar correlation between different pulsar pairs as a function of their angular separations on the sky. This work was limited in sensitivity by the precision and stability of the pulsar clocks in the array. Following the discovery of the first millisecond pulsar in 1982, Foster and Backer [22] improved the sensitivity to gravitational waves by applying in 1990 the Hellings-Downs analysis to an array of highly stable millisecond pulsars.

The advent of digital data acquisition systems, new radio telescopes and receiver systems, and the discoveries of many new millisecond pulsars advanced the sensitivity of the pulsar timing array to gravitational waves in the early stages of the international effort. [23] The five-year data release, analysis, and first NANOGrav limit on the stochastic gravitational wave background were described in 2013 by Demorest et al. [24] It was followed by the nine-year and 11-year data releases in 2015 and 2018, respectively. Each further limited the gravitational wave background and, in the second case, techniques to precisely determine the barycenter of the solar system were refined.

In 2020, the collaboration presented the 12.5-year data release, which included strong evidence for a power-law stochastic process with common strain amplitude and spectral index across all pulsars, but statistically inconclusive data for the critical Hellings-Downs quadrupolar spatial correlation. [25] [26]

In June 2023, NANOGrav published the 15-year data release, which contained the first evidence for a stochastic gravitational wave background. In particular, it included the first measurement of the Hellings-Downs curve, [27] the tell-tale sign of the gravitational wave origin of the observations. [28] [29]

Related Research Articles

<span class="mw-page-title-main">Neutron star</span> Collapsed core of a massive star

A neutron star is the collapsed core of a massive supergiant star. It results from the supernova explosion of a massive star—combined with gravitational collapse—that compresses the core past white dwarf star density to that of atomic nuclei. Surpassed only by black holes, neutron stars are the second smallest and densest known class of stellar objects. Neutron stars have a radius on the order of 10 kilometers (6 mi) and a mass of about 1.4 M☉. Stars that collapse into neutron stars have a total mass of between 10 and 25 solar masses (M☉), or possibly more for those that are especially rich in elements heavier than hydrogen and helium.

<span class="mw-page-title-main">Einstein@Home</span> BOINC volunteer computing project that analyzes data from LIGO to detect gravitational waves

Einstein@Home is a volunteer computing project that searches for signals from spinning neutron stars in data from gravitational-wave detectors, from large radio telescopes, and from a gamma-ray telescope. Neutron stars are detected by their pulsed radio and gamma-ray emission as radio and/or gamma-ray pulsars. They also might be observable as continuous gravitational wave sources if they are rapidly spinning and non-axisymmetrically deformed. The project was officially launched on 19 February 2005 as part of the American Physical Society's contribution to the World Year of Physics 2005 event.

<span class="mw-page-title-main">Pulsar</span> Rapidly rotating neutron star

A pulsar is a highly magnetized rotating neutron star that emits beams of electromagnetic radiation out of its magnetic poles. This radiation can be observed only when a beam of emission is pointing toward Earth, and is responsible for the pulsed appearance of emission. Neutron stars are very dense and have short, regular rotational periods. This produces a very precise interval between pulses that ranges from milliseconds to seconds for an individual pulsar. Pulsars are one of the candidates for the source of ultra-high-energy cosmic rays.

<span class="mw-page-title-main">Crab Pulsar</span> Pulsar in the constellation Taurus

The Crab Pulsar is a relatively young neutron star. The star is the central star in the Crab Nebula, a remnant of the supernova SN 1054, which was widely observed on Earth in the year 1054. Discovered in 1968, the pulsar was the first to be connected with a supernova remnant.

<span class="mw-page-title-main">Hulse–Taylor pulsar</span> Pulsar in the constellation Aquila

The Hulse–Taylor pulsar is a binary star system composed of a neutron star and a pulsar which orbit around their common center of mass. It is the first binary pulsar ever discovered.

<span class="mw-page-title-main">Gravitational wave background</span> Random background of gravitational waves permeating the Universe

The gravitational wave background is a random background of gravitational waves permeating the Universe, which is detectable by gravitational-wave experiments, like pulsar timing arrays. The signal may be intrinsically random, like from stochastic processes in the early Universe, or may be produced by an incoherent superposition of a large number of weak independent unresolved gravitational-wave sources, like supermassive black-hole binaries. Detecting the gravitational wave background can provide information that is inaccessible by any other means about astrophysical source population, like hypothetical ancient supermassive black-hole binaries, and early Universe processes, like hypothetical primordial inflation and cosmic strings.

<span class="mw-page-title-main">Binary pulsar</span> Two pulsars orbiting each other

A binary pulsar is a pulsar with a binary companion, often a white dwarf or neutron star. Binary pulsars are one of the few objects which allow physicists to test general relativity because of the strong gravitational fields in their vicinities. Although the binary companion to the pulsar is usually difficult or impossible to observe directly, its presence can be deduced from the timing of the pulses from the pulsar itself, which can be measured with extraordinary accuracy by radio telescopes.

<span class="mw-page-title-main">Gravitational wave</span> Aspect of relativity in physics

Gravitational waves are transient displacements in a gravitational field – generated by the relative motion of gravitating masses – that radiate outward from their source at the speed of light. They were first proposed by Oliver Heaviside in 1893 and then later by Henri Poincaré in 1905 as the gravitational equivalent of electromagnetic waves. In 1916, Albert Einstein demonstrated that gravitational waves result from his general theory of relativity as ripples in spacetime.

<span class="mw-page-title-main">Gravitational-wave observatory</span> Device used to measure gravitational waves

A gravitational-wave detector is any device designed to measure tiny distortions of spacetime called gravitational waves. Since the 1960s, various kinds of gravitational-wave detectors have been built and constantly improved. The present-day generation of laser interferometers has reached the necessary sensitivity to detect gravitational waves from astronomical sources, thus forming the primary tool of gravitational-wave astronomy.

<span class="mw-page-title-main">Gravitational-wave astronomy</span> Branch of astronomy using gravitational waves

Gravitational-wave astronomy is a subfield of astronomy concerned with the detection and study of gravitational waves emitted by astrophysical sources.

<span class="mw-page-title-main">PSR B1937+21</span> Pulsar in the constellation Vulpecula

PSR B1937+21 is a pulsar located in the constellation Vulpecula a few degrees in the sky away from the first discovered pulsar, PSR B1919+21. The name PSR B1937+21 is derived from the word "pulsar" and the declination and right ascension at which it is located, with the "B" indicating that the coordinates are for the 1950.0 epoch. PSR B1937+21 was discovered in 1982 by Don Backer, Shri Kulkarni, Carl Heiles, Michael Davis, and Miller Goss.

A pulsar timing array (PTA) is a set of galactic pulsars that is monitored and analyzed to search for correlated signatures in the pulse arrival times on Earth. As such, they are galactic-sized detectors. Although there are many applications for pulsar timing arrays, the best known is the use of an array of millisecond pulsars to detect and analyse long-wavelength gravitational wave background. Such a detection would entail a detailed measurement of a gravitational wave (GW) signature, like the GW-induced quadrupolar correlation between arrival times of pulses emitted by different millisecond pulsar pairings that depends only on the pairings' angular separations in the sky. Larger arrays may be better for GW detection because the quadrupolar spatial correlations induced by GWs can be better sampled by many more pulsar pairings. With such a GW detection, millisecond pulsar timing arrays would open a new low-frequency window in gravitational-wave astronomy to peer into potential ancient astrophysical sources and early Universe processes, inaccessible by any other means.

PSR J0108−1431 is a solitary pulsar located at a distance of about 130 parsecs (424 light-years) in the constellation Cetus. This pulsar was discovered in 1994 during the Parkes Southern Pulsar Survey. It is considered a very old pulsar with an estimated age of 166 million years and a rotation period of 0.8 seconds. The rotational energy being generated by the spin-down of this pulsar is 5.8 × 1023 W and the surface magnetic field is 2.5 × 107 T. As of 2008, it is the second faintest known pulsar.

PSR J1614–2230 is a pulsar in a binary system with a white dwarf in the constellation Scorpius. It was discovered in 2006 with the Parkes telescope in a survey of unidentified gamma ray sources in the Energetic Gamma Ray Experiment Telescope catalog. PSR J1614–2230 is a millisecond pulsar, a type of neutron star, that spins on its axis roughly 317 times per second, corresponding to a period of 3.15 milliseconds. Like all pulsars, it emits radiation in a beam, similar to a lighthouse. Emission from PSR J1614–2230 is observed as pulses at the spin period of PSR J1614–2230. The pulsed nature of its emission allows for the arrival of individual pulses to be timed. By measuring the arrival time of pulses, astronomers observed the delay of pulse arrivals from PSR J1614–2230 when it was passing behind its companion from the vantage point of Earth. By measuring this delay, known as the Shapiro delay, astronomers determined the mass of PSR J1614–2230 and its companion. The team performing the observations found that the mass of PSR J1614–2230 is 1.97 ± 0.04 M☉. This mass made PSR J1614–2230 the most massive known neutron star at the time of discovery, and rules out many neutron star equations of state that include exotic matter such as hyperons and kaon condensates.

The North American Nanohertz Observatory for Gravitational Waves (NANOGrav) is a consortium of astronomers who share a common goal of detecting gravitational waves via regular observations of an ensemble of millisecond pulsars using the Green Bank Telescope, Arecibo Observatory, the Very Large Array, and the Canadian Hydrogen Intensity Mapping Experiment (CHIME). Future observing plans include up to 25% total time of the Deep Synoptic Array 2000 (DSA2000). This project is being carried out in collaboration with international partners in the Parkes Pulsar Timing Array in Australia, the European Pulsar Timing Array, and the Indian Pulsar Timing Array as part of the International Pulsar Timing Array.

The International Pulsar Timing Array (IPTA) is a multi-institutional, multi-telescope collaboration comprising the European Pulsar Timing Array (EPTA), the North American Nanohertz Observatory for Gravitational Waves (NANOGrav), the Parkes Pulsar Timing Array (PPTA) in Australia, and the Indian Pulsar Timing Array Project (InPTA). The goal of the IPTA is to detect ultra-low-frequency gravitational waves, such as from mergers of supermassive black holes, using an array of approximately 30 pulsars. This goal is shared by each of the participating institutions, but they have all recognized that their goal will be achieved more quickly by combining their respective efforts and resources.

<span class="mw-page-title-main">PSR J1311–3430</span> Pulsar

PSR J1311–3430 is a pulsar with a spin period of 2.5 milliseconds. It is the first millisecond pulsar found via gamma-ray pulsations. The source was originally identified by the Energetic Gamma Ray Experiment Telescope as a bright gamma ray source, but was not recognized as a pulsar until observations with the Fermi Gamma-ray Space Telescope discovered pulsed gamma ray emission. The pulsar has a helium-dominated companion much less massive than itself, and the two are in an orbit with a period of 93.8 minutes. The system is explained by a model where mass from the low mass companion was transferred on to the pulsar, increasing the mass of the pulsar and decreasing its period. These systems are known as Black Widow Pulsars, named after the original such system discovered, PSR B1957+20, and may eventually lead to the companion being completely vaporized. Among systems like these, the orbital period of PSR J1311–3430 is the shortest ever found. Spectroscopic observations of the companion suggest that the mass of the pulsar is 2.7 . Though there is considerable uncertainty in this estimate, the minimum mass for the pulsar that the authors find adequately fits the data is 2.15 , which is still more massive than PSR J1614−2230, the previous record holder for most massive known pulsar.

<span class="mw-page-title-main">PSR J0348+0432</span> Pulsar–white dwarf binary system in Taurus constellation

PSR J0348+0432 is a pulsar–white dwarf binary system in the constellation Taurus. It was discovered in 2007 with the National Radio Astronomy Observatory's Robert C. Byrd Green Bank Telescope in a drift-scan survey.

<span class="mw-page-title-main">Hellings-Downs curve</span> Gravitational wave detection tool

The Hellings-Downs curve is a theoretical tool used to establish the telltale signature that a galactic-scale pulsar timing array has detected gravitational waves, typically of wavelengths . The method entails searching for spatial correlations of the timing residuals from pairs of pulsars and comparing the data with the Hellings-Downs curve. When the data fit exceeds the standard 5 sigma threshold, the pulsar timing array can declare detection of gravitational waves. More precisely, the Hellings-Downs curve is the expected correlations of the timing residuals from pairs of pulsars as a function of their angular separation on the sky as seen from Earth. This theoretical correlation function assumes Einstein's general relativity and a gravitational wave background that is isotropic.

References

  1. ↑ Bhattacharya, D.; Van Den Heuvel, E. P. J. (1991). "Formation and evolution of binary and millisecond radio pulsars". Physics Reports. 203 (1–2): 1. Bibcode:1991PhR...203....1B. doi:10.1016/0370-1573(91)90064-S.
  2. ↑ Tauris, T. M.; Van Den Heuvel, E. P. J. (2006). Formation and evolution of compact stellar X-ray sources. Bibcode:2006csxs.book..623T.
  3. ↑ Kızıltan, Bülent; Thorsett, S. E. (2009). "Constraints on Pulsar Evolution: The Joint Period-Spin-down Distribution of Millisecond Pulsars". The Astrophysical Journal Letters . 693 (2): L109–L112. arXiv: 0902.0604 . Bibcode:2009ApJ...693L.109K. doi:10.1088/0004-637X/693/2/L109. S2CID   2156395.
  4. ↑ Naeye, Robert (2009). "Surprising Trove of Gamma-Ray Pulsars". Sky & Telescope .
  5. ↑ Freire, Paulo. "Pulsars in globular clusters". Arecibo Observatory . Retrieved 2007-01-18.
  6. ↑ Backer, D. C.; Kulkarni, S. R.; Heiles, C.; Davis, M. M.; Goss, W. M. (1982), "A millisecond pulsar", Nature, 300 (5893): 615–618, Bibcode:1982Natur.300..615B, doi:10.1038/300615a0, S2CID   4247734
  7. ↑ "The ATNF Pulsar Database" . Retrieved 2009-05-17.
  8. ↑ Hessels, Jason; Ransom, Scott M.; Stairs, Ingrid H.; Freire, Paulo C. C.; Kaspi, Victoria M.; Camilo, Fernando (2006). "A Radio Pulsar Spinning at 716 Hz". Science . 311 (5769): 1901–1904. arXiv: astro-ph/0601337 . Bibcode:2006Sci...311.1901H. doi:10.1126/science.1123430. PMID   16410486. S2CID   14945340.
  9. ↑ Naeye, Robert (2006-01-13). "Spinning Pulsar Smashes Record". Sky & Telescope . Archived from the original on 2007-12-29. Retrieved 2008-01-18.
  10. ↑ Cook, G. B.; Shapiro, S. L.; Teukolsky, S. A. (1994). "Recycling Pulsars to Millisecond Periods in General Relativity". Astrophysical Journal Letters. 423: 117–120. Bibcode:1994ApJ...423L.117C. doi:10.1086/187250.
  11. ↑ Haensel, P.; Lasota, J. P.; Zdunik, J. L. (1999). "On the minimum period of uniformly rotating neutron stars". Astronomy and Astrophysics. 344: 151–153. Bibcode:1999A&A...344..151H.
  12. ↑ Chakrabarty, D.; Morgan, E. H.; Muno, M. P.; Galloway, D. K.; Wijnands, R.; van der Klis, M.; Markwardt, C. B. (2003). "Nuclear-powered millisecond pulsars and the maximum spin frequency of neutron stars". Nature. 424 (6944): 42–44. arXiv: astro-ph/0307029 . Bibcode:2003Natur.424...42C. doi:10.1038/nature01732. PMID   12840751. S2CID   1938122.
  13. ↑ Kiziltan, Bulent; Thorsett, Stephen E. (2007-02-19). "Integral points to the fastest spinning neutron star". Spaceflight Now. 693 (2). European Space Agency. arXiv: 0902.0604 . Bibcode:2009ApJ...693L.109K. doi:10.1088/0004-637X/693/2/L109. S2CID   2156395 . Retrieved 2007-02-20.
  14. ↑ Matsakis, D. N.; Taylor, J. H.; Eubanks, T. M. (1997). "A Statistic for Describing Pulsar and Clock Stabilities" (PDF). Astronomy and Astrophysics. 326: 924–928. Bibcode:1997A&A...326..924M. Archived from the original (PDF) on 2011-07-25. Retrieved 2010-04-03.
  15. ↑ Hartnett, John G.; Luiten, Andre N. (2011-01-07). "Colloquium: Comparison of astrophysical and terrestrial frequency standards". Reviews of Modern Physics. 83 (1): 1–9. arXiv: 1004.0115 . Bibcode:2011RvMP...83....1H. doi:10.1103/revmodphys.83.1. ISSN   0034-6861. S2CID   118396798.
  16. ↑ Rasio, Frederic (2011). "Planet Discovery near Pulsars". Science . doi:10.1126/science.1212489.
  17. ↑ Sazhin, M.V. (1978). "Opportunities for detecting ultralong gravitational waves". Sov. Astron. 22: 36–38. Bibcode:1978SvA....22...36S.
  18. ↑ Detweiler, S.L. (1979). "Pulsar timing measurements and the search for gravitational waves". Astrophysical Journal . 234: 1100–1104. Bibcode:1979ApJ...234.1100D. doi:10.1086/157593.
  19. ↑ "ShieldSquare Captcha". iopscience.iop.org.
  20. ↑ "After 15 years, pulsar timing yields evidence of cosmic gravitational wave background". Berkeley. August 11, 2022.
  21. ↑ Hellings, R.W.; Downs, G.S. (1983). "Upper limits on the isotropic gravitational radiation background from pulsar timing analysis". Astrophysical Journal Letters . 265: L39–L42. Bibcode:1983ApJ...265L..39H. doi: 10.1086/183954 .
  22. ↑ Foster, R.S.; Backer, D.C. (1990). "Constructing a pulsar timing array". Astrophysical Journal . 361: 300–308. Bibcode:1990ApJ...361..300F. doi:10.1086/169195.
  23. ↑ Hobbs, G.; et al. (2010). "The International Pulsar Timing Array project: using pulsars as a gravitational wave detector". Classical and Quantum Gravity . 27 (8): 084013. arXiv: 0911.5206 . Bibcode:2010CQGra..27h4013H. doi:10.1088/0264-9381/27/8/084013. S2CID   56073764.
  24. ↑ Demorest, P.; et al. (2013). "Limits on the Stochastic Gravitational Wave Background from the North American Nanohertz Observatory for Gravitational Waves". Astrophysical Journal . 762 (2): 94–118. arXiv: 1201.6641 . Bibcode:2013ApJ...762...94D. doi:10.1088/0004-637X/762/2/94. S2CID   13883914.
  25. ↑ Arzoumanian, Zaven; Baker, Paul T.; Blumer, Harsha; Bécsy, Bence; Brazier, Adam; Brook, Paul R.; Burke-Spolaor, Sarah; Chatterjee, Shami; Chen, Siyuan; Cordes, James M.; Cornish, Neil J.; Crawford, Fronefield; Cromartie, H. Thankful; Decesar, Megan E.; Demorest, Paul B. (2020-12-01). "The NANOGrav 12.5 yr Data Set: Search for an Isotropic Stochastic Gravitational-wave Background". The Astrophysical Journal. 905 (2): L34. arXiv: 2009.04496 . Bibcode:2020ApJ...905L..34A. doi: 10.3847/2041-8213/abd401 . ISSN   0004-637X. S2CID   221586395.
  26. ↑ O'Neill, Ian; Cofield, Calla (11 January 2021). "Gravitational Wave Search Finds Tantalizing New Clue". NASA . Retrieved 11 January 2021.
  27. ↑ "Hellings and Downs curve". astro.vaporia.com. Retrieved 29 June 2023.
  28. ↑ Agazie, Gabriella; Anumarlapudi, Akash; Archibald, Anne M.; Arzoumanian, Zaven; Baker, Paul T.; Bécsy, Bence; Blecha, Laura; Brazier, Adam; Brook, Paul R.; Burke-Spolaor, Sarah; Burnette, Rand; Case, Robin; Charisi, Maria; Chatterjee, Shami; Chatziioannou, Katerina (2023-07-01). "The NANOGrav 15 yr Data Set: Evidence for a Gravitational-wave Background". The Astrophysical Journal Letters. 951 (1): L8. arXiv: 2306.16213 . Bibcode:2023ApJ...951L...8A. doi: 10.3847/2041-8213/acdac6 . ISSN   2041-8205. S2CID   259274684.
  29. ↑ NANOGrav Collaboration (29 June 2023). "Focus on NANOGrav's 15 yr Data Set and the Gravitational Wave Background". The Astrophysical Journal Letters.
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