Editing Millisecond pulsar (section)

==Gravitational wave detection using pulsar timing==
{{main|Pulsar timing array}}
[[Gravitational wave]]s 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The proposal to use pulsars as gravitational wave detectors was originally made by Sazhin<ref>
{{Cite journal
 | last=Sazhin | first=M.V.
 | date=1978
 | title=Opportunities for detecting ultralong gravitational waves
 | journal=[[Sov. Astron.]]
 | volume=22 | pages=36–38
|bibcode = 1978SvA....22...36S }}</ref> and Detweiler<ref>
{{Cite journal
 | last=Detweiler | first=S.L.
 | date=1979
 | title=Pulsar timing measurements and the search for gravitational waves
 | journal=[[Astrophysical Journal]]
 | volume=234 | pages=1100–1104 | bibcode = 1979ApJ...234.1100D
 | doi = 10.1086/157593
}}</ref> 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.

[[File:correlation_vs_angular_separation_between_pulsars.svg|thumb|upright=1.5|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)<ref>{{Cite web|url=http://iopscience.iop.org/collections/apjl-230623-245-Focus-on-NANOGrav-15-year|title=ShieldSquare Captcha|website=iopscience.iop.org}}</ref><ref>{{Cite web|url=https://news.berkeley.edu/2023/06/28/after-15-years-pulsar-timing-yields-evidence-of-cosmic-gravitational-wave-background|title=After 15 years, pulsar timing yields evidence of cosmic gravitational wave background|date=August 11, 2022|website=Berkeley}}</ref>]]
Hellings and Downs<ref>
{{Cite journal
 | author=Hellings, R.W.
 | author2=Downs, G.S.
 | date=1983
 | title=Upper limits on the isotropic gravitational radiation background from pulsar timing analysis
 | journal=[[Astrophysical Journal Letters]]
 | volume=265 | pages=L39–L42 | bibcode = 1983ApJ...265L..39H
|doi = 10.1086/183954 | doi-access=free
 }}</ref> 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 [[Donald C. Backer|Backer]]<ref>
{{Cite journal
 | author=Foster, R.S.
 | author2=Backer, D.C.
 | date=1990
 | title=Constructing a pulsar timing array
 | journal=[[Astrophysical Journal]]
 | volume=361 | pages=300–308 | doi = 10.1086/169195 
 | bibcode = 1990ApJ...361..300F
}}</ref> improved the sensitivity to gravitational waves by applying in 1990 the [[Hellings-Downs curve|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.<ref>
{{Cite journal
 | author=Hobbs, G.
 | display-authors=etal
 | date=2010
 | title=The International Pulsar Timing Array project: using pulsars as a gravitational wave detector
 | journal=[[Classical and Quantum Gravity]]
 | volume=27 | issue = 8 | pages=084013 | doi = 10.1088/0264-9381/27/8/084013
|bibcode = 2010CQGra..27h4013H |arxiv = 0911.5206 | s2cid=56073764
 }}</ref> The five-year data release, analysis, and first NANOGrav limit on the stochastic gravitational wave background were described in 2013 by Demorest et al.<ref>
{{Cite journal
 | author=Demorest, P.
 | display-authors=etal
 | date=2013
 | title=Limits on the Stochastic Gravitational Wave Background from the North American Nanohertz Observatory for Gravitational Waves
 | journal=[[Astrophysical Journal]]
 | volume=762 | issue = 2 | pages=94–118 | doi = 10.1088/0004-637X/762/2/94
|bibcode = 2013ApJ...762...94D |arxiv = 1201.6641 | s2cid=13883914
 }}</ref> 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.<ref>{{Cite journal |last1=Arzoumanian |first1=Zaven |last2=Baker |first2=Paul T. |last3=Blumer |first3=Harsha |last4=Bécsy |first4=Bence |last5=Brazier |first5=Adam |last6=Brook |first6=Paul R. |last7=Burke-Spolaor |first7=Sarah |last8=Chatterjee |first8=Shami |last9=Chen |first9=Siyuan |last10=Cordes |first10=James M. |last11=Cornish |first11=Neil J. |last12=Crawford |first12=Fronefield |last13=Cromartie |first13=H. Thankful |last14=Decesar |first14=Megan E. |last15=Demorest |first15=Paul B. |date=2020-12-01 |title=The NANOGrav 12.5 yr Data Set: Search for an Isotropic Stochastic Gravitational-wave Background |journal=The Astrophysical Journal |volume=905 |issue=2 |pages=L34 |doi=10.3847/2041-8213/abd401 |arxiv=2009.04496 |bibcode=2020ApJ...905L..34A |s2cid=221586395 |issn=0004-637X |doi-access=free }}</ref><ref name="NASA-20210111">{{cite news |last1=O'Neill |first1=Ian |last2=Cofield |first2=Calla |title=Gravitational Wave Search Finds Tantalizing New Clue |url=https://www.jpl.nasa.gov/news/news.php?feature=7809 |date=11 January 2021 |work=[[NASA]] |accessdate=11 January 2021 }}</ref>

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,<ref name="Vaporia">{{cite web |title=Hellings and Downs curve |url=http://astro.vaporia.com/start/hdcurve.html |website=astro.vaporia.com |access-date=29 June 2023}}</ref> the tell-tale sign of the gravitational wave origin of the observations.<ref>{{Cite journal |last1=Agazie |first1=Gabriella |last2=Anumarlapudi |first2=Akash |last3=Archibald |first3=Anne M. |last4=Arzoumanian |first4=Zaven |last5=Baker |first5=Paul T. |last6=Bécsy |first6=Bence |last7=Blecha |first7=Laura |last8=Brazier |first8=Adam |last9=Brook |first9=Paul R. |last10=Burke-Spolaor |first10=Sarah |last11=Burnette |first11=Rand |last12=Case |first12=Robin |last13=Charisi |first13=Maria |last14=Chatterjee |first14=Shami |last15=Chatziioannou |first15=Katerina |date=2023-07-01 |title=The NANOGrav 15 yr Data Set: Evidence for a Gravitational-wave Background |journal=The Astrophysical Journal Letters |volume=951 |issue=1 |pages=L8 |doi=10.3847/2041-8213/acdac6 |arxiv=2306.16213 |bibcode=2023ApJ...951L...8A |s2cid=259274684 |issn=2041-8205 |doi-access=free }}</ref><ref>{{Cite journal |author=NANOGrav Collaboration |date=29 June 2023 |title=Focus on NANOGrav's 15 yr Data Set and the Gravitational Wave Background |url=https://iopscience.iop.org/collections/apjl-230623-245-Focus-on-NANOGrav-15-year |journal=The Astrophysical Journal Letters}}</ref>