Millisecond pulsar

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.{{cite journal |last1=Kızıltan |first1=Bülent |title=Constraints on Pulsar Evolution: The Joint Period-Spin-down Distribution of Millisecond Pulsars |year=2009 |last2=Thorsett |first2=S. E. |periodical=The Astrophysical Journal Letters |volume=693 |issue=2 |pages=L109–L112 |doi=10.1088/0004-637X/693/2/L109 |bibcode = 2009ApJ...693L.109K |arxiv = 0902.0604 |s2cid=2156395 }} But the nature of the other process remains a mystery.{{Cite news |last=Naeye |first=Robert |year=2009 |title=Surprising Trove of Gamma-Ray Pulsars |periodical=Sky & Telescope |url=http://www.skyandtelescope.com/astronomy-news/surprising-trove-of-gamma-ray-pulsars }}

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.{{cite web

| last = Freire

| first = Paulo

| title = Pulsars in globular clusters

| publisher = Arecibo Observatory

| url = http://www2.naic.edu/~pfreire/GCpsr.html

| access-date =2007-01-18 }} The globular cluster Terzan 5 contains 37 of these, followed by 47 Tucanae with 22 and M28 and M15 with 8 pulsars each.

File:The star cluster Terzan 5.jpg]]

The first millisecond pulsar, PSR B1937+21, was discovered in 1982 by Backer et al.{{Citation | last1 = Backer | first1 = D. C. | last2 = Kulkarni | first2 = S. R. | last3 = Heiles | first3 = C. | last4 = Davis | first4 = M. M. | last5 = Goss | first5 = W. M. | title = A millisecond pulsar | year = 1982 | journal = Nature | volume = 300 | issue = 5893 | pages = 615–618 | bibcode = 1982Natur.300..615B|doi = 10.1038/300615a0 | s2cid = 4247734 }} Spinning roughly 641 times per second, it remains the second fastest-spinning millisecond pulsar of the approximately 200 that have been discovered.{{cite web | title = The ATNF Pulsar Database | url= http://www.atnf.csiro.au/research/pulsar/psrcat/proc_form.php?Name=Name&P0=P0&P1=P1&startUserDefined=true&c1_val=&c2_val=&c3_val=&c4_val=&sort_attr=p0&sort_order=asc&condition=&pulsar_names=&ephemeris=short&coords_unit=raj%2Fdecj&radius=&coords_1=&coords_2=&style=Long+with+last+digit+error&no_value=*&fsize=3&x_axis=&x_scale=linear&y_axis=&y_scale=linear&state=query&table_bottom.x=74&table_bottom.y=20 | access-date = 2009-05-17}} Pulsar PSR J1748-2446ad, discovered in 2004, is the fastest-spinning pulsar known, as of 2023, spinning 716 times per second.{{Cite journal |last1=Hessels |first1=Jason |last2=Ransom |first2=Scott M. |last3=Stairs |first3=Ingrid H. |last4=Freire |first4=Paulo C. C. |author5-link=Victoria Kaspi |last5=Kaspi |first5=Victoria M. |last6=Camilo |first6=Fernando |title=A Radio Pulsar Spinning at 716 Hz |journal=Science |volume=311 |issue=5769 |pages=1901–1904 |year=2006 |doi=10.1126/science.1123430 |pmid=16410486 |bibcode=2006Sci...311.1901H|arxiv = astro-ph/0601337 |s2cid=14945340 }}{{Cite news

| last = Naeye

| first = Robert

| date = 2006-01-13

| title = Spinning Pulsar Smashes Record

| periodical = Sky & Telescope

| url = http://www.skyandtelescope.com/news/3311021.html?page=1&c=y

| access-date = 2008-01-18

| archive-url = https://web.archive.org/web/20071229113749/http://www.skyandtelescope.com/news/3311021.html?page=1&c=y

| archive-date = 2007-12-29

| url-status = dead

}}

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,{{cite journal |author1=Cook, G. B. |author2=Shapiro, S. L. |author3=Teukolsky, S. A. | title = Recycling Pulsars to Millisecond Periods in General Relativity | journal = Astrophysical Journal Letters | volume = 423 | pages = 117–120 | year = 1994 | bibcode = 1994ApJ...423L.117C | doi = 10.1086/187250}}{{cite journal |author1=Haensel, P. |author2=Lasota, J. P. |author3=Zdunik, J. L. | title = On the minimum period of uniformly rotating neutron stars | journal = Astronomy and Astrophysics | volume = 344 | pages = 151–153 | year = 1999 | bibcode = 1999A&A...344..151H}} 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.{{cite journal |author1=Chakrabarty, D. |author2=Morgan, E. H. |author3=Muno, M. P. |author4=Galloway, D. K. |author5=Wijnands, R. |author6=van der Klis, M. |author7=Markwardt, C. B. | title = Nuclear-powered millisecond pulsars and the maximum spin frequency of neutron stars | journal = Nature | volume = 424 | issue = 6944 | pages = 42–44 | year = 2003 | doi = 10.1038/nature01732 | pmid = 12840751|arxiv = astro-ph/0307029 |bibcode = 2003Natur.424...42C |s2cid=1938122 }}

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.{{Cite journal

| title = Integral points to the fastest spinning neutron star

| journal = Spaceflight Now

| publisher = European Space Agency

| date = 2007-02-19

| url = http://www.spaceflightnow.com/news/n0702/19neutronstar/

| access-date = 2007-02-20

|bibcode=2009ApJ...693L.109K |arxiv = 0902.0604 |doi = 10.1088/0004-637X/693/2/L109 | last1 = Kiziltan

| first1 = Bulent

| last2 = Thorsett

| first2 = Stephen E.

| volume = 693

| issue = 2

| s2cid = 2156395

}} 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.{{cite journal | author = Matsakis, D. N. | author2 = Taylor, J. H. | author3 = Eubanks, T. M. | url = http://aa.springer.de/papers/7326003/2300924.pdf | title = A Statistic for Describing Pulsar and Clock Stabilities | journal = Astronomy and Astrophysics | volume = 326 | date = 1997 | pages = 924–928 | access-date = 2010-04-03 | bibcode = 1997A&A...326..924M | archive-date = 2011-07-25 | archive-url = https://web.archive.org/web/20110725022625/http://aa.springer.de/papers/7326003/2300924.pdf | url-status = dead }}{{Cite journal|last1=Hartnett|first1=John G.|last2=Luiten|first2=Andre N.|date=2011-01-07|title=Colloquium: Comparison of astrophysical and terrestrial frequency standards|journal=Reviews of Modern Physics|volume=83|issue=1|pages=1–9|doi=10.1103/revmodphys.83.1|arxiv=1004.0115|bibcode=2011RvMP...83....1H|s2cid=118396798|issn=0034-6861}} 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.{{Cite news |last=Rasio|first=Frederic|year=2011 |title=Planet Discovery near Pulsars |periodical=Science |doi=10.1126/science.1212489 |url=https://www.science.org/doi/full/10.1126/science.1212489 }}

{{main|Pulsar timing array}}

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

{{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 }} and Detweiler

{{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

}} 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

Hellings and Downs

{{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

}} 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

{{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

}} 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.

{{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

}} The five-year data release, analysis, and first NANOGrav limit on the stochastic gravitational wave background were described in 2013 by Demorest et al.

{{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

}} 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.{{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 }}{{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 }}

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,{{cite web |title=Hellings and Downs curve |url=http://astro.vaporia.com/start/hdcurve.html |website=astro.vaporia.com |access-date=29 June 2023}} the tell-tale sign of the gravitational wave origin of the observations.{{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 }}{{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}}

{{Reflist|30em}}

• {{Cite web |title=Millisecond Pulsar Catalog|date=30 September 2013 |url=https://blacksidus.com/millisecond-pulsar-catalogue/|language=en-US}}
• "[http://universetoday.com/am/publish/origin_of_millisecond_pulsars_47tucw.html How Millisecond Pulsars Spin So Fast]". Universe Today.
• "[https://web.archive.org/web/20070813052324/http://www.newscientist.com/article.ns?id=dn7052 Fast-Spinning Star Could Test Gravitational Waves]". New Scientist.
• "[http://www.astronomynow.com/090610Astronomicalwhirlingdervisheshidetheiragewell.html Astronomical whirling dervishes hide their age well]". Astronomy Now.
• [http://www.astronomycast.com/astronomy/stars/compact-objects/ep-158-pulsars/ Audio: Cain/Gay - Pulsars] Astronomy Cast - Nov 2009.

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*Millisecond pulsar