Editing Neutron star

{{short description|Collapsed core of a massive star}}
{{other uses|Neutron Star (disambiguation)}}

[[File:Moving heart of the Crab Nebula.jpg|thumb|upright=1.4|Central neutron star at the heart of the [[Crab Nebula]]]]
[[File:PIA18848-PSRB1509-58-ChandraXRay-WiseIR-20141023.jpg|thumb|upright=1.4|Radiation from the rapidly spinning [[pulsar]] [[PSR B1509-58]] makes nearby gas emit [[X-ray]]s (gold) and illuminates the rest of the [[nebula]], here seen in [[infrared]] (blue and red).]]

A '''neutron star''' is the [[Gravitational collapse|collapsed]] [[Stellar structure|core]] of a massive [[supergiant star]]. It results from the [[supernova]] explosion of a [[stellar evolution#Massive star|massive star]]—combined with [[gravitational collapse]]—that compresses the core past [[white dwarf]] star density to that of [[Atomic nucleus|atomic nuclei]]. Surpassed only by [[black hole]]s, neutron stars are the second smallest and densest known class of stellar objects.<ref>{{cite book |title=Compact Stars: Nuclear Physics, Particle Physics and General Relativity |edition=illustrated |first1=Norman K. |last1=Glendenning |publisher=Springer Science & Business Media |year=2012 |isbn=978-1-4684-0491-3 |page=1 |url=https://books.google.com/books?id=cCDlBwAAQBAJ&pg=PA1 |access-date=2016-03-21 |archive-date=2017-01-31 |archive-url=https://web.archive.org/web/20170131202613/https://books.google.com/books?id=cCDlBwAAQBAJ&pg=PA1 |url-status=live }}</ref> Neutron stars have a radius on the order of {{convert|10|km|sigfig=1|sp=us}} and a mass of about {{solar mass|1.4}}.<ref>{{cite book |title=Astronomy: The Solar System and Beyond |edition=6th |first1=Michael |last1=Seeds |first2=Dana |last2=Backman |publisher=Cengage Learning |year=2009 |isbn=978-0-495-56203-0 |page=339 |url=https://books.google.com/books?id=DajpkyXS-NUC&pg=PT356 |access-date=2018-02-22 |archive-date=2021-02-06 |archive-url=https://web.archive.org/web/20210206222508/https://books.google.com/books?id=DajpkyXS-NUC&pg=PT356 |url-status=live }}</ref> Stars that collapse into neutron stars have a total [[mass]] of between 10 and 25 [[solar mass]]es ({{solar mass}}), or possibly more for those that are especially rich in [[Metallicity|elements heavier than hydrogen and helium]].<ref>{{Cite journal |last1=Heger |first1=A.|last2=Fryer |first2=C. L.|last3=Woosley |first3=S. E.|last4=Langer |first4=N.|last5=Hartmann |first5=D. H.|year=2003|title=How Massive Single Stars End Their Life|journal=[[Astrophysical Journal]]|volume=591 |issue=1|pages=288–300|arxiv=astro-ph/0212469|bibcode=2003ApJ...591..288H|doi=10.1086/375341|s2cid=59065632}}</ref>

Once formed, neutron stars no longer actively generate heat and cool over time, but they may still evolve further through [[Stellar collision|collisions]] or [[Accretion (astrophysics)|accretion]]. Most of the basic models for these objects imply that they are composed almost entirely of [[neutron]]s, as the extreme pressure causes the [[electron]]s and [[proton]]s present in normal matter to combine into additional neutrons. These stars are partially supported against further collapse by [[Degenerate matter#Neutron degeneracy|neutron degeneracy pressure]], just as [[white dwarf]]s are supported against collapse by [[electron degeneracy pressure]]. However, this is not by itself sufficient to hold up an object beyond {{Solar mass|0.7|link=y}}<ref>{{cite journal |first=R. C. |last=Tolman |date=1939 |title=Static Solutions of Einstein's Field Equations for Spheres of Fluid |journal=[[Physical Review]] |volume=55 |issue=4 |pages=364–373 |doi=10.1103/PhysRev.55.364 |bibcode=1939PhRv...55..364T |url=https://authors.library.caltech.edu/4362/1/TOLpr39.pdf |access-date=2019-06-30 |archive-date=2018-07-22 |archive-url=https://web.archive.org/web/20180722071018/https://authors.library.caltech.edu/4362/1/TOLpr39.pdf |url-status=live }}</ref><ref>{{cite journal |first1=J. R. |last1=Oppenheimer |first2=G. M. |last2=Volkoff |date=1939 |title=On Massive Neutron Cores |journal=[[Physical Review]] |volume=55 |issue=4 |pages=374–381 |doi=10.1103/PhysRev.55.374 |bibcode=1939PhRv...55..374O}}</ref> and repulsive nuclear forces increasingly contribute to supporting more massive neutron stars.<ref>{{cite web |title=Neutron Stars |url=https://www.astro.princeton.edu/~burrows/classes/403/neutron.stars.pdf |website=www.astro.princeton.edu |access-date=14 December 2018 |archive-date=9 September 2021 |archive-url=https://web.archive.org/web/20210909160017/https://www.astro.princeton.edu/~burrows/classes/403/neutron.stars.pdf |url-status=live }}</ref><ref>{{Cite journal|last1=Douchin|first1=F.|last2=Haensel|first2=P.|date=December 2001|title=A unified equation of state of dense matter and neutron star structure|journal=Astronomy & Astrophysics|volume=380|issue=1|pages=151–167|doi=10.1051/0004-6361:20011402|issn=0004-6361|arxiv=astro-ph/0111092|bibcode=2001A&A...380..151D|s2cid=17516814}}</ref> If the remnant star has a [[mass]] exceeding the [[Tolman–Oppenheimer–Volkoff limit]], which ranges from {{nowrap|2.2–2.9 {{solar mass}},}} the combination of degeneracy pressure and nuclear forces is insufficient to support the neutron star, causing it to collapse and form a [[black hole]]. The most massive neutron star detected so far, [[PSR J0952–0607]], is estimated to be {{val|2.35|0.17|u=solar mass}}.<ref name=blackwidow/>

Newly formed neutron stars may have surface temperatures of ten million K or more. However, since neutron stars generate no new heat through fusion, they inexorably cool down after their formation. Consequently, a given neutron star reaches a surface temperature of one million K when it is between one thousand and one million years old.<ref name="Chandra">"[https://Chandra.harvard.edu/resources/faq/sources/snr/snr-39.html Q&A: Supernova Remnants and Neutron Stars"], ''Chandra.harvard.edu'' (September 5, 2008)</ref> Older and even-cooler neutron stars are still easy to discover. For example, the well-studied neutron star, {{nowrap|[[RX J1856.5−3754]],}} has an average surface temperature of about 434,000 K.<ref>{{cite journal|arxiv=astro-ph/0612145 |doi=10.1111/j.1365-2966.2006.11376.x |doi-access=free |title=Magnetic hydrogen atmosphere models and the neutron star RX J1856.5-3754 |date=2007 |last1=Ho |first1=W. C. G. |last2=Kaplan |first2=D. L. |last3=Chang |first3=P. |last4=Van Adelsberg |first4=M. |last5=Potekhin |first5=A. Y. |journal=Monthly Notices of the Royal Astronomical Society |volume=375 |issue=3 |pages=821–830 |bibcode=2007MNRAS.375..821H }}. The authors calculated what they considered to be "a more realistic model, which accounts for magnetic field and temperature variations over the neutron star surface as well as general relativistic effects," which yielded an average surface temperature of {{val|4.34|e=5|+0.02|-0.06|u=K}} at a confidence level of 2𝜎 (95%); see §4, ''Fig.&nbsp;6'' in their paper for details.</ref> For comparison, the Sun has an effective surface temperature of 5,780 K.<ref>{{cite journal |quote=The Sun is less active than other solar-like stars |arxiv=2005.01401 |doi=10.1126/science.aay3821 |title=The Sun is less active than other solar-like stars |date=2020 |last1=Reinhold |first1=Timo |last2=Shapiro |first2=Alexander I. |last3=Solanki |first3=Sami K. |last4=Montet |first4=Benjamin T. |last5=Krivova |first5=Natalie A. |last6=Cameron |first6=Robert H. |last7=Amazo-Gómez |first7=Eliana M. |journal=Science |volume=368 |issue=6490 |pages=518–521 |pmid=32355029 |bibcode=2020Sci...368..518R }}</ref>

Neutron star material is remarkably [[Density|dense]]: a normal-sized [[Phillumeny#Matchbox|matchbox]] containing neutron-star material would have a weight of approximately 3 [[billion]] tonnes, the same weight as a 0.5-cubic-kilometer chunk of the Earth (a cube with edges of about 800 meters<!-- Do not change this to 500 metres: note that (800m)³ = (0.8 km)³ = 0.512 km³-->) from Earth's surface.<ref>{{cite web|url=https://heasarc.gsfc.nasa.gov/docs/xte/learning_center/ASM/ns.html|website=heasarc.gsfc.nasa.gov|title=Tour the ASM Sky|access-date=2016-05-23|archive-date=2021-10-01|archive-url=https://web.archive.org/web/20211001133602/https://heasarc.gsfc.nasa.gov/docs/xte/learning_center/ASM/ns.html|url-status=live}}</ref><ref>{{Cite web| url=http://www.universetoday.com/26771/density-of-the-earth/| title=Density of the Earth| date=2009-03-10| access-date=2016-05-23| archive-date=2013-11-12| archive-url=https://web.archive.org/web/20131112145139/http://www.universetoday.com/26771/density-of-the-earth/| url-status=live}}</ref>

As a star's core collapses, its rotation rate increases due to [[conservation of angular momentum]], so newly formed neutron stars typically rotate at up to several hundred times per second. Some neutron stars emit beams of electromagnetic radiation that make them detectable as pulsars, and the discovery of pulsars by [[Jocelyn Bell Burnell]] and [[Antony Hewish]] in 1967 was the first observational suggestion that neutron stars exist. The fastest-spinning neutron star known is [[PSR J1748−2446ad]], rotating at a rate of 716 times per second<ref>{{Cite journal |last1=Hessels |first1=Jason |display-authors=4 |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 (journal)|Science]] |volume=311 |issue=5769 |pages=1901–1904 |date=2006 |doi=10.1126/science.1123430 |pmid=16410486 |bibcode=2006Sci...311.1901H|arxiv = astro-ph/0601337 |citeseerx=10.1.1.257.5174 |s2cid=14945340 }}</ref><ref>{{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 }}</ref> or 43,000 [[revolutions per minute]], giving a linear (tangential) speed at the surface on the order of 0.24''c'' (i.e., nearly a quarter the [[speed of light]]).

There are thought to be around one billion neutron stars in the [[Milky Way]],<ref>{{cite web| url = https://www.nasa.gov/mission_pages/GLAST/science/neutron_stars.html| title = NASA.gov| access-date = 2020-08-05| archive-date = 2018-09-08| archive-url = https://web.archive.org/web/20180908042354/https://www.nasa.gov/mission_pages/GLAST/science/neutron_stars.html| url-status = live}}</ref> and at a minimum several hundred million, a figure obtained by estimating the number of stars that have undergone supernova explosions.<ref>{{cite book |last1=Camenzind |first1=Max |title=Compact Objects in Astrophysics: White Dwarfs, Neutron Stars and Black Holes |date=24 February 2007 |publisher=Springer Science & Business Media |isbn=978-3-540-49912-1 |page=269 |url=https://books.google.com/books?id=Nh68nl0abhMC&pg=PA269 |bibcode=2007coaw.book.....C |access-date=6 September 2017 |archive-date=29 April 2021 |archive-url=https://web.archive.org/web/20210429203757/https://books.google.com/books?id=Nh68nl0abhMC&pg=PA269 |url-status=live }}</ref> However, many of them have existed for a long period of time and have cooled down considerably. These stars radiate very little electromagnetic radiation; most neutron stars that have been detected occur only in certain situations in which they do radiate, such as if they are a pulsar or a part of a binary system. Slow-rotating and non-accreting neutron stars are difficult to detect, due to the absence of electromagnetic radiation; however, since the [[Hubble Space Telescope]]'s detection of [[RX J1856.5−3754]] in the 1990s, a few nearby neutron stars that appear to emit only thermal radiation have been detected.

Neutron stars in binary systems can undergo accretion, in which case they emit large amounts of [[X-ray]]s. During this process, matter is deposited on the surface of the stars, forming "hotspots" that can be sporadically identified as [[X-ray pulsar]] systems. Additionally, such accretions are able to "recycle" old pulsars, causing them to gain mass and rotate extremely quickly, forming [[millisecond pulsar]]s. Furthermore, binary systems such as these continue to [[Stellar evolution|evolve]], with many companions eventually becoming [[Compact star|compact objects]] such as white dwarfs or neutron stars themselves, though other possibilities include a complete destruction of the companion through [[ablation]] or collision.

The study of neutron star systems is central to [[gravitational wave]] astronomy. The [[Neutron star merger|merger of binary neutron stars]] produces gravitational waves and may be associated with [[kilonova]]e and [[gamma-ray burst|short-duration gamma-ray burst]]s. In 2017, the [[LIGO]] and [[Virgo interferometer|Virgo]] interferometer sites observed [[GW170817]], the first direct detection of gravitational waves from such an event.<ref>{{cite journal |year=2017 |title=Multi-messenger Observations of a Binary Neutron Star Merger |journal=The Astrophysical Journal Letters|volume=848 |issue=2 |pages=L12 |arxiv=1710.05833 |bibcode=2017ApJ...848L..12A |doi=10.3847/2041-8213/aa91c9 | last1 = Abbott | first1 = B. P. | last2 = Abbott | first2 = R. | last3 = Abbott | first3 = T. D. | last4 = Acernese | first4 = F. | last5 = Ackley | first5 = K. | last6 = Adams | first6 = C. | last7 = Adams | first7 = T. | last8 = Addesso | first8 = P. | last9 = Richard | last10 = Howard | last11 = Adhikari | first11 = R. X. | last12 = Huang-Wei |s2cid=217162243 |doi-access=free }}</ref> Prior to this, indirect evidence for gravitational waves was inferred by studying the gravity radiated from the orbital decay of a different type of (unmerged) binary neutron system, the [[Hulse–Taylor pulsar]].

==Formation==
[[File:Neutronstarsimple.png|thumb|Simplified representation of the formation of neutron stars]]
Any [[main sequence|main-sequence]] star with an initial mass of greater than {{Solar mass|8|link=y}} (eight times the mass of the [[Sun]]) has the potential to become a neutron star. As the star evolves away from the main sequence, [[stellar nucleosynthesis]] produces an iron-rich core. When all nuclear fuel in the core has been exhausted, the core must be supported by degeneracy pressure alone. Further deposits of mass from shell burning cause the core to exceed the [[Chandrasekhar limit]]. Electron-degeneracy pressure is overcome, and the core collapses further, causing temperatures to rise to over {{val|5|e=9|u=K}} (5 billion K). At these temperatures, [[photodisintegration]] (the breakdown of iron nuclei into [[alpha particle]]s due to high-energy gamma rays) occurs. As the temperature of the core continues to rise, electrons and protons combine to form neutrons via [[electron capture]], releasing a flood of [[neutrino]]s. When densities reach a nuclear density of {{val|4|e=17|u=kg/m3}}, a combination of [[strong force]] repulsion and neutron degeneracy pressure halts the contraction.<ref>{{cite journal |first=I. |last=Bombaci |date=1996 |title=The Maximum Mass of a Neutron Star |journal=[[Astronomy and Astrophysics]] |volume=305 | pages=871–877 |bibcode=1996A&A...305..871B}}</ref> The contracting outer envelope of the star is halted and rapidly flung outwards by a flux of neutrinos produced in the creation of the neutrons, resulting in a [[supernova]] and leaving behind a neutron star. However, if the remnant has a mass greater than about {{Solar mass|3}}, it instead becomes a black hole.<ref>{{cite book |title=The Birth of Stars and Planets |edition=illustrated |first1=John |last1=Bally |first2=Bo |last2=Reipurth |publisher=Cambridge University Press |year=2006 |isbn=978-0-521-80105-8 |page=207 |url=https://books.google.com/books?id=Pwy9OtT8u6QC&pg=PA207 |access-date=2016-06-30 |archive-date=2017-01-31 |archive-url=https://web.archive.org/web/20170131193108/https://books.google.com/books?id=Pwy9OtT8u6QC&pg=PA207 |url-status=live }}</ref>

As the core of a massive star is compressed during a [[Type II supernova]] or a [[Type Ib and Ic supernovae|Type Ib or Type Ic]] supernova, and collapses into a neutron star, it retains most of its [[angular momentum]]. Because it has only a tiny fraction of its parent's radius (sharply reducing its [[moment of inertia]]), a neutron star is formed with very high rotation speed and then, over a very long period, it slows. Neutron stars are known that have rotation periods from about 1.4&nbsp;ms to 30&nbsp;s. The neutron star's density also gives it very high [[surface gravity]], with typical values ranging from {{val|e=12}} to {{val|e=13|u=m/s2}} (more than {{val|e=11}} times that of [[Earth]]).<ref name="Haensel">{{cite book |title=Neutron Stars |first1=Paweł |last1=Haensel |first2=Alexander Y. |last2=Potekhin |first3=Dmitry G. |last3=Yakovlev |isbn=978-0-387-33543-8 |publisher=Springer |date=2007 }}</ref> One measure of such immense gravity is the fact that neutron stars have an [[escape velocity]] of over half the [[speed of light]].<ref name="ChandraBlog 2013">{{cite web | title=The Remarkable Properties of Neutron Stars - Fresh Chandra News | website=ChandraBlog | date=2013-03-28 | url=https://chandra.harvard.edu/blog/node/432 | access-date=2022-05-16}}</ref> The neutron star's gravity accelerates infalling matter to tremendous speed, and [[tidal force]]s near the surface can cause [[spaghettification]].<ref name="ChandraBlog 2013"/>

==Properties==
{{More citations needed section|date=May 2024}}

=== Equation of state ===
The [[equation of state]] of neutron stars is not currently known. This is because neutron stars are the second most dense known object in the universe, only less dense than black holes. The extreme density means there is no way to replicate the material on Earth in laboratories, which is how equations of state for other things like ideal gases are tested. The closest neutron star is many parsecs away, meaning there is no feasible way to study it directly. While it is known neutron stars should be similar to a [[Degenerate matter#:~:text=Degenerate gases are gases composed,white dwarfs are two examples.|degenerate gas]], it cannot be modeled strictly like one (as white dwarfs are) because of the extreme gravity. [[General relativity]] must be considered for the neutron star equation of state because [[Newton's law of universal gravitation|Newtonian gravity]] is no longer sufficient in those conditions. Effects such as [[Quantum chromodynamics|quantum chromodynamics (QCD)]], [[superconductivity]], and [[superfluidity]] must also be considered.

At the extraordinarily high densities of neutron stars, ordinary matter is squeezed to nuclear densities. Specifically, the matter ranges from nuclei embedded in a sea of electrons at low densities in the outer crust, to increasingly neutron-rich structures in the inner crust, to the extremely neutron-rich uniform matter in the outer core, and possibly exotic states of matter at high densities in the inner core.<ref name=":1">{{Cite journal |last1=Hebeler |first1=K. |last2=Lattimer |first2=J. M. |last3=Pethick |first3=C. J. |last4=Schwenk |first4=A. |date=2013-07-19 |title=Equation of State and Neutron Star Properties Constrained by Nuclear Physics and Observation |url=https://iopscience.iop.org/article/10.1088/0004-637X/773/1/11 |journal=The Astrophysical Journal |volume=773 |issue=1 |pages=11 |doi=10.1088/0004-637X/773/1/11 |arxiv=1303.4662 |bibcode=2013ApJ...773...11H |issn=0004-637X}}</ref>

Understanding the nature of the matter present in the various layers of neutron stars, and the phase transitions that occur at the boundaries of the layers is a major unsolved problem in fundamental physics. The neutron star equation of state encodes information about the structure of a neutron star and thus tells us how matter behaves at the extreme densities found inside neutron stars. Constraints on the neutron star equation of state would then provide constraints on how the [[Strong interaction|strong force]] of the [[Standard Model|standard model]] works, which would have profound implications for nuclear and atomic physics. This makes neutron stars natural laboratories for probing fundamental physics.

For example, the exotic states that may be found at the cores of neutron stars are types of [[QCD matter]]. At the extreme densities at the centers of neutron stars, neutrons become disrupted giving rise to a sea of quarks. This matter's equation of state is governed by the laws of [[quantum chromodynamics]] and since QCD matter cannot be produced in any laboratory on Earth, most of the current knowledge about it is only theoretical.

Different equations of state lead to different values of observable quantities. While the equation of state is only directly relating the density and pressure, it also leads to calculating observables like the speed of sound, mass, radius, and [[Love number]]s. Because the equation of state is unknown, there are many proposed ones, such as FPS, UU, APR, L, and SLy, and it is an active area of research. Different factors can be considered when creating the equation of state such as phase transitions.

Another aspect of the equation of state is whether it is a soft or stiff equation of state. This relates to how much pressure there is at a certain energy density, and often corresponds to phase transitions. When the material is about to go through a phase transition, the pressure will tend to increase until it shifts into a more comfortable state of matter. A soft equation of state would have a gently rising pressure versus energy density while a stiff one would have a sharper rise in pressure. In neutron stars, nuclear physicists are still testing whether the equation of state should be stiff or soft, and sometimes it changes within individual equations of state depending on the phase transitions within the model. This is referred to as the equation of state stiffening or softening, depending on the previous behavior. Since it is unknown what neutron stars are made of, there is room for different phases of matter to be explored within the equation of state.

===Density and pressure===
[[File:White dwarf vs neutron star.svg|thumb|right|Comparison of a 10 km radius neutron star (top left corner) and a 6000 km radius [[white dwarf]], the latter roughly the size of [[Earth]].]]
Neutron stars have overall densities of {{val|3.7|e=17}} to {{val|5.9|e=17|u=kg/m3}} ({{val|2.6|e=14}} to {{val|4.1|e=14}} times the density of the Sun),<ref group="lower-alpha">{{val|3.7|e=17|u=kg/m3}} derives from mass {{val|2.68|e=30|u=kg}} / volume of star of radius 12&nbsp;km; {{val|5.9|e=17|u=kg/m3}} derives from mass {{val|4.2|e=30|u=kg}} per volume of star radius 11.9&nbsp;km</ref> which is comparable to the approximate density of an atomic nucleus of {{val|3|e=17|u=kg/m3}}.<ref>{{cite web |url=http://heasarc.gsfc.nasa.gov/docs/xte/learning_center/ASM/ns.html |title=Calculating a Neutron Star's Density |access-date=2006-03-11 |archive-date=2006-02-24 |archive-url=https://web.archive.org/web/20060224011955/http://heasarc.gsfc.nasa.gov/docs/xte/learning_center/ASM/ns.html |url-status=live }} NB {{val|3|e=17|u=kg/m3}} is {{val|3|e=14|u=g/cm3}}</ref> The density increases with depth, varying from about {{val|1|e=9|u=kg/m3}} at the crust to an estimated {{val|6|e=17}} or {{val|8|e=17|u=kg/m3}} deeper inside.<ref name="Miller">{{cite journal |title=Introduction to neutron stars |journal=American Institute of Physics Conference Series |volume=1645 |issue=1 |pages=61–78 |bibcode=2015AIPC.1645...61L |last1=Lattimer |first1=James M. |year=2015 |doi=10.1063/1.4909560 |series=AIP Conference Proceedings |doi-access=free }}</ref> Pressure increases accordingly, from about {{val|3.2|u=Pa|e=31}} (32&nbsp;[[quetta-|Q]]Pa) at the inner crust to {{val|1.6|e=34|u=Pa}} in the center.<ref>{{Cite journal |last1=Ozel |first1=Feryal |last2=Freire |first2=Paulo |title=Masses, Radii, and the Equation of State of Neutron Stars |journal=Annu. Rev. Astron. Astrophys. |volume=54 |issue=1 |pages=401–440 |date=2016 |doi=10.1146/annurev-astro-081915-023322 |bibcode=2016ARA&A..54..401O |arxiv = 1603.02698 |s2cid=119226325 }}</ref>

A neutron star is so dense that one teaspoon (5 [[milliliter]]s) of its material would have a mass over {{val|5.5|e=12|u=kg}}, about 900 times the mass of the [[Great Pyramid of Giza]].<ref group="lower-alpha">The average density of material in a neutron star of radius 10&nbsp;km is {{val|1.1|e=12|u=kg/cm3}}. Therefore, 5&nbsp;ml of such material is {{val|5.5|e=12|u=kg}}, or 5,500,000,000 [[metric ton]]s. This is about 15 times the total mass of the human world population. Alternatively, 5&nbsp;ml from a neutron star of radius 20&nbsp;km radius (average density {{val|8.35|e=10|u=kg/cm3}}) has a mass of about 400 million metric tons, or about the mass of all humans. The gravitational field is ca. {{val|2|e=11}}''g'' or ca. {{val|2|e=12}} N/kg. Moon weight is calculated at 1''g''.</ref> The entire mass of the Earth at neutron star density would fit into a sphere 305&nbsp;m in diameter, about the size of the [[Arecibo Telescope]].

In popular scientific writing, neutron stars are sometimes described as macroscopic [[atomic nucleus|atomic nuclei]]. Indeed, both states are composed of [[nucleon]]s, and they share a similar density to within an order of magnitude. However, in other respects, neutron stars and atomic nuclei are quite different. A nucleus is held together by the [[strong interaction]], whereas a neutron star is held together by [[gravity]]. The density of a nucleus is uniform, while neutron stars are [[#Structure|predicted to consist of multiple layers]] with varying compositions and densities.<ref>{{Cite journal |last1=Baym |first1=G |last2=Pethick |first2=C |date=December 1975 |title=Neutron Stars |journal=Annual Review of Nuclear Science |language=en |volume=25 |issue=1 |pages=27–77 |doi=10.1146/annurev.ns.25.120175.000331 |issn=0066-4243 |bibcode=1975ARNPS..25...27B |doi-access=free }}</ref>

=== Current constraints ===
Because equations of state for neutron stars lead to different observables, such as different mass-radius relations, there are many astronomical constraints on equations of state. These come mostly from [[LIGO]],<ref>{{Cite web |title=LIGO Lab {{!}} Caltech {{!}} MIT |url=https://www.ligo.caltech.edu/ |access-date=2024-05-10 |website=LIGO Lab {{!}} Caltech}}</ref> which is a gravitational wave observatory, and [[Neutron Star Interior Composition Explorer|NICER]],<ref>{{Cite web |title=NICER - NASA Science |url=https://science.nasa.gov/mission/nicer/ |access-date=2024-05-10 |website=science.nasa.gov |language=en-US}}</ref> which is an X-ray telescope.

NICER's observations of [[pulsar]]s in binary systems, from which the pulsar mass and radius can be estimated, can constrain the neutron star equation of state. A 2021 measurement of the pulsar [[PSR J0740+6620]] was able to constrain the radius of a 1.4 solar mass neutron star to {{val|12.33|0.76|0.8}} km with 95% confidence.<ref>{{Cite journal |last1=Raaijmakers |first1=G. |last2=Greif |first2=S. K. |last3=Hebeler |first3=K. |last4=Hinderer |first4=T. |last5=Nissanke |first5=S. |last6=Schwenk |first6=A. |last7=Riley |first7=T. E. |last8=Watts |first8=A. L. |last9=Lattimer |first9=J. M. |last10=Ho |first10=W. C. G. |date=2021-09-01 |title=Constraints on the Dense Matter Equation of State and Neutron Star Properties from NICER's Mass–Radius Estimate of PSR J0740+6620 and Multimessenger Observations |journal=The Astrophysical Journal Letters |volume=918 |issue=2 |pages=L29 |doi=10.3847/2041-8213/ac089a |doi-access=free |arxiv=2105.06981 |bibcode=2021ApJ...918L..29R |issn=2041-8205}}</ref> These mass-radius constraints, combined with [[Chiral perturbation theory|chiral effective field theory]] calculations, tightens constraints on the neutron star equation of state.<ref name=":1" />

Equation of state constraints from LIGO gravitational wave detections start with nuclear and atomic physics researchers, who work to propose theoretical equations of state (such as FPS, UU, APR, L, SLy, and others). The proposed equations of state can then be passed onto astrophysics researchers who run simulations of [[Neutron star merger|binary neutron star mergers]]. From these simulations, researchers can extract [[gravitational wave]]forms, thus studying the relationship between the equation of state and gravitational waves emitted by binary neutron star mergers. Using these relations, one can constrain the neutron star equation of state when gravitational waves from binary neutron star mergers are observed. Past [[numerical relativity]] simulations of binary neutron star mergers have found relationships between the equation of state and frequency dependent peaks of the gravitational wave signal that can be applied to [[LIGO]] detections.<ref>{{Cite journal |last1=Takami |first1=Kentaro |last2=Rezzolla |first2=Luciano |last3=Baiotti |first3=Luca |date=2014-08-28 |title=Constraining the Equation of State of Neutron Stars from Binary Mergers |url=https://link.aps.org/doi/10.1103/PhysRevLett.113.091104 |journal=Physical Review Letters |language=en |volume=113 |issue=9 |page=091104 |doi=10.1103/PhysRevLett.113.091104 |pmid=25215972 |arxiv=1403.5672 |bibcode=2014PhRvL.113i1104T |issn=0031-9007}}</ref> For example, the LIGO detection of the binary neutron star merger [[GW170817]] provided limits on the tidal deformability of the two neutron stars which dramatically reduced the family of allowed equations of state.<ref>{{Cite journal |last1=Annala |first1=Eemeli |last2=Gorda |first2=Tyler |last3=Kurkela |first3=Aleksi |last4=Vuorinen |first4=Aleksi |date=2018-04-25 |title=Gravitational-Wave Constraints on the Neutron-Star-Matter Equation of State |url=https://link.aps.org/doi/10.1103/PhysRevLett.120.172703 |journal=Physical Review Letters |language=en |volume=120 |issue=17 |page=172703 |doi=10.1103/PhysRevLett.120.172703 |pmid=29756823 |arxiv=1711.02644 |bibcode=2018PhRvL.120q2703A |issn=0031-9007}}</ref> Future gravitational wave signals with next generation detectors like [[Cosmic Explorer (gravitational wave observatory)|Cosmic Explorer]] can impose further constraints.<ref>{{Cite journal |last1=Finstad |first1=Daniel |last2=White |first2=Laurel V. |last3=Brown |first3=Duncan A. |date=2023-09-01 |title=Prospects for a Precise Equation of State Measurement from Advanced LIGO and Cosmic Explorer |journal=The Astrophysical Journal |volume=955 |issue=1 |pages=45 |doi=10.3847/1538-4357/acf12f |doi-access=free |arxiv=2211.01396 |bibcode=2023ApJ...955...45F |issn=0004-637X}}</ref>

When nuclear physicists are trying to understand the likelihood of their equation of state, it is good to compare with these constraints to see if it predicts neutron stars of these masses and radii.<ref>{{cite arXiv |last1=Lovato |first1=Alessandro |last2=Dore |first2=Travis |display-authors=1 |title=Long Range Plan: Dense matter theory for heavy-ion collisions and neutron stars |date=2022 |class=nucl-th |eprint=2211.02224}}</ref> There is also recent work on constraining the equation of state with the speed of sound through hydrodynamics.<ref>{{cite journal|last1=Hippert |first1=Mauricio |last2=Noronha |first2=Jorge |last3=Romatschke |first3=Paul |title=Upper Bound on the Speed of Sound in Nuclear Matter from Transport |journal=Physics Letters B |date=2025 |volume=860 |doi=10.1016/j.physletb.2024.139184 |arxiv=2402.14085|bibcode=2025PhLB..86039184H }}</ref>

=== Tolman-Oppenheimer-Volkoff Equation ===
The [[Tolman–Oppenheimer–Volkoff equation|Tolman-Oppenheimer-Volkoff (TOV) equation]] can be used to describe a neutron star. The equation is a solution to Einstein's equations from general relativity for a spherically symmetric, time invariant metric. With a given equation of state, solving the equation leads to observables such as the mass and radius. There are many codes that numerically solve the TOV equation for a given equation of state to find the mass-radius relation and other observables for that equation of state.

The following differential equations can be solved numerically to find the neutron star observables:<ref>{{cite journal |last1=Silbar |first1=Richard R. |last2=Reddy |first2=Sanjay |title=Neutron stars for undergraduates |journal=American Journal of Physics |date=1 July 2004 |volume=72 |issue=7 |pages=892–905 |doi=10.1119/1.1703544|arxiv=nucl-th/0309041 |bibcode=2004AmJPh..72..892S }}</ref>

<math display="block">\frac{dp}{dr} = - \frac{G\epsilon(r) M(r)}{c^2 r^2} \left(1+\frac{p(r)}{\epsilon(r)}\right) \left(1+\frac{4\pi r^3p(r)}{M(r)c^2}\right) \left(1-\frac{2GM(r)}{c^2r}\right)</math>
<math display="block">\frac{dM}{dr} = \frac{4\pi}{c^2} r^2 \epsilon(r)</math>

where <math>G</math> is the gravitational constant, <math>p(r)</math> is the pressure, <math>\epsilon(r)</math> is the energy density (found from the equation of state), and <math>c</math> is the speed of light.

=== Mass-Radius relation ===
Using the TOV equations and an equation of state, a mass-radius curve can be found. The idea is that for the correct equation of state, every neutron star that could possibly exist would lie along that curve. This is one of the ways equations of state can be constrained by astronomical observations. To create these curves, one must solve the TOV equations for different central densities. For each central density, one numerically solve the mass and pressure equations until the pressure goes to zero, which is the outside of the star. Each solution gives a corresponding mass and radius for that central density.

Mass-radius curves determine what the maximum mass is for a given equation of state. Through most of the mass-radius curve, each radius corresponds to a unique mass value. At a certain point, the curve will reach a maximum and start going back down, leading to repeated mass values for different radii. This maximum point is what is known as the maximum mass. Beyond that mass, the star will no longer be stable, i.e. no longer be able to hold itself up against the force of gravity, and would collapse into a black hole. Since each equation of state leads to a different mass-radius curve, they also lead to a unique maximum mass value. The maximum mass value is unknown as long as the equation of state remains unknown.

This is very important when it comes to constraining the equation of state. Oppenheimer and Volkoff came up with the [[Tolman–Oppenheimer–Volkoff limit|Tolman-Oppenheimer-Volkoff limit]] using a degenerate gas equation of state with the TOV equations that was ~0.7 Solar masses. Since the neutron stars that have been observed are more massive than that, that maximum mass was discarded. The most recent massive neutron star that was observed was [[PSR J0952–0607|PSR J0952-0607]] which was {{val|2.35|0.17}} solar masses. Any equation of state with a mass less than that would not predict that star and thus is much less likely to be correct.

An interesting phenomenon in this area of astrophysics relating to the maximum mass of neutron stars is what is called the "mass gap". The mass gap refers to a range of masses from roughly 2-5 solar masses where very few compact objects were observed. This range is based on the current assumed maximum mass of neutron stars (~2 solar masses) and the minimum black hole mass (~5 solar masses).<ref>{{cite journal |last1=Kumar |first1=N. |last2=Sokolov |first2=V. V. |title=Mass Distribution and "Mass Gap" of Compact Stellar Remnants in Binary Systems |journal=Astrophysical Bulletin |date=June 2022 |volume=77 |issue=2 |pages=197–213 |doi=10.1134/S1990341322020043|arxiv=2204.07632 |bibcode=2022AstBu..77..197K }}</ref> Recently, some objects have been discovered that fall in that mass gap from gravitational wave detections. If the true maximum mass of neutron stars was known, it would help characterize compact objects in that mass range as either neutron stars or black holes.

=== I-Love-Q Relations ===
There are three more properties of neutron stars that are dependent on the equation of state but can also be astronomically observed: the [[moment of inertia]], the [[quadrupole moment]], and the [[Love number]]. The moment of inertia of a neutron star describes how fast the star can rotate at a fixed spin momentum. The quadrupole moment of a neutron star specifies how much that star is deformed out of its spherical shape. The Love number of the neutron star represents how easy or difficult it is to deform the star due to [[tidal force]]s, typically important in binary systems.

While these properties depend on the material of the star and therefore on the equation of state, there is a relation between these three quantities that is independent of the equation of state. This relation assumes slowly and uniformly rotating stars and uses general relativity to derive the relation. While this relation would not be able to add constraints to the equation of state, since it is independent of the equation of state, it does have other applications. If one of these three quantities can be measured for a particular neutron star, this relation can be used to find the other two. In addition, this relation can be used to break the degeneracies in detections by gravitational wave detectors of the quadrupole moment and spin, allowing the average spin to be determined within a certain confidence level.<ref>{{cite journal |last1=Yagi |first1=Kent |last2=Yunes |first2=Nicolás |title=I-Love-Q relations in neutron stars and their applications to astrophysics, gravitational waves, and fundamental physics |journal=Physical Review D |date=19 July 2013 |volume=88 |issue=2 |page=023009 |doi=10.1103/PhysRevD.88.023009|arxiv=1303.1528 |bibcode=2013PhRvD..88b3009Y }}</ref>

===Temperature===

The temperature inside a newly formed neutron star is from around {{val|e=11}} to {{val|e=12|ul=kelvin}}.<ref name="Miller" /> However, the huge number of [[neutrino]]s it emits carries away so much energy that the temperature of an isolated neutron star falls within a few years to around {{val|e=6|u=kelvin}}.<ref name="Miller" /> At this lower temperature, most of the light generated by a neutron star is in X-rays.

Some researchers have proposed a neutron star classification system using [[Roman numerals]] (not to be confused with the [[Stellar classification|Yerkes luminosity classes]] for non-degenerate stars) to sort neutron stars by their mass and cooling rates: type I for neutron stars with low mass and cooling rates, type II for neutron stars with higher mass and cooling rates, and a proposed type III for neutron stars with even higher mass, approaching {{solar mass|2}}, and with higher cooling rates and possibly candidates for [[exotic star]]s.<ref>{{Cite journal |last1=Yakovlev |first1=D. G. |last2=Kaminker |first2=A. D. |last3=Haensel |first3=P. |last4=Gnedin |first4=O. Y. |year=2002 |title=The cooling neutron star in 3C 58 |journal=Astronomy & Astrophysics |volume=389 |pages=L24–L27 |arxiv=astro-ph/0204233 |bibcode=2002A&A...389L..24Y |doi=10.1051/0004-6361:20020699 |s2cid=6247160}}</ref>

===Magnetic field===
The magnetic field strength on the surface of neutron stars ranges from {{circa|{{val|e=4}}}} to {{val|e=11}}&nbsp;[[Tesla (unit)|tesla]] (T).<ref name="reisenegger">{{cite arXiv |first=A. |last=Reisenegger |year=2003 |title=Origin and Evolution of Neutron Star Magnetic Fields |eprint=astro-ph/0307133 }}</ref> These are orders of magnitude higher than in any other object: for comparison, a continuous 16&nbsp;T field has been achieved in the laboratory and is sufficient to levitate a living frog due to [[diamagnetic levitation]]. Variations in magnetic field strengths are most likely the main factor that allows different types of neutron stars to be distinguished by their spectra, and explains the periodicity of pulsars.<ref name="reisenegger"/>

The neutron stars known as [[magnetar]]s have the strongest magnetic fields, in the range of {{val|e=8}} to {{val|e=11|u=T}},<ref name="mcgill">{{cite web |title=McGill SGR/AXP Online Catalog |url=http://www.physics.mcgill.ca/~pulsar/magnetar/main.html |access-date=2 Jan 2014 |archive-date=23 July 2020 |archive-url=https://web.archive.org/web/20200723080137/http://www.physics.mcgill.ca/~pulsar/magnetar/main.html |url-status=live }}</ref> and have become the widely accepted hypothesis for neutron star types [[soft gamma repeater]]s (SGRs)<ref name="sa">{{cite journal |first1=Chryssa |last1=Kouveliotou |first2=Robert C. |last2=Duncan |first3=Christopher |last3=Thompson |date=February 2003 |title=Magnetars |journal=Scientific American |volume=288 |issue=2 |pages=34–41 |doi=10.1038/scientificamerican0203-34 |pmid=12561456 |bibcode=2003SciAm.288b..34K }}</ref> and [[anomalous X-ray pulsar]]s (AXPs).<ref>{{cite journal |first1=V.M. |last1=Kaspi |first2=F.P. |last2=Gavriil |year=2004 |title=(Anomalous) X-ray pulsars |journal=Nuclear Physics B |series=Proceedings Supplements |volume=132 |pages=456–465 |doi=10.1016/j.nuclphysbps.2004.04.080 |arxiv=astro-ph/0402176 |bibcode=2004NuPhS.132..456K|s2cid=15906305 }}</ref> The magnetic [[energy density]] of a {{val|e=8|u=T}} field is extreme, greatly exceeding the [[theoretical total mass-energy|mass-energy]] density of ordinary matter.{{efn|Magnetic [[energy density]] for a [[magnetic field|field B]] is {{nowrap| U {{=}} {{frac|[[Vacuum permeability|μ<sub>0</sub>]] B<sup>2</sup>|2}} .}}<ref>{{cite web |url=http://scienceworld.wolfram.com/physics/MagneticFieldEnergyDensity.html |title=Eric Weisstein's World of Physics |website=scienceworld.wolfram.com |archive-url=https://web.archive.org/web/20190423232524/http://scienceworld.wolfram.com/physics/MagneticFieldEnergyDensity.html |archive-date=2019-04-23}}</ref> Substituting {{nowrap| B {{=}} {{val|e=8|u=T}} ,}} get {{nowrap|U {{=}} {{val|4|e=21|u=J|up=m3}} .}} Dividing by c<sup>2</sup> one obtains the equivalent mass density of {{val|44500|u=kg|up=m3}}, which exceeds the [[standard temperature and pressure]] density of all known materials. Compare with {{val|22590|u=kg|up=m3}} for [[osmium]], the densest stable element.}} Fields of this strength are able to [[Vacuum polarization|polarize the vacuum]] to the point that the vacuum becomes [[birefringent]]. Photons can merge or split in two, and virtual particle-antiparticle pairs are produced. The field changes electron energy levels and atoms are forced into thin cylinders. Unlike in an ordinary pulsar, magnetar spin-down can be directly powered by its magnetic field, and the magnetic field is strong enough to stress the crust to the point of fracture. Fractures of the crust cause [[Starquake (astrophysics)#Starquake|starquake]]s, observed as extremely luminous millisecond hard gamma ray bursts. The fireball is trapped by the magnetic field, and comes in and out of view when the star rotates, which is observed as a periodic soft gamma repeater (SGR) emission with a period of 5–8&nbsp;seconds and which lasts for a few minutes.<ref>{{cite web |url=http://solomon.as.utexas.edu/magnetar.html |title='Magnetars', soft gamma repeaters & very strong magnetic fields |first=Robert C. |last=Duncan |date=March 2003 |access-date=2018-04-17 |archive-date=2020-01-19 |archive-url=https://web.archive.org/web/20200119142438/http://solomon.as.utexas.edu/magnetar.html |url-status=live }}</ref>

The origins of the strong magnetic field are as yet unclear.<ref name="reisenegger"/> One hypothesis is that of "flux freezing", or conservation of the original [[magnetic flux]] during the formation of the neutron star.<ref name="reisenegger"/> If an object has a certain magnetic flux over its surface area, and that area shrinks to a smaller area, but the magnetic flux is conserved, then the [[magnetic field]] would correspondingly increase. Likewise, a collapsing star begins with a much larger surface area than the resulting neutron star, and conservation of magnetic flux would result in a far stronger magnetic field. However, this simple explanation does not fully explain magnetic field strengths of neutron stars.<ref name="reisenegger"/>

===Gravity===
{{See also|Tolman–Oppenheimer–Volkoff equation|White dwarf#Mass–radius relationship}}

[[File:Neutronstar 2Rs.svg|thumb|Gravitational light deflection at a neutron star. Due to relativistic light deflection over half the surface is visible (each grid patch represents 30 by 30 degrees).<ref name="Zahn" /> In [[Geometrized unit system|natural units]], this star's mass is 1 and its radius is 4, or twice its [[Schwarzschild radius]].<ref name="Zahn" />]]

The gravitational field at a neutron star's surface is about {{val|2|e=11}} times [[Standard gravity|stronger than on Earth]], at around {{val|2.0|e=12|u=m/s2}}.<ref>{{cite book |title=An Introduction to the Sun and Stars |edition=illustrated |first1=Simon F. |last1=Green |first2=Mark H. |last2=Jones |first3=S. Jocelyn |last3=Burnell |publisher=Cambridge University Press |year=2004 |isbn=978-0-521-54622-5 |page=322 |url=https://books.google.com/books?id=lb5owLGIQGsC&pg=PA322 |access-date=2016-06-09 |archive-date=2017-01-31 |archive-url=https://web.archive.org/web/20170131005503/https://books.google.com/books?id=lb5owLGIQGsC&pg=PA322 |url-status=live }}</ref> Such a strong gravitational field acts as a [[gravitational lens]] and bends the radiation emitted by the neutron star such that parts of the normally invisible rear surface become visible.<ref name="Zahn">{{cite web |first=Corvin |last=Zahn |title=Tempolimit Lichtgeschwindigkeit |date=1990-10-09 |url=http://www.tempolimit-lichtgeschwindigkeit.de/galerie/galerie.html |language=de |quote=Durch die gravitative Lichtablenkung ist mehr als die Hälfte der Oberfläche sichtbar. Masse des Neutronensterns: 1, Radius des Neutronensterns: 4, ... dimensionslosen Einheiten (''c'', ''G'' = 1) |access-date=2009-10-09 |archive-date=2021-01-26 |archive-url=https://web.archive.org/web/20210126171353/https://www.tempolimit-lichtgeschwindigkeit.de/galerie/galerie.html |url-status=live }}</ref>
If the radius of the neutron star is 3''GM''/''c''<sup>2</sup> or less, then the photons may be [[photon sphere|trapped in an orbit]], thus making the whole surface of that neutron star visible from a single vantage point, along with destabilizing photon orbits at or below the 1 radius distance of the star.

A fraction of the mass of a star that collapses to form a neutron star is released in the supernova explosion from which it forms (from the law of mass–energy equivalence, {{nowrap|1=''E'' = ''mc''<sup>2</sup>}}). The energy comes from the [[gravitational binding energy]] of a neutron star.

Hence, the gravitational force of a typical neutron star is huge. If an object were to fall from a height of one meter on a neutron star 12 kilometers in radius, it would reach the ground at around 1,400 kilometers per second.<ref>{{cite web |title=Peligroso lugar para jugar tenis |url=http://www.datosfreak.org/datos/slug/Aceleracion-de-superficie-estrella-de-neutrones |website=Datos Freak |access-date=3 June 2016 |language=es |archive-date=11 June 2016 |archive-url=https://web.archive.org/web/20160611022635/http://www.datosfreak.org/datos/slug/Aceleracion-de-superficie-estrella-de-neutrones |url-status=live }}</ref> However, even before impact, the [[tidal force]] would cause [[spaghettification]], breaking any sort of an ordinary object into a stream of material.

Because of the enormous gravity, [[time dilation]] between a neutron star and Earth is significant. For example, eight years could pass on the surface of a neutron star, yet ten years would have passed on Earth, not including the time-dilation effect of the star's very rapid rotation.<ref>{{cite book|author=Marcia Bartusiak | title=Black Hole: How an Idea Abandoned by Newtonians, Hated by Einstein, and Gambled on by Hawking Became Loved| url=https://archive.org/details/blackholehowidea0000bart |url-access=registration |year=2015 | publisher=Yale University Press | isbn=978-0-300-21363-8 |page=[https://archive.org/details/blackholehowidea0000bart/page/130 130]}}</ref>

Neutron star relativistic equations of state describe the relation of radius vs. mass for various models.<ref>[http://www.ns-grb.com/PPT/Lattimer.pdf Neutron Star Masses and Radii] {{Webarchive|url=https://web.archive.org/web/20111217102314/http://www.ns-grb.com/PPT/Lattimer.pdf |date=2011-12-17 }}, p. 9/20, bottom</ref> The most likely radii for a given neutron star mass are bracketed by models AP4 (smallest radius) and MS2 (largest radius). ''E''<sub>B</sub> is the ratio of gravitational binding energy mass equivalent to the observed neutron star gravitational mass of ''M'' kilograms with radius ''R'' meters,<ref>{{Cite journal |arxiv = astro-ph/0002232|last1 = Hessels|first1 = Jason W. T|title = Neutron Star Structure and the Equation of State | journal = The Astrophysical Journal | volume = 550 | issue = 426|pages = 426–442|last2 = Ransom|first2 = Scott M|last3 = Stairs|first3 = Ingrid H|last4 = Freire | first4 = Paulo C. C | last5 = Kaspi|first5 = Victoria M|last6 = Camilo|first6 = Fernando|year = 2001|doi = 10.1086/319702|bibcode = 2001ApJ...550..426L|s2cid = 14782250}}</ref>
<math display="block">E_\text{B} = \frac{0.60\,\beta}{1 - \frac{\beta}{2}}</math><math display="block">\beta \ = G\,M/R\,{c}^{2}</math>
Given current values
*<math>G = 6.67408\times10^{-11}\, \text{m}^3\text{kg}^{-1}\text{s}^{-2}</math><ref name="CODATA 2014">CODATA 2014</ref>
*<math>c = 2.99792458 \times10^{8}\, \text{m}/\text{s}</math><ref name="CODATA 2014" />
*<math>M_\odot = 1.98855\times10^{30}\, \text{kg}</math>
and star masses "M" commonly reported as multiples of one solar mass,
<math display="block">M_x = \frac{M}{M_\odot}</math>
then the relativistic fractional binding energy of a neutron star is
<math display="block">E_\text{B} = \frac{886.0 \,M_x}{R_{\left[\text{in meters}\right]} - 738.3\,M_x}</math>

A {{Solar mass|2}} neutron star would not be more compact than 10,970 meters radius (AP4 model). Its mass fraction gravitational binding energy would then be 0.187, −18.7% (exothermic). This is not near 0.6/2 = 0.3, −30%.

==Structure==
[[Image:Neutron star cross section.svg|thumb|Cross-section of neutron star. Densities are in terms of ''ρ<sub>0</sub>'' the saturation [[Nuclear density|nuclear matter density]], where nucleons begin to touch.]]

Current understanding of the structure of neutron stars is defined by existing mathematical models, but it might be possible to infer some details through studies of [[neutron-star oscillations]]. [[Asteroseismology]], a study applied to ordinary stars, can reveal the inner structure of neutron stars by analyzing observed [[Frequency spectrum|spectra]] of stellar oscillations.<ref name="Haensel" />

Current models indicate that matter at the surface of a neutron star is composed of ordinary [[atomic nucleus|atomic nuclei]] crushed into a solid lattice with a sea of [[electron]]s flowing through the gaps between them. It is possible that the nuclei at the surface are [[iron]], due to iron's high [[binding energy]] per nucleon.<ref name="Surface">{{Cite journal |doi=10.1070/pu1999v042n11ABEH000665 |pages=1173–1174 |title=Radio pulsars |date=1999 |last1=Beskin |first1=Vasilii S. |journal=Physics-Uspekhi |volume=42 |issue=11 |bibcode = 1999PhyU...42.1071B |s2cid=250831196 |doi-access=free }}</ref> It is also possible that heavy elements, such as iron, simply sink beneath the surface, leaving only light nuclei like [[helium]] and [[hydrogen]].<ref name="Surface" /> If the surface temperature exceeds {{val|e=6|u=kelvins}} (as in the case of a young pulsar), the surface should be fluid instead of the solid phase that might exist in cooler neutron stars (temperature <{{val|e=6|u=kelvins}}).<ref name="Surface" />

The "atmosphere" of a neutron star is hypothesized to be at most several micrometers thick, and its dynamics are fully controlled by the neutron star's magnetic field. Below the atmosphere one encounters a solid "crust". This crust is extremely hard and very smooth (with maximum surface irregularities on the order of millimeters or less), due to the extreme gravitational field.<ref>{{Cite web|url=http://www.daviddarling.info/encyclopedia/N/neutronstar.html|title=neutron star|first=David|last=Darling|website=www.daviddarling.info|access-date=2009-01-12|archive-date=2009-01-24|archive-url=https://web.archive.org/web/20090124222032/http://daviddarling.info/encyclopedia/N/neutronstar.html|url-status=live}}</ref><ref name=mt-ls/>

Proceeding inward, one encounters nuclei with ever-increasing numbers of neutrons; such nuclei would decay quickly on Earth, but are kept stable by tremendous pressures. As this process continues at increasing depths, the [[neutron drip line|neutron drip]] becomes overwhelming, and the concentration of free neutrons increases rapidly.

After a [[supernova]] explosion of a [[supergiant]] star, neutron stars are born from the remnants. A neutron star is composed mostly of [[neutron]]s (neutral particles) and contains a small fraction of [[proton]]s (positively charged particles) and [[electron]]s (negatively charged particles), as well as nuclei. In the extreme density of a neutron star, many neutrons are free neutrons, meaning they are not bound in atomic nuclei and move freely within the star's dense matter, especially in the densest regions of the star—the inner crust and core. Over the star's lifetime, as its density increases, the energy of the electrons also increases, which generates more neutrons.<ref name="burrows">Burrows, A.</ref>

In neutron stars, the neutron drip is the transition point where nuclei become so neutron-rich that they can no longer hold additional neutrons, leading to a sea of free neutrons being formed. The sea of neutrons formed after neutron drip provides additional pressure support, which helps maintain the star's structural integrity and prevents gravitational collapse. The neutron drip takes place within the inner crust of the neutron star and starts when the density becomes so high that nuclei can no longer hold additional neutrons.<ref name="sorlin2008">Sorlin, O. and Porquet, M. (2008).</ref>

At the beginning of the neutron drip, the pressure in the star from neutrons, electrons, and the total pressure is roughly equal. As the density of the neutron star increases, the nuclei break down, and the neutron pressure of the star becomes dominant. When the density reaches a point where nuclei touch and subsequently merge, they form a fluid of neutrons with a sprinkle of electrons and protons. This transition marks the neutron drip, where the dominant pressure in the neutron star shifts from degenerate electrons to neutrons.

At very high densities, the neutron pressure becomes the primary pressure holding up the star, with neutrons being non-relativistic (moving slower than the speed of light) and extremely compressed. However, at extremely high densities, neutrons begin to move at relativistic speeds (close to the speed of light). These high speeds significantly increase the star's overall pressure, altering the star's equilibrium state, and potentially leading to the formation of exotic states of matter.

In that region, there are nuclei, free electrons, and free neutrons. The nuclei become increasingly small (gravity and pressure overwhelming the [[strong force]]) until the core is reached, by definition the point where mostly neutrons exist. The expected hierarchy of phases of nuclear matter in the inner crust has been characterized as "[[nuclear pasta]]", with fewer voids and larger structures towards higher pressures.<ref>{{cite journal |title=Too much "pasta" for pulsars to spin down |date=2013 |last1=Pons |first1=José A. |first2= Daniele |last2=Viganò |first3=Nanda |last3=Rea |doi=10.1038/nphys2640 |journal=Nature Physics |volume=9 |issue=7 |pages=431–434 |arxiv=1304.6546 |bibcode=2013NatPh...9..431P |s2cid=119253979 }}</ref>
The composition of the superdense matter in the core remains uncertain. One model describes the core as [[superfluid]] [[Degenerate matter#Neutron degeneracy|neutron-degenerate matter]] (mostly neutrons, with some protons and electrons). More exotic forms of matter are possible, including degenerate [[strange matter]] (containing [[strange quark]]s in addition to [[up quark|up]] and [[down quark]]s), matter containing high-energy [[pion]]s and [[kaon]]s in addition to neutrons,<ref name="Haensel" /> or ultra-dense [[Degenerate matter#Quark degeneracy|quark-degenerate matter]].

==Radiation==
[[File:Pulsar anim.ogv|thumb|Animation of a rotating pulsar. The sphere in the middle represents the neutron star, the curves indicate the magnetic field lines and the protruding cones represent the emission zones.]]

===Pulsars===
{{Main|Pulsar}}

Neutron stars are detected from their [[electromagnetic radiation]]. Neutron stars are usually observed to [[Pulse (physics)|pulse]] [[radio wave]]s and other electromagnetic radiation, and neutron stars observed with pulses are called pulsars.

Pulsars' radiation is thought to be caused by particle acceleration near their [[Poles of astronomical bodies#Magnetic poles|magnetic poles]], which need not be aligned with the [[axis of rotation|rotational axis]] of the neutron star. It is thought that a large [[electrostatic field]] builds up near the magnetic poles, leading to [[electron emission]].<ref name="nrao" /> These electrons are magnetically accelerated along the field lines, leading to [[curvature radiation]], with the radiation being strongly [[Polarization (waves)|polarized]] towards the plane of curvature.<ref name="nrao" /> In addition, high-energy [[photons]] can interact with lower-energy photons and the magnetic field for [[electron−positron pair production]], which through [[electron–positron annihilation]] leads to further high-energy photons.<ref name="nrao" />

The radiation emanating from the magnetic poles of neutron stars can be described as ''magnetospheric radiation'', in reference to the [[magnetosphere]] of the neutron star.<ref name="pavlov" /> It is not to be confused with ''[[Multipole radiation|magnetic dipole radiation]]'', which is emitted because the [[poles of astronomical bodies#Magnetic poles|magnetic]] [[Rotation around a fixed axis|axis]] is not aligned with the rotational axis, with a radiation frequency the same as the neutron star's rotational frequency.<ref name="nrao" />

If the axis of rotation of the neutron star is different from the magnetic axis, external viewers will only see these beams of radiation whenever the magnetic axis point towards them during the neutron star rotation. Therefore, [[Periodic function|periodic]] pulses are observed, at the same rate as the rotation of the neutron star.

In May 2022, astronomers reported an ultra-long-period radio-emitting neutron star [[PSR J0901-4046]], with spin properties distinct from the known neutron stars.<ref>{{Cite journal |last1=Caleb |first1=Manisha|author1-link=Manisha Caleb |last2=Heywood |first2=Ian |last3=Rajwade |first3=Kaustubh |last4=Malenta |first4=Mateusz |last5=Willem Stappers |first5=Benjamin |last6=Barr |first6=Ewan |last7=Chen |first7=Weiwei |last8=Morello |first8=Vincent |last9=Sanidas |first9=Sotiris |last10=van den Eijnden |first10=Jakob |last11=Kramer |first11=Michael |date=2022-05-30 |title=Discovery of a radio-emitting neutron star with an ultra-long spin period of 76 s |journal=Nature Astronomy |volume=6 |issue=7 |language=en |pages=828–836 |doi=10.1038/s41550-022-01688-x |pmid=35880202 |pmc=7613111 |arxiv=2206.01346 |bibcode=2022NatAs...6..828C |s2cid=249212424 |issn=2397-3366}}</ref> It is unclear how its radio emission is generated, and it challenges the current understanding of how pulsars evolve.<ref>{{Cite web |title=Unusual neutron star discovered in stellar graveyard |url=https://www.sydney.edu.au/news-opinion/news/2022/05/31/unusual-neutron-star-discovered-in-stellar-graveyard.html |access-date=2022-06-01 |website=The University of Sydney |language=en-AU}}</ref>

===Non-pulsating neutron stars===
In addition to pulsars, non-pulsating neutron stars have also been identified, although they may have minor periodic variation in luminosity.<ref name="cco"/><ref name="non-pulsating">{{cite journal |title=A non-pulsating neutron star in the supernova remnant HESS J1731-347 / G353.6–0.7 with a carbon atmosphere |first1=D. |last1=Klochkov |first2=G. |last2=Puehlhofer |first3=V. |last3=Suleimanov |first4=S. |last4=Simon |first5=K. |last5=Werner |first6=A. |last6=Santangelo |journal=Astronomy & Astrophysics |volume=556 |pages=A41 |year=2013 |doi=10.1051/0004-6361/201321740 |arxiv=1307.1230 |bibcode=2013A&A...556A..41K |s2cid=119184617 }}</ref> This seems to be a characteristic of the X-ray sources known as [[Central Compact Object]]s in [[supernova remnant]]s (CCOs in SNRs), which are thought to be young, radio-quiet isolated neutron stars.<ref name="cco">{{Cite journal |arxiv=0712.2209 |year=2008 |first=Andrea |last=De Luca |volume=983 |pages=311–319 |doi=10.1063/1.2900173 |title=Central Compact Objects in Supernova Remnants |journal=AIP Conference Proceedings |citeseerx=10.1.1.769.699 |bibcode=2008AIPC..983..311D |s2cid=118470472 }}</ref>

===Spectra===
In addition to [[radio wave|radio]] emissions, neutron stars have also been identified in other parts of the [[electromagnetic spectrum]]. This includes [[Light|visible light]], [[near infrared]], [[ultraviolet]], [[X-ray]]s, and [[gamma ray]]s.<ref name="pavlov">{{cite web |url=http://www.pulsarastronomy.net/IAUS291/download/Oral/IAUS291_PavlovG.pdf |title=X-ray Properties of Rotation Powered Pulsars and Thermally Emitting Neutron Stars |publisher=pulsarastronomy.net |access-date=6 April 2016 |first=George |last=Pavlov |archive-date=6 December 2015 |archive-url=https://web.archive.org/web/20151206215220/http://www.pulsarastronomy.net/IAUS291/download/Oral/IAUS291_PavlovG.pdf |url-status=live }}</ref> Pulsars observed in X-rays are known as [[Accretion-powered pulsars|X-ray pulsars if accretion-powered]], while those identified in visible light are known as [[optical pulsar]]s. The majority of neutron stars detected, including those identified in optical, X-ray, and gamma rays, also emit radio waves;<ref name="jb">{{cite web |url=http://www.jb.man.ac.uk/distance/frontiers/pulsars/section7.html |title=7. Pulsars at Other Wavelengths |publisher=Jodrell Bank Centre for Astrophysics |website=Frontiers of Modern Astronomy |access-date=6 April 2016 |archive-date=10 April 2016 |archive-url=https://web.archive.org/web/20160410062808/http://www.jb.man.ac.uk/distance/frontiers/pulsars/section7.html |url-status=live }}</ref> the [[Crab Pulsar]] produces electromagnetic emissions across the spectrum.<ref name="jb" /> However, there exist neutron stars called [[radio-quiet neutron star]]s, with no radio emissions detected.<ref name="ras">{{cite journal |title=The implications of radio-quiet neutron stars |first1=K. T. S. |last1=Brazier |first2=S. |last2=Johnston |name-list-style=amp |journal=Monthly Notices of the Royal Astronomical Society |volume=305 |issue=3 |pages=671 |date=August 2013 |doi=10.1046/j.1365-8711.1999.02490.x |doi-access=free |arxiv=astro-ph/9803176 |bibcode=1999MNRAS.305..671B |s2cid=6777734 }}</ref>

==Rotation==

Neutron stars rotate extremely rapidly after their formation due to the conservation of angular momentum; in analogy to spinning ice skaters pulling in their arms, the slow rotation of the original star's core speeds up as it shrinks. A newborn neutron star can rotate many times a second.

===Spin down===
[[Image:PPdot2.png|thumb|''P''–''P''-dot diagram for known [[rotation-powered pulsar]]s (red), anomalous X-ray pulsars (green), high-energy emission pulsars (blue) and [[binary pulsar]]s (pink)]]
Over time, neutron stars slow, as their rotating magnetic fields in effect radiate energy associated with the rotation; older neutron stars may take several seconds for each revolution. This is called ''spin down''. The rate at which a neutron star slows its rotation is usually constant and very small.

The [[periodic time]] (''P'') is the [[Rotation period|rotational period]], the time for one rotation of a neutron star. The spin-down rate, the rate of slowing of rotation, is then given the symbol <math>\dot{P}</math> (''P''-dot), the [[derivative]] of ''P'' with respect to time. It is defined as periodic time increase per unit time; it is a [[dimensionless quantity]], but can be given the units of s⋅s<sup>−1</sup> (seconds per second).<ref name="nrao">{{cite web |url=https://www.cv.nrao.edu/~sransom/web/Ch6.html |title=Pulsar Properties (Essential radio Astronomy) |publisher=National Radio Astronomy Observatory |access-date=24 March 2016 |first1=J. J. |last1=Condon |first2=S. M. |last2=Ransom |name-list-style=amp |archive-date=10 April 2016 |archive-url=https://web.archive.org/web/20160410113528/http://www.cv.nrao.edu/~sransom/web/Ch6.html |url-status=live }}</ref>

The spin-down rate (''P''-dot) of neutron stars usually falls within the range of {{val|e=−22}} to {{val|e=−9|u=s⋅s<sup>−1</sup>}}, with the shorter period (or faster rotating) observable neutron stars usually having smaller ''P''-dot. As a neutron star ages, its rotation slows (as ''P'' increases); eventually, the rate of rotation will become too slow to power the radio-emission mechanism, so radio emission from the neutron star no longer can be detected.<ref name="nrao" />

''P'' and ''P''-dot allow minimum magnetic fields of neutron stars to be estimated.<ref name="nrao" /> ''P'' and ''P''-dot can be also used to calculate the ''characteristic age'' of a pulsar, but gives an estimate which is somewhat larger than the true age when it is applied to young pulsars.<ref name="nrao" />

''P'' and ''P''-dot can also be combined with neutron star's [[moment of inertia]] to estimate a quantity called ''spin-down [[luminosity]]'', which is given the symbol <math>\dot{E}</math> (''E''-dot). It is not the measured luminosity, but rather the calculated loss rate of rotational energy that would manifest itself as radiation. For neutron stars where the spin-down luminosity is comparable to the actual [[luminosity]], the neutron stars are said to be "[[rotation powered pulsar|rotation powered]]".<ref name="nrao" /><ref name="pavlov" /> The observed luminosity of the [[Crab Pulsar]] is comparable to the spin-down luminosity, supporting the model that rotational kinetic energy powers the radiation from it.<ref name="nrao" /> With neutron stars such as magnetars, where the actual luminosity exceeds the spin-down luminosity by about a factor of one hundred, it is assumed that the luminosity is powered by magnetic dissipation, rather than being rotation powered.<ref name="ufrgs">{{cite web |url=http://www.if.ufrgs.br/hadrons/zhang.pdf |title=Spin-Down Power of Magnetars |publisher=Universidade Federal do Rio Grande do Sul |access-date=24 March 2016 |first=B. |last=Zhang |archive-date=6 February 2021 |archive-url=https://web.archive.org/web/20210206223627/http://www.if.ufrgs.br/hadrons/zhang.pdf |url-status=live }}</ref>

''P'' and ''P''-dot can also be plotted for neutron stars to create a ''P''–''P''-dot diagram. It encodes a tremendous amount of information about the pulsar population and its properties, and has been likened to the [[Hertzsprung–Russell diagram]] in its importance for neutron stars.<ref name="nrao" />

===Spin up===
[[File:Neutron Star X-ray beaming with accretion disk.jpg|thumb|A computer simulation depicting a neutron star with accretion disk, spewing out X-rays through the magnetic axis]]
{{Main|Neutron star spin-up}}
Neutron star rotational speeds can increase, a process known as spin up. Sometimes neutron stars absorb orbiting matter from companion stars, increasing the rotation rate and reshaping the neutron star into an [[oblate spheroid]]. This causes an increase in the rate of rotation of the neutron star of over a hundred times per second in the case of millisecond pulsars.

The most rapidly rotating neutron star currently known, [[PSR J1748-2446ad]], rotates at 716 revolutions per second.<ref>{{Cite journal |arxiv = astro-ph/0601337|last1 = Hessels|first1 = Jason W. T|title = A Radio Pulsar Spinning at 716 Hz|journal = Science|volume = 311|issue = 5769|pages = 1901–1904|last2 = Ransom|first2 = Scott M|last3 = Stairs|first3 = Ingrid H|last4 = Freire|first4 = Paulo C. C|last5 = Kaspi|first5 = Victoria M|last6 = Camilo|first6 = Fernando|year = 2006|doi = 10.1126/science.1123430|pmid = 16410486|citeseerx = 10.1.1.257.5174|bibcode = 2006Sci...311.1901H|s2cid = 14945340}}</ref> A 2007 paper reported the detection of an X-ray burst oscillation, which provides an indirect measure of spin, of 1122&nbsp;[[Hertz|Hz]] from the neutron star [[XTE J1739-285]],<ref name="KaaretPrieskorn2007">{{cite journal|last1=Kaaret|first1=P.|last2=Prieskorn|first2=Z.|last3=Zand|first3=J. J. M. in 't|last4=Brandt|first4=S.|last5=Lund|first5=N.|last6=Mereghetti|first6=S.|last7=Götz|first7=D.|last8=Kuulkers|first8=E.|last9=Tomsick|first9=J. A.|title=Evidence of 1122 Hz X-Ray Burst Oscillations from the Neutron Star X-Ray Transient XTE J1739-285|journal=The Astrophysical Journal|volume=657|issue=2|year=2007|pages=L97–L100|issn=0004-637X|doi=10.1086/513270|arxiv=astro-ph/0611716|bibcode=2007ApJ...657L..97K|s2cid=119405361}}</ref> suggesting 1122 rotations a second. However, at present, this signal has only been seen once, and should be regarded as tentative until confirmed in another burst from that star.

===Glitches and starquakes===
[[Image:2004 stellar quake full.jpg|thumb|NASA artist's conception of a "[[Starquake (astrophysics)#Starquake|starquake]]", or "stellar quake"]]
Sometimes a neutron star will undergo a [[glitch (astronomy)|glitch]], a sudden small increase of its rotational speed or spin up.<ref name=":0">{{Citation |last1=Antonelli |first1=Marco |title=Astrophysics in the XXI Century with Compact Stars |date=November 2022 |pages=219–281 |last2=Montoli |first2=Alessandro |last3=Pizzochero |first3=Pierre|chapter=Insights into the Physics of Neutron Star Interiors from Pulsar Glitches |doi=10.1142/9789811220944_0007 |arxiv=2301.12769 |isbn=978-981-12-2093-7 }}</ref> Glitches are thought to be the effect of a [[starquake (astrophysics)|starquake]]—as the rotation of the neutron star slows, its shape becomes more spherical. Due to the stiffness of the "neutron" crust, this happens as discrete events when the crust ruptures, creating a starquake similar to earthquakes. After the starquake, the star will have a smaller equatorial radius, and because angular momentum is conserved, its rotational speed has increased.

Starquakes occurring in [[magnetars]], with a resulting glitch, is the leading hypothesis for the gamma-ray sources known as soft gamma repeaters.<ref name="sa"/>

Recent work, however, suggests that a starquake would not release sufficient energy for a neutron star glitch; it has been suggested that glitches may instead be caused by transitions of vortices in the theoretical superfluid core of the neutron star from one metastable energy state to a lower one, thereby releasing energy that appears as an increase in the rotation rate.<ref>{{cite web |url=http://physicsworld.com/cws/article/print/1756 |date=1 January 1998 |title=Pulsars, glitches and superfluids |publisher=Physicsworld.com |first=M. Ali |last=Alpar |access-date=12 January 2009 |archive-date=6 December 2008 |archive-url=https://web.archive.org/web/20081206090618/http://physicsworld.com/cws/article/print/1756 |url-status=live }}</ref><ref name=":0" />

===Anti-glitches===

An anti-glitch, a sudden small decrease in rotational speed, or spin down, of a neutron star has also been reported.<ref name="nature">{{cite journal |title=An anti-glitch in a magnetar |journal=Nature |doi=10.1038/nature12159 |year=2013 |first1=R. F. |last1=Archibald |first2=V. M. |last2=Kaspi |first3=C. Y. |last3=Ng |first4=K. N. |last4=Gourgouliatos |first5=D. |last5=Tsang |first6=P. |last6=Scholz |first7=A. P. |last7=Beardmore |first8=N. |last8=Gehrels |first9=J. A. |last9=Kennea |pages=591–593 |volume=497 |issue=7451 |hdl=10722/186148 |pmid=23719460 |arxiv=1305.6894 |bibcode=2013Natur.497..591A |s2cid=4382559 }}</ref><ref>{{cite web |last1=Reddy |first1=Francis |title=NASA's Swift Reveals New Phenomenon in a Neutron Star |url=https://www.nasa.gov/universe/nasas-swift-reveals-new-phenomenon-in-a-neutron-star/ |website=NASA.gov |date=29 May 2013 |publisher=National Aeronautics and Space Administration |access-date=26 September 2024}}</ref> It occurred in the magnetar [[1E 2259+586]], that in one case produced an X-ray luminosity increase of a factor of 20, and a significant spin-down rate change. Current neutron star models do not predict this behavior. If the cause were internal this suggests differential rotation of the solid outer crust and the superfluid component of the magnetar's inner structure.<ref name="nature" /><ref name=":0" />

==Population and distances==
At present, there are about 3,200 known neutron stars in the [[Milky Way]] and the [[Magellanic Clouds]], the majority of which have been detected as radio pulsars. Neutron stars are mostly concentrated along the disk of the Milky Way, although the spread perpendicular to the disk is large because the supernova explosion process can impart high translational speeds (400&nbsp;km/s) to the newly formed neutron star.

Some of the closest known neutron stars are RX J1856.5−3754, which is about 400 [[light-year]]s from Earth, and [[PSR J0108−1431]] about 424 light-years.<ref name="aaa496">{{cite journal |last1=Posselt |first1=B. |last2=Neuhäuser |first2=R. |last3=Haberl |first3=F. |title=Searching for substellar companions of young isolated neutron stars |journal=Astronomy and Astrophysics |volume=496 |issue=2 |date=March 2009 |pages=533–545 |doi=10.1051/0004-6361/200810156 |bibcode=2009A&A...496..533P |arxiv=0811.0398 |s2cid=10639250 }}</ref> RX J1856.5-3754 is a member of a close group of neutron stars called [[The Magnificent Seven (neutron stars)|The Magnificent Seven]]. Another nearby neutron star that was detected transiting the backdrop of the constellation Ursa Minor has been nicknamed [[Calvera (X-ray source)|Calvera]] by its Canadian and American discoverers, after the villain in the 1960 film ''[[The Magnificent Seven]]''. This rapidly moving object was discovered using the [[ROSAT]] Bright Source Catalog.

Neutron stars are only detectable with modern technology during the earliest stages of their lives (almost always less than 1 million years) and are vastly outnumbered by older neutron stars that would only be detectable through their [[Black-body radiation|blackbody radiation]] and gravitational effects on other stars.

==Binary neutron star systems==
{{anchor|Binary neutron stars}}<!-- used by incoming redirects -->
[[File:15-137-CircinusX1-XRayLightRings-NeutronStar-Chandra-20150624.jpg|thumb|[[Circinus X-1]]: X-ray light rings from a binary neutron star (24 June 2015; [[Chandra X-ray Observatory]])]]

About 5% of all known neutron stars are members of a [[binary system (astronomy)|binary system]]. The formation and evolution of binary neutron stars<ref>{{cite book |bibcode=2006csxs.book..623T |year=2006 |title=Formation and evolution of compact stellar X-ray sources |last1=Tauris |first1=T. M. |last2=Van Den Heuvel |first2=E. P. J. |quote=Fig. 16.4. Illustration of the relative distribution of all ~ 1500 radio pulsars observed. About 4% are members of a binary system.}}</ref> and double neutron stars<ref name="TaurisKramerFreire2017">{{cite journal | last1 = Tauris | first1 = T. M. | last2 = Kramer | first2 = M. | last3 = Freire | first3 = P. C. C. | last4 = Wex | first4 = N. | last5 = Janka | first5 = H.-T. | last6 = Langer | first6 = N. | last7 = Podsiadlowski | first7 = Ph. | last8 = Bozzo | first8 = E. | last9 = Chaty | first9 = S. | last10 = Kruckow | first10 = M. U. | last11 = Heuvel | first11 = E. P. J. van den | last12 = Antoniadis | first12 = J. | last13 = Breton | first13 = R. P. | last14 = Champion | first14 = D. J. | title = Formation of Double Neutron Star Systems | journal = The Astrophysical Journal | date = 13 September 2017 | volume = 846 | issue = 2 | page = 170 | eissn = 1538-4357 | doi = 10.3847/1538-4357/aa7e89 | pmid = | arxiv = 1706.09438 | bibcode = 2017ApJ...846..170T | s2cid = 119471204 | doi-access = free }}</ref> can be a complex process. Neutron stars have been observed in binaries with ordinary [[main-sequence star]]s, [[red giant]]s, white dwarfs, or other neutron stars. According to modern theories of binary evolution, it is expected that neutron stars also exist in binary systems with black hole companions. The merger of binaries containing two neutron stars, or a neutron star and a black hole, has been observed through the emission of [[gravitational waves]].<ref>{{cite journal | last1=Abbott | first1=B. P. | last2=Abbott | first2=R. | last3=Abbott | first3=T. D. | last4=Acernese | first4=F. | last5=Ackley | first5=K. | last6=Adams | first6=C. | last7=Adams | first7=T. | last8=Addesso | first8=P. | last9=Adhikari | first9=R. X. | last10=Adya | first10=V. B. |display-authors=5 |collaboration=LIGO Scientific Collaboration and Virgo Collaboration| title=GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral | journal=Physical Review Letters | volume=119 | issue=16 | date=2017-10-16 | issn=0031-9007 | doi=10.1103/physrevlett.119.161101 | page=161101| pmid=29099225 | arxiv=1710.05832 | bibcode=2017PhRvL.119p1101A |doi-access=free}}</ref><ref>{{cite journal | last1=Abbott | first1=B. P. | last2=Abbott | first2=R. | last3=Abbott | first3=T. D. | last4=Abernathy | first4=M. R. | last5=Acernese | first5=F. | last6=Ackley | first6=K. | last7=Adams | first7=C. | last8=Adams | first8=T. | last9=Addesso | first9=P. | last10=Adhikari | first10=R. X. | display-authors=5|collaboration=LIGO Scientific Collaboration and Virgo Collaboration| title=Observation of Gravitational Waves from a Binary Black Hole Merger | journal=Physical Review Letters | volume=116 | issue=6 | date=2016-02-11 | issn=0031-9007 | doi=10.1103/physrevlett.116.061102 | page=1161102| pmid=26918975 | arxiv=1602.03837 | bibcode=2016PhRvL.116f1102A |doi-access=free}}</ref>

===X-ray binaries===
{{main|X-ray binary}}
Binary systems containing neutron stars often emit X-rays, which are emitted by hot gas as it falls towards the surface of the neutron star. The source of the gas is the companion star, the outer layers of which can be stripped off by the gravitational force of the neutron star if the two stars are sufficiently close. As the neutron star accretes this gas, its mass can increase; if enough mass is accreted, the neutron star may collapse into a black hole.<ref name=lewin2010>{{cite book |bibcode=2010csxs.book.....L |year=2010 |title=Compact Stellar X-ray Sources |last1=Lewin |first1=Walter |last2=Van Der Klis |first2=Michiel }}</ref>

===Neutron star binary mergers and nucleosynthesis===
{{Main|Neutron star merger}}

{{Multiple image
|perrow=2
|total_width=300
|image1=Neutron Stars Rip Each Other Apart to Form Black Hole (GSFC 20171208 Archive e001098).jpg
|image2=Neutron Stars Rip Each Other Apart to Form Black Hole (GSFC 20171208 Archive e001099).jpg
|image3=Neutron Stars Rip Each Other Apart to Form Black Hole (GSFC 20171208 Archive e001100).jpg
|image4=Neutron Stars Rip Each Other Apart to Form Black Hole (GSFC 20171208 Archive e001101).jpg
|footer=Four snapshots from a computer simulation of a neutron star merger. Clockwise, from top left:
#The two neutron stars make initial contact
#Immense tidal forces begin to disrupt the outer layers of the neutron stars
#The neutron stars are completely tidally disrupted
#A black hole forms, surrounded by an accretion disc
}}

The distance between two neutron stars in a close binary system is observed to shrink as [[gravitational waves]] are emitted.<ref>{{cite journal |last1=Taylor |first1=J. H. |last2=Weisberg |first2=J. M. |title=A new test of general relativity – Gravitational radiation and the binary pulsar PSR 1913+16 |journal=The Astrophysical Journal |date=15 February 1982 |volume=253 |page=908 |doi=10.1086/159690 |bibcode=1982ApJ...253..908T }}</ref> Ultimately, the neutron stars will come into contact and coalesce. The coalescence of binary neutron stars is one of the leading models for the origin of [[Gamma-ray burst#Short gamma-ray bursts|short gamma-ray bursts]]. Strong evidence for this model came from the observation of a [[kilonova]] associated with the short-duration gamma-ray burst GRB 130603B,<ref>{{cite journal |last1=Tanvir |first1=N. |last2=Levan |first2=A. J. |last3=Fruchter |first3=A. S. |last4=Hjorth |first4=J. |last5=Hounsell |first5=R. A. |last6=Wiersema |first6=K. |last7=Tunnicliffe |first7=R. L. |title=A 'kilonova' associated with the short-duration gamma-ray burst GRB 130603B |journal=Nature |date=2013 |volume=500 |issue=7464 |pages=547–549 |doi=10.1038/nature12505 |bibcode=2013Natur.500..547T |pmid=23912055 |arxiv=1306.4971 |s2cid=205235329 }}</ref> and was finally confirmed by detection of gravitational wave [[GW170817]] and short [[GRB 170817A]] by [[LIGO]], [[Virgo interferometer|Virgo]], and 70 observatories covering the electromagnetic spectrum observing the event.<ref name="SM-20171016">{{cite news |last=Cho |first=Adrian |title=Merging neutron stars generate gravitational waves and a celestial light show |url=https://www.science.org/content/article/merging-neutron-stars-generate-gravitational-waves-and-celestial-light-show |date=16 October 2017 |work=[[Science (magazine)|Science]] |access-date=16 October 2017 |archive-date=18 October 2017 |archive-url=https://web.archive.org/web/20171018011625/http://www.sciencemag.org/news/2017/10/merging-neutron-stars-generate-gravitational-waves-and-celestial-light-show |url-status=live }}</ref><ref name="NYT-20171016">{{cite news |last=Overbye |first=Dennis |author-link=Dennis Overbye |title=LIGO Detects Fierce Collision of Neutron Stars for the First Time |url=https://www.nytimes.com/2017/10/16/science/ligo-neutron-stars-collision.html |date=16 October 2017 |work=[[The New York Times]] |access-date=16 October 2017 |archive-date=16 October 2017 |archive-url=https://web.archive.org/web/20171016143216/https://www.nytimes.com/2017/10/16/science/ligo-neutron-stars-collision.html |url-status=live }}</ref><ref name="NAT-20170825">{{cite journal |last=Casttelvecchi |first=Davide |title=Rumours swell over new kind of gravitational-wave sighting |journal=[[Nature (journal)|Nature News]] |date=2017 |doi=10.1038/nature.2017.22482 }}</ref><ref name="PhysRev">{{cite journal|last1=Abbott|first1=B. P.|collaboration=[[LIGO Scientific Collaboration]] & [[Virgo interferometer|Virgo Collaboration]]|title=GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral|journal=Physical Review Letters|date=16 October 2017|volume=119|issue=16|pages=161101|doi=10.1103/PhysRevLett.119.161101|pmid=29099225|arxiv=1710.05832|bibcode=2017PhRvL.119p1101A|s2cid=217163611}}</ref> The light emitted in the kilonova is believed to come from the radioactive decay of material ejected in the merger of the two neutron stars. The merger momentarily creates an environment of such extreme neutron flux that the [[r-process|''r''-process]] can occur; this—as opposed to [[supernova nucleosynthesis]]—may be responsible for the production of around half the isotopes in [[chemical element]]s beyond [[iron]].<ref>{{cite web |url=http://www.cnn.com/2013/07/20/opinion/urry-gold-stars/index.html |title=Gold comes from stars |first=Meg |last=Urry |author-link=Meg Urry |work=CNN|date=July 20, 2013 |access-date=July 20, 2013 |archive-date=July 22, 2017 |archive-url=https://web.archive.org/web/20170722200821/http://www.cnn.com/2013/07/20/opinion/urry-gold-stars/index.html |url-status=live }}</ref>

==Planets==
{{main|Pulsar planet|Habitability of neutron star systems}}

Neutron stars can host [[exoplanet]]s. These can be original, [[circumbinary planet|circumbinary]], captured, or the result of a second round of planet formation. Pulsars can also strip the atmosphere off from a star, leaving a planetary-mass remnant, which may be understood as a [[chthonian planet]] or a stellar object depending on interpretation. For pulsars, such [[pulsar planet]]s can be detected with the [[pulsar timing method]], which allows for high precision and detection of much smaller planets than with other methods. Two systems have been definitively confirmed. The first exoplanets ever to be detected were the three planets [[PSR B1257+12 A|Draugr]], [[PSR B1257+12 B|Poltergeist]] and [[PSR B1257+12 C|Phobetor]] around the pulsar [[PSR B1257+12|Lich]], discovered in 1992–1994. Of these, Draugr is the smallest exoplanet ever detected, at a mass of twice that of the Moon. Another system is [[PSR B1620−26]], where a [[circumbinary planet]] orbits a neutron star-white dwarf binary system. Also, there are several unconfirmed candidates. Pulsar planets receive little visible light, but massive amounts of ionizing radiation and high-energy stellar wind, which makes them rather hostile environments to life as presently understood.

==History of discoveries==
[[File:Isolated Neutron Star RX J185635-3754 - opo9732a.jpg|thumb|left|The first direct observation of an isolated neutron star in visible light. The neutron star is RX J1856.5−3754.]]

At the meeting of the [[American Physical Society]] in December 1933 (the proceedings were published in January 1934), [[Walter Baade]] and [[Fritz Zwicky]] proposed the existence of neutron stars,<ref>{{cite journal |journal=Physical Review |volume=46 |title=Remarks on Super-Novae and Cosmic Rays |issue=1 |last1=Baade |first1=Walter |author-link=Walter Baade |last2=Zwicky |first2=Fritz |author-link2=Fritz Zwicky |name-list-style=amp |pages=76–77 |doi=10.1103/PhysRev.46.76.2 |date=1934 |bibcode=1934PhRv...46...76B |url=https://authors.library.caltech.edu/5999/1/BAApr34.pdf |access-date=2019-09-16 |archive-date=2021-02-24 |archive-url=https://web.archive.org/web/20210224205601/https://authors.library.caltech.edu/5999/1/BAApr34.pdf |url-status=live }}</ref>{{refn |group="lower-alpha" |Even before the discovery of neutron, in 1931, neutron stars were ''anticipated'' by [[Lev Landau]], who wrote about stars where "atomic nuclei come in close contact, forming one gigantic nucleus".<ref>{{cite journal |journal=Phys. Z. Sowjetunion |volume=1 |title=On the theory of stars |last=Landau |first=Lev D. |pages=285–288 |date=1932 }}</ref> However, the widespread opinion that Landau ''predicted'' neutron stars proves to be wrong.<ref>{{Cite book |bibcode = 2007ASSL..326.....H|title = Neutron Stars 1 : Equation of State and Structure|series= Astrophysics and Space Science Library|volume = 326|editor-last1 = Haensel|editor-first1 = P|editor-last2 = Potekhin|editor-first2 = A. Y|editor-last3 = Yakovlev|editor-first3 = D. G|year = 2007 |isbn=978-0387335438 |publisher=Springer |author=<!--Deny Citation Bot -->}}</ref>}} less than two years after [[Discovery of the neutron|the discovery of the neutron]] by [[James Chadwick]].<ref>{{cite journal
 | journal=Nature | volume=129
 | issue=3252 | pages=312
 | title=On the possible existence of a neutron
 | first=James | last=Chadwick
 | doi=10.1038/129312a0 | date=1932 |bibcode = 1932Natur.129Q.312C | s2cid=4076465
 | doi-access=free }}</ref> In seeking an explanation for the origin of a [[supernova]], they tentatively proposed that in supernova explosions ordinary stars are turned into stars that consist of extremely closely packed neutrons that they called neutron stars. Baade and Zwicky correctly proposed at that time that the release of the gravitational binding energy of the neutron stars powers the supernova: "In the supernova process, mass in bulk is annihilated". Neutron stars were thought to be too faint to be detectable and little work was done on them until November 1967, when [[Franco Pacini]] pointed out that if the neutron stars were spinning and had large magnetic fields, then electromagnetic waves would be emitted. Unknown to him, radio astronomer [[Antony Hewish]] and his graduate student [[Jocelyn Bell]] at Cambridge were shortly to detect radio pulses from stars that are now believed to be highly magnetized, rapidly spinning neutron stars, known as pulsars.

In 1965, Antony Hewish and [[Samuel Okoye]] discovered "an unusual source of high radio brightness temperature in the [[Crab Nebula]]".<ref>{{cite journal |journal=Nature |volume=207 |issue=4992 |pages=59–60 |title=Evidence of an unusual source of high radio brightness temperature in the Crab Nebula |last1=Hewish |first1=A. |last2=Okoye |first2=S. E. |name-list-style=amp |doi=10.1038/207059a0 |date=1965 |bibcode=1965Natur.207...59H |s2cid=123416790 }}</ref> This source turned out to be the Crab Pulsar that resulted from the great [[SN 1054|supernova of 1054]].

In 1967, [[Iosif Shklovsky]] examined the X-ray and optical observations of [[Scorpius X-1]] and correctly concluded that the radiation comes from a neutron star at the stage of [[accretion (astrophysics)|accretion]].<ref>{{Cite journal |last=Shklovsky |first=I. S. |title=On the Nature of the Source of X-Ray Emission of SCO XR-1 |journal=Astrophysical Journal |volume=148 |issue=1 |pages=L1–L4 |date=April 1967 |doi=10.1086/180001 |bibcode=1967ApJ...148L...1S }}</ref>

In 1967, Jocelyn Bell Burnell and Antony Hewish discovered regular radio pulses from [[PSR B1919+21]]. This pulsar was later interpreted as an isolated, rotating neutron star. The energy source of the pulsar is the rotational energy of the neutron star. The majority of known neutron stars (about 2000, as of 2010) have been discovered as pulsars, emitting regular radio pulses.

In 1968, [[Richard V. E. Lovelace]] and collaborators discovered period <math>P\!\approx 33</math> ms of the [[Crab pulsar]] using [[Arecibo Observatory]].<ref name="Lovelace1969">{{cite journal |bibcode=1969Natur.221..453C |title=Crab Nebula Pulsar NP 0532 |last1=Comella |first1=J. M. |last2=Craft |first2=H. D. |last3=Lovelace |first3=R. V. E. |last4=Sutton |first4=J. M. |journal=Nature |year=1969 |volume=221 |issue=5179 |page=453 |doi=10.1038/221453a0 |s2cid=4213758 }}</ref><ref name="Lovelace1969a">{{cite journal |bibcode=1969Natur.222..231L |title=Digital Search Methods for Pulsars |last1=Lovelace |first1=R. V. E. |last2=Sutton |first2=J. M. |journal=Nature |year=1969 |volume=222 |issue=5190 |page=231 |doi=10.1038/222231a0 |s2cid=4294389 }}</ref> After this discovery, scientists concluded that [[pulsars]] were rotating [[neutron stars]].<ref name="LovelaceTyler2012">{{cite journal |bibcode=2012Obs...132..186L |title=On the discovery of the period of the Crab Nebular pulsar |last1=Lovelace |first1=R. V. E. |last2=Tyler |first2=G. L. |journal=The Observatory |year=2012 |volume=132 |issue=3 |page=186 }}</ref> Before that, many scientists believed that pulsars were pulsating [[white dwarfs]].

In 1971, [[Riccardo Giacconi]], Herbert Gursky, Ed Kellogg, R. Levinson, E. Schreier, and H. Tananbaum discovered 4.8 second pulsations in an X-ray source in the [[constellation]] [[Centaurus]], [[Centaurus X-3|Cen X-3]].<ref>{{cite book |title=Rotation and Accretion Powered Pulsars |edition=illustrated |first1=Pranab |last1=Ghosh |publisher=World Scientific |year=2007 |isbn=978-981-02-4744-7 |page=8 |url=https://books.google.com/books?id=fmtqDQAAQBAJ&pg=PA8 |access-date=2016-11-29 |archive-date=2021-02-06 |archive-url=https://web.archive.org/web/20210206222506/https://books.google.com/books?id=fmtqDQAAQBAJ&pg=PA8 |url-status=live }}</ref> They interpreted this as resulting from a rotating hot neutron star. The energy source is gravitational and results from a [[Accretion (astrophysics)|rain of gas falling]] onto the surface of the [[Accretion-powered pulsar|neutron star]] from a [[companion star]] or the [[interstellar medium]].

In 1974, [[Antony Hewish]] was awarded the [[Nobel Prize in Physics]] "for his decisive role in the discovery of pulsars" without [[Jocelyn Bell]] who shared in the discovery.<ref>{{cite book |title=A Companion to Astronomy and Astrophysics: Chronology and Glossary with Data Tables |edition=illustrated |first1=Kenneth |last1=Lang |publisher=Springer Science & Business Media |year=2007 |isbn=978-0-387-33367-0 |page=82 |url=https://books.google.com/books?id=aUjkKuaVIloC&pg=PA82 |access-date=2016-11-29 |archive-date=2021-02-06 |archive-url=https://web.archive.org/web/20210206223425/https://books.google.com/books?id=aUjkKuaVIloC&pg=PA82 |url-status=live }}</ref>

In 1974, [[Joseph Hooton Taylor Jr.|Joseph Taylor]] and [[Russell Hulse]] discovered the first binary pulsar, [[PSR B1913+16]], which consists of two neutron stars (one seen as a pulsar) orbiting around their center of mass. [[Albert Einstein]]'s [[general relativity|general theory of relativity]] predicts that massive objects in short binary orbits should emit [[gravitational wave]]s, and thus that their orbit should decay with time. This was indeed observed, precisely as general relativity predicts, and in 1993, Taylor and Hulse were awarded the [[Nobel Prize in Physics]] for this discovery.<ref>{{cite book |title=Neutron Stars 1: Equation of State and Structure |edition=illustrated |first1=Paweł |last1=Haensel |first2=Alexander Y. |last2=Potekhin |first3=Dmitry G. |last3=Yakovlev |publisher=Springer Science & Business Media |year=2007 |isbn=978-0-387-47301-7 |page=474 |url=https://books.google.com/books?id=fgj_TZ06niYC&pg=PA474 |access-date=2016-11-29 |archive-date=2021-02-06 |archive-url=https://web.archive.org/web/20210206223723/https://books.google.com/books?id=fgj_TZ06niYC&pg=PA474 |url-status=live }}</ref>

In 1982, [[Don Backer]] and colleagues discovered the first millisecond pulsar, [[PSR B1937+21]].<ref>{{cite book |title=Pulsar Astronomy |edition=illustrated |first1=Francis |last1=Graham-Smith |publisher=Cambridge University Press |year=2006 |isbn=978-0-521-83954-9 |page=11 |url=https://books.google.com/books?id=AK9N3zxL4ToC&pg=PA11 |access-date=2016-11-29 |archive-date=2021-02-06 |archive-url=https://web.archive.org/web/20210206223536/https://books.google.com/books?id=AK9N3zxL4ToC&pg=PA11 |url-status=live }}</ref> This object spins 642 times per second, a value that placed fundamental constraints on the mass and radius of neutron stars. Many millisecond pulsars were later discovered, but PSR B1937+21 remained the fastest-spinning known pulsar for 24 years, until [[PSR J1748-2446ad]] (which spins ~716 times a second) was discovered.

In 2003, [[Marta Burgay]] and colleagues discovered the first double neutron star system where both components are detectable as pulsars, [[PSR J0737−3039]].<ref>{{cite book |title=Rotation and Accretion Powered Pulsars |edition=illustrated |first1=Pranab |last1=Ghosh |publisher=World Scientific |year=2007 |isbn=978-981-02-4744-7 |page=281 |url=https://books.google.com/books?id=fmtqDQAAQBAJ&pg=PA281 |access-date=2016-11-29 |archive-date=2021-02-06 |archive-url=https://web.archive.org/web/20210206223426/https://books.google.com/books?id=fmtqDQAAQBAJ&pg=PA281 |url-status=live }}</ref> The discovery of this system allows a total of 5 different tests of general relativity, some of these with unprecedented precision.

In 2010, Paul Demorest and colleagues measured the mass of the millisecond pulsar [[PSR J1614−2230]] to be {{Solar mass|{{val|1.97|0.04}}}}, using [[Shapiro delay]].<ref>{{cite journal |doi=10.1038/nature09466 |last1=Demorest |first1=Paul B. |last2=Pennucci |first2=T. |last3=Ransom |first3=S. M. |last4=Roberts |first4=M. S. |last5=Hessels |first5=J. W. |title= A two-solar-mass neutron star measured using Shapiro delay |journal=Nature |volume=467 |issue=7319 |pages=1081–1083 |bibcode=2010Natur.467.1081D |year=2010 |pmid=20981094 |arxiv=1010.5788 |s2cid=205222609 }}</ref> This was substantially higher than any previously measured neutron star mass ({{Solar mass|1.67}}, see [[PSR J1903+0327]]), and places strong constraints on the interior composition of neutron stars.

In 2013, [[John Antoniadis]] and colleagues measured the mass of [[PSR J0348+0432]] to be {{Solar mass|{{val|2.01|0.04}}}}, using white dwarf spectroscopy.<ref>{{cite journal |doi=10.1126/science.1233232 |last1=Antoniadis |first1=John |title=A Massive Pulsar in a Compact Relativistic Binary |journal=Science |volume=340 |issue=6131 |bibcode=2013Sci...340..448A |date=2012 |arxiv=1304.6875 |pages=1233232 |pmid=23620056 |citeseerx=10.1.1.769.4180 |s2cid=15221098 }}</ref> This confirmed the existence of such massive stars using a different method. Furthermore, this allowed, for the first time, a test of [[general relativity]] using such a massive neutron star.

In August 2017, LIGO and Virgo made first detection of gravitational waves produced by colliding neutron stars ([[GW170817]]),<ref>{{cite web |url=https://www.ligo.caltech.edu/news/ligo20171016 |title=LIGO Detection of Colliding Neutron Stars Spawns Global Effort to Study the Rare Event |first=Kimberly M. |last=Burtnyk |date=16 October 2017 |access-date=17 November 2017 |archive-date=23 October 2017 |archive-url=https://web.archive.org/web/20171023230823/https://www.ligo.caltech.edu/news/ligo20171016 |url-status=live }}</ref> leading to further discoveries about neutron stars.

In October 2018, astronomers reported that [[GRB 150101B]], a [[gamma-ray burst]] event detected in 2015, may be directly related to the historic GW170817 and associated with the [[Neutron star merger|merger of two neutron stars]]. The similarities between the two events, in terms of [[gamma ray]], [[optical]] and x-ray emissions, as well as to the nature of the associated host [[Galaxy|galaxies]], are "striking", suggesting the two separate events may both be the result of the merger of neutron stars, and both may be a [[kilonova]], which may be more common in the universe than previously understood, according to the researchers.<ref name="EA-20181016">{{cite news |author=University of Maryland |title=All in the family: Kin of gravitational wave source discovered - New observations suggest that kilonovae -- immense cosmic explosions that produce silver, gold and platinum--may be more common than thought |url=https://www.eurekalert.org/pub_releases/2018-10/uom-ait101518.php |date=16 October 2018 |work=[[EurekAlert!]] |access-date=17 October 2018 |author-link=University of Maryland |archive-date=16 October 2018 |archive-url=https://web.archive.org/web/20181016142323/https://www.eurekalert.org/pub_releases/2018-10/uom-ait101518.php |url-status=live }}</ref><ref name="NC-20181016">{{cite journal |author=Troja, E.|display-authors=etal|title=A luminous blue kilonova and an off-axis jet from a compact binary merger at z = 0.1341 |date=16 October 2018 |journal=[[Nature Communications]] |volume=9 |pages=4089|number=4089 (2018) |doi=10.1038/s41467-018-06558-7 |pmid=30327476|pmc=6191439|bibcode=2018NatCo...9.4089T|arxiv=1806.10624}}</ref><ref name="NASA-20181016">{{cite news |last=Mohon |first=Lee |title=GRB 150101B: A Distant Cousin to GW170817 |url=https://www.nasa.gov/mission_pages/chandra/images/grb-150101b-a-distant-cousin-to-gw170817.html |date=16 October 2018 |work=[[NASA]] |access-date=17 October 2018 |archive-date=22 March 2019 |archive-url=https://web.archive.org/web/20190322010201/https://www.nasa.gov/mission_pages/chandra/images/grb-150101b-a-distant-cousin-to-gw170817.html |url-status=live }}</ref><ref name="SPC-20181017">{{cite web |last=Wall |first=Mike |title=Powerful Cosmic Flash Is Likely Another Neutron-Star Merger |url=https://www.space.com/42158-another-neutron-star-crash-detected.html |date=17 October 2018 |work=[[Space.com]] |access-date=17 October 2018 |archive-date=17 October 2018 |archive-url=https://web.archive.org/web/20181017144255/https://www.space.com/42158-another-neutron-star-crash-detected.html |url-status=live }}</ref>

In July 2019, astronomers reported that a new method to determine the [[Hubble constant]], and resolve the discrepancy of earlier methods, has been proposed based on the mergers of pairs of neutron stars, following the detection of the neutron star merger of GW170817.<ref name="EA-20190708">{{cite news |author=National Radio Astronomy Observatory |title=New method may resolve difficulty in measuring universe's expansion - Neutron star mergers can provide new 'cosmic ruler' |url=https://www.eurekalert.org/pub_releases/2019-07/nrao-nmm070819.php |date=8 July 2019 |work=[[EurekAlert!]] |access-date=8 July 2019 |author-link=National Radio Astronomy Observatory |archive-date=8 July 2019 |archive-url=https://web.archive.org/web/20190708195937/https://www.eurekalert.org/pub_releases/2019-07/nrao-nmm070819.php |url-status=live }}</ref><ref name="NRAO-20190708">{{cite news |last=Finley |first=Dave |title=New Method May Resolve Difficulty in Measuring Universe's Expansion |url=https://public.nrao.edu/news/new-method-measuring-universe-expansion/ |date=8 July 2019 |work=[[National Radio Astronomy Observatory]] |access-date=8 July 2019 |archive-date=8 July 2019 |archive-url=https://web.archive.org/web/20190708231326/https://public.nrao.edu/news/new-method-measuring-universe-expansion/ |url-status=live }}</ref> Their measurement of the Hubble constant is {{val|70.3|+5.3|-5.0}} (km/s)/Mpc.<ref name="NAT-20190708">{{cite journal |author=Hotokezaka, K. |display-authors=et al. |title=A Hubble constant measurement from superluminal motion of the jet in GW170817 |date=8 July 2019 |journal=[[Nature Astronomy]] |volume=3 |issue=10 |pages=940–944 |doi=10.1038/s41550-019-0820-1 |arxiv=1806.10596 |bibcode=2019NatAs...3..940H |s2cid=119547153 }}</ref>

A 2020 study by [[University of Southampton]] PhD student Fabian Gittins suggested that surface irregularities ("mountains") may only be fractions of a millimeter tall (about 0.000003% of the neutron star's diameter), hundreds of times smaller than previously predicted, a result bearing implications for the non-detection of gravitational waves from spinning neutron stars.<ref name=mt-ls>{{cite web |url=https://www.livescience.com/millimeter-tall-neutron-star-mountains.html |title=Neutron star 'mountains' are actually microscopic bumps less than a millimeter tall |last=Baker |first=Harry |date=21 July 2021 |publisher=[[Live Science]] |access-date=25 July 2021 |archive-date=25 July 2021 |archive-url=https://web.archive.org/web/20210725063709/https://www.livescience.com/millimeter-tall-neutron-star-mountains.html |url-status=live }}</ref><ref name=mt-syfy>{{cite web |url=https://www.syfy.com/syfywire/tallest-mountain-neutron-star-fraction-millimeter-tall |title=The tallest mountain on a neutron star may be a fraction of a millimeter tall |last=Plait |first=Phil |date=23 July 2021 |publisher=[[Syfy]] |access-date=25 July 2021 |archive-date=25 July 2021 |archive-url=https://web.archive.org/web/20210725045955/https://www.syfy.com/syfywire/tallest-mountain-neutron-star-fraction-millimeter-tall |url-status=live }}</ref><ref name=gittins>{{cite journal |last1=Gittins |first1=Fabian |last2=Andersson |first2=Nils |date=2021 |title=Modelling neutron star mountains in relativity |journal=[[Monthly Notices of the Royal Astronomical Society]] |volume=507 |number=stab2048 |pages=116–128 |doi=10.1093/mnras/stab2048 |doi-access=free |arxiv=2105.06493}}</ref>

Using the [[James Webb Space Telescope|JWST]], astronomers have identified a neutron star within the remnants of the [[Supernova 1987A]] [[stellar explosion]] after seeking to do so for 37 years, according to a 23 February 2024 ''[[Science (journal)|Science]]'' article. In a paradigm shift, new JWST data provides the elusive direct confirmation of neutron stars within supernova remnants as well as a deeper understanding of the processes at play within SN 1987A's remnants.<ref name="Fransson_20240223">{{cite journal | doi=10.1126/SCIENCE.ADJ5796 | title=Emission lines due to ionizing radiation from a compact object in the remnant of Supernova 1987A | date=2024 | last1=Fransson | first1=C. | last2=Barlow | first2=M. J. | last3=Kavanagh | first3=P. J. | last4=Larsson | first4=J. | last5=Jones | first5=O. C. | last6=Sargent | first6=B. | last7=Meixner | first7=M. | last8=Bouchet | first8=P. | last9=Temim | first9=T. | last10=Wright | first10=G. S. | last11=Blommaert | first11=J. A. D. L. | last12=Habel | first12=N. | last13=Hirschauer | first13=A. S. | last14=Hjorth | first14=J. | last15=Lenkić | first15=L. | last16=Tikkanen | first16=T. | last17=Wesson | first17=R. | last18=Coulais | first18=A. | last19=Fox | first19=O. D. | last20=Gastaud | first20=R. | last21=Glasse | first21=A. | last22=Jaspers | first22=J. | last23=Krause | first23=O. | last24=Lau | first24=R. M. | last25=Nayak | first25=O. | last26=Rest | first26=A. | last27=Colina | first27=L. | last28=Van Dishoeck | first28=E. F. | last29=Güdel | first29=M. | last30=Henning | first30=Th. | journal=Science | volume=383 | issue=6685 | pages=898–903 | arxiv=2403.04386 | bibcode=2024Sci...383..898F | display-authors=1 }}</ref>

==Subtypes==
[[File:PIA23863-NeutronStarTypes-20200624.jpg|thumb|Different Types of Neutron Stars]]
[[File:Neutron star magnetic fields simulation.jpg|thumb|right|Computer renders of a neutron star with [[accretion disk]], with magnetic field lines projected, showing [[X-ray burster|bursts of powerful X-rays]]. The simulations are taken from 2017 data from NASA's NuSTAR and Swift, and ESA's XMM-Newton observatories.]]
There are a number of types of object that consist of or contain a neutron star:
* Isolated neutron star (INS):<ref name="pavlov" /><ref name="cco" /><ref name="ins">{{cite book |arxiv=1008.2891 |date=April 2010 |first=Sandro |last=Mereghetti |title=High-Energy Emission from Pulsars and their Systems |volume=21 |pages=345–363 |doi=10.1007/978-3-642-17251-9_29 |chapter=X-ray emission from isolated neutron stars |series=Astrophysics and Space Science Proceedings |isbn=978-3-642-17250-2 |bibcode=2011ASSP...21..345M |s2cid=117102095 }}</ref><ref name="slac">{{cite journal |bibcode=2000IAUS..195..103P |title=Thermal Radiation from Isolated Neutron Stars |last1=Pavlov |first1=G. G. |last2=Zavlin |first2=V. E. |journal=Highly Energetic Physical Processes and Mechanisms for Emission from Astrophysical Plasmas |year=2000 |volume=195 |page=103 }}</ref> not in a binary system.
** [[Rotation-powered pulsar]] (RPP or "radio pulsar"):<ref name="cco" /> neutron stars that emit directed pulses of radiation towards us at regular intervals (due to their strong magnetic fields).
*** [[Rotating radio transient]] (RRATs):<ref name="cco" /> are thought to be pulsars which emit more sporadically and/or with higher pulse-to-pulse variability than the bulk of the known pulsars.
** [[Magnetar]]: a neutron star with an extremely strong magnetic field (1000 times more than a regular neutron star), and long rotation periods (5 to 12 seconds).
*** [[Soft gamma repeater]] (SGR).<ref name="pavlov" />
*** [[Anomalous X-ray pulsar]] (AXP).<ref name="pavlov" />
** [[Radio-quiet neutron star]]s.
*** X-ray dim isolated neutron stars.<ref name="cco" />
*** [[Central compact object]]s in [[supernova remnant]]s (CCOs in SNRs): young, radio-quiet non-pulsating X-ray sources, thought to be Isolated Neutron Stars surrounded by supernova remnants.<ref name="cco" />
* [[X-ray pulsar]]s or "accretion-powered pulsars": a class of [[X-ray binaries]].
** Low-mass X-ray binary pulsars: a class of [[low-mass X-ray binaries]] (LMXB), a pulsar with a main sequence star, white dwarf or red giant.
*** [[Millisecond pulsar]] (MSP) ("recycled pulsar").
**** "Spider Pulsar", a pulsar where their companion is a semi-degenerate star.<ref>{{cite journal |bibcode=2019ApJ...886..148P |title=Eight Millisecond Pulsars Discovered in the Arecibo PALFA Survey |last1=Parent |first1=E. |last2=Kaspi |first2=V. M. |last3=Ransom |first3=S. M. |last4=Freire |first4=P. C. C. |last5=Brazier |first5=A. |last6=Camilo |first6=F. |last7=Chatterjee |first7=S. |last8=Cordes |first8=J. M. |last9=Crawford |first9=F. |last10=Deneva |first10=J. S. |last11=Ferdman |first11=R. D. |last12=Hessels |first12=J. W. T. |last13=Van Leeuwen |first13=J. |last14=Lyne |first14=A. G. |last15=Madsen |first15=E. C. |last16=McLaughlin |first16=M. A. |last17=Patel |first17=C. |last18=Scholz |first18=P. |last19=Stairs |first19=I. H. |last20=Stappers |first20=B. W. |last21=Zhu |first21=W. W. |journal=The Astrophysical Journal |year=2019 |volume=886 |issue=2 |page=148 |doi=10.3847/1538-4357/ab4f85 |arxiv=1908.09926 |s2cid=201646167 |doi-access=free }}</ref>
***** "Black Widow" pulsar, a pulsar that falls under the "Spider Pulsar" if the companion has extremely low mass (less than {{solar mass|0.1}}).
***** "Redback" pulsar, are if the companion is more massive.
**** Sub-millisecond pulsar.<ref>{{cite journal |bibcode=1989PThPh..81.1006N |title=Binary Sub-Millisecond Pulsar and Rotating Core Collapse Model for SN1987A |first=T. |last=Nakamura |doi=10.1143/PTP.81.1006 |journal=Progress of Theoretical Physics |volume=81 |issue=5 |pages=1006–1020 |date=1989 |doi-access= }}</ref>
*** [[X-ray burster]]: a neutron star with a low mass binary companion from which matter is accreted resulting in irregular bursts of energy from the surface of the neutron star.
** Intermediate-mass X-ray binary pulsars: a class of [[intermediate-mass X-ray binaries]] (IMXB), a pulsar with an intermediate mass star.
** High-mass X-ray binary pulsars: a class of [[high-mass X-ray binaries]] (HMXB), a pulsar with a massive star.
** [[Binary pulsar]]s: a [[pulsar]] with a [[binary star|binary companion]], often a [[white dwarf]] or neutron star.
** X-ray tertiary (theorized).<ref>{{cite journal |bibcode=2020MNRAS.491..495D |title=The dynamical Roche lobe in hierarchical triples |last1=Di Stefano |first1=Rosanne |journal=Monthly Notices of the Royal Astronomical Society |year=2020 |volume=491 |issue=1 |page=495 |doi=10.1093/mnras/stz2572 |doi-access=free |arxiv=1903.11618 }}</ref>

There are also a number of theorized compact stars with similar properties that are not actually neutron stars.
* Protoneutron star (PNS),<ref>{{cite journal |bibcode=2001ApJ...562..887T |title=The Physics of Proto-Neutron Star Winds: Implications for r-Process Nucleosynthesis |last1=Thompson |first1=Todd A. |last2=Burrows |first2=Adam |last3=Meyer |first3=Bradley S. |journal=The Astrophysical Journal |year=2001 |volume=562 |issue=2 |page=887 |doi=10.1086/323861 |arxiv=astro-ph/0105004 |s2cid=117093903 }}</ref> a theorized intermediate–stage object that cools and contracts to form a neutron star or a black hole<ref>{{cite journal | last1=Gondek-Rosińska | first1=D. | last2=Haensel | first2=P. | last3=Zdunik | first3=J. L. | date=January 2000 | title=Protoneutron stars and neutron stars | series=ASP Conference Series | journal=Pulsar Astronomy - 2000 and Beyond; Proceedings of the 177th Colloquium of the IAU Held in Bonn, Germany, 30 August – 3 September 1999 | editor1-first=M. | editor1-last=Kramer | editor2-first=N. | editor2-last=Wex | editor3-first=N. | editor3-last=Wielebinski | volume=202 | pages=663–664 | publisher=Cambridge University Press | arxiv=astro-ph/0012543 | bibcode=2000ASPC..202..663G }}</ref>
* [[Exotic star]]
** [[Thorne–Żytkow object]]: currently a hypothetical merger of a neutron star into a red giant star.
** [[Quark star]]: currently a hypothetical type of neutron star composed of [[quark matter]], or [[strange matter]]. As of 2018, there are three candidates.
** [[Electroweak star]]: currently a hypothetical type of extremely heavy neutron star, in which the quarks are converted to leptons through the electroweak force, but the gravitational collapse of the neutron star is prevented by radiation pressure. As of 2018, there is no evidence for their existence.
** [[Preon star]]: currently a hypothetical type of neutron star composed of [[preon matter]]. As of 2018, there is no evidence for the existence of [[preon]]s.

==Examples of neutron stars==
[[File:Artist's concept of PSR B1257+12 system.jpg|thumb|An artist's conception of the pulsar planet [[PSR B1257+12 C]], with bright aurorae]]
{{See also|Pulsar#Significant pulsars}}
* [[Black Widow Pulsar]] – a millisecond pulsar that is very massive
* [[PSR J0952-0607]] – the heaviest neutron star with {{Solar mass|{{val|2.35|0.17|0.17}}}}, a type of Black Widow Pulsar<ref name=blackwidow>{{Cite web |last=Croswell |first=Ken |date=2022-07-22 |title=The heaviest neutron star on record is 2.35 times the mass of the sun |url=https://www.sciencenews.org/article/heaviest-neutron-star-mass-sun-record-black-holes |access-date=2022-07-25 |website=Science News |language=en-US}}</ref><ref>{{cite journal |last1=Romani |first1=Roger W. |last2=Kandel |first2=D. |last3=Filippenko |first3=Alexei V. |last4=Brink |first4=Thomas G. |last5=Zheng |first5=WeiKang |date=2022-07-11 |title=PSR J0952−0607: The Fastest and Heaviest Known Galactic Neutron Star |journal=The Astrophysical Journal Letters |volume=934 |issue=2 |pages=L17 |doi=10.3847/2041-8213/ac8007 |arxiv=2207.05124 |bibcode=2022ApJ...934L..17R |s2cid=250451299 |doi-access=free }}</ref>
* [[LGM-1]] (now known as PSR B1919+21) – the first recognized radio-pulsar. It was discovered by [[Jocelyn Bell Burnell]] in 1967.
* [[PSR B1257+12]] (Also known as Lich) – the first neutron star discovered with planets (a millisecond pulsar).
* [[PSR B1509−58]] – source of the "Hand of God" photo shot by the [[Chandra X-ray Observatory]]
* [[RX J1856.5−3754]] – the closest neutron star
* [[The Magnificent Seven (neutron stars)|The Magnificent Seven]] – a group of nearby, X-ray dim isolated neutron stars
* [[PSR J0348+0432]] – the most massive neutron star with a well-constrained mass, {{Solar mass|{{val|2.01|0.04}}}}
* [[SWIFT J1756.9-2508]] – a millisecond pulsar with a stellar-type companion with planetary range mass (below brown dwarf)
*[[Swift J1818.0-1607]] – the youngest-known magnetar

==Gallery==
<gallery mode="packed" class="center">
File:Neutron Star Manhattan.ogv|Neutron stars containing 500,000 Earth-masses in {{convert|25|km||sp=us|adj=mid|-diameter}} sphere
File:Crash and Burst.ogv|[[neutron star collision|Neutron stars colliding]]
File:Neutron star collision.ogv|Neutron star collision
File:Neutron_Star_simulation.png|Artist's impression of a neutron star bending light
</gallery>

==See also==
<!-- Please keep entries in alphabetical order & add a short description [[WP:SEEALSO]] -->
{{div col|colwidth=20em|small=yes}}
* [[IRAS 00500+6713]] (in 10,000 y)
* [[Neutron star merger]]
* [[Neutron stars in fiction]]
** {{Section link|Stars in fiction|Neutron stars}}
* [[Neutronium]]
* [[Planck star]]
* [[Degenerate matter#Preon degeneracy hypothesis|Preon-degenerate matter]]
* [[Rotating radio transient]]
{{div col end}}
<!-- please keep entries in alphabetical order -->

==Notes==
{{reflist|group=lower-alpha}}

==References==
{{reflist}}

===Sources===
{{Refbegin}}
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* {{cite book
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}}
* {{cite journal
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 |last9=Tomsick    |first9=J.A. 
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 }}
{{Refend}}

==External links==
{{Commons category|Neutron stars}}
* {{cite book |editor-last=Moustakidis |editor-first=Charalampos |title=The Nuclear Physics of Neutron Stars |year=2024 |publisher=[[MDPI]] |url=https://www.mdpi.com/books/reprint/9492-the-nuclear-physics-of-neutron-stars |isbn=978-3-7258-1600-2}}
* {{Cite journal |arxiv=nucl-th/0309041|last1=Hessels|first1=Jason W. T|title=Neutron Stars for Undergraduates |journal= American Journal of Physics|volume=72|issue=2004|pages=892–905|last2=Ransom|first2=Scott M|last3=Stairs|first3=Ingrid H|last4=Freire|first4=Paulo C. C|last5=Kaspi|first5=Victoria M|last6=Camilo|first6=Fernando|year=2003|doi=10.1119/1.1703544|bibcode=2004AmJPh..72..892S|s2cid=27807404}}
** {{cite journal |year=2005 |journal=American Journal of Physics |volume=73 |issue= 3|pages=286 |doi=10.1119/1.1852544|title= Erratum: "Neutron stars for undergraduates" &#91;Am. J. Phys. 72 (7), 892–905 (2004)&#93;|last1= Silbar|first1= Richard R|last2= Reddy|first2= Sanjay|arxiv= nucl-th/0309041|bibcode= 2005AmJPh..73..286S}}
* "[https://www.spacedaily.com/reports/NASA_Sees_Hidden_Structure_Of_Neutron_Star_In_Starquake.html NASA Sees Hidden Structure Of Neutron Star In Starquake]". SpaceDaily.com. April 26, 2006
* "[https://www.newscientist.com/article/dn9397-mysterious-x-ray-sources-may-be-lone-neutron-stars/ Mysterious X-ray sources may be lone neutron stars]" David Shiga. ''New Scientist''. 23 June 2006
* "[https://www.newscientist.com/article/dn9428-massive-neutron-star-rules-out-exotic-matter/ Massive neutron star rules out exotic matter]". ''New Scientist''. According to a new analysis, exotic states of matter such as free quarks or BECs do not arise inside neutron stars.
* "[https://www.newscientist.com/article/dn9730-neutron-star-clocked-at-mind-boggling-velocity Neutron star clocked at mind-boggling velocity]". ''New Scientist''. A neutron star has been clocked traveling at more than 1500 kilometers per second.

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