Aneutron star is thecollapsedcore of a massivesupergiant star. It results from thesupernova explosion of amassive star—combined withgravitational collapse—that compresses the core pastwhite dwarf star density to that ofatomic nuclei. Surpassed only byblack holes, neutron stars are the second smallest and densest known class of stellar objects.^[1] Neutron stars have a radius on the order of 10 kilometers (6 mi) and a mass of about 1.4 M_☉.^[2] Stars that collapse into neutron stars have a totalmass of between 10 and 25solar masses (M_☉), or possibly more for those that are especially rich inelements heavier than hydrogen and helium.^[3]

Once formed, neutron stars no longer actively generate heat and cool over time, but they may still evolve further throughcollisions oraccretion. Most of the basic models for these objects imply that they are composed almost entirely ofneutrons, as the extreme pressure causes theelectrons andprotons present in normal matter to combine into additional neutrons. These stars are partially supported against further collapse byneutron degeneracy pressure, just aswhite dwarfs are supported against collapse byelectron degeneracy pressure. However, this is not by itself sufficient to hold up an object beyond 0.7 M_☉^[4][5] and repulsive nuclear forces increasingly contribute to supporting more massive neutron stars.^[6][7] If the remnant star has amass exceeding theTolman–Oppenheimer–Volkoff limit, which ranges from2.2–2.9M_☉, the combination of degeneracy pressure and nuclear forces is insufficient to support the neutron star, causing it to collapse and form ablack hole. The most massive neutron star detected so far,PSR J0952–0607, is estimated to be2.35±0.17 M_☉.^[8]

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.^[9] Older and even-cooler neutron stars are still easy to discover. For example, the well-studied neutron star,RX J1856.5−3754, has an average surface temperature of about 434,000 K.^[10] For comparison, the Sun has an effective surface temperature of 5,780 K.^[11]

Neutron star material is remarkablydense: a normal-sizedmatchbox containing neutron-star material would have a weight of approximately 3billion tonnes, the same weight as a 0.5-cubic-kilometer chunk of the Earth (a cube with edges of about 800 meters) from Earth's surface.^[12][13]

As a star's core collapses, its rotation rate increases due toconservation 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 byJocelyn Bell Burnell andAntony Hewish in 1967 was the first observational suggestion that neutron stars exist. The fastest-spinning neutron star known isPSR J1748−2446ad, rotating at a rate of 716 times per second^[14][15] or 43,000revolutions per minute, giving a linear (tangential) speed at the surface on the order of 0.24c (i.e., nearly a quarter thespeed of light).

There are thought to be around one billion neutron stars in theMilky Way,^[16] and at a minimum several hundred million, a figure obtained by estimating the number of stars that have undergone supernova explosions.^[17] 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 theHubble Space Telescope's detection ofRX 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 ofX-rays. During this process, matter is deposited on the surface of the stars, forming "hotspots" that can be sporadically identified asX-ray pulsar systems. Additionally, such accretions are able to "recycle" old pulsars, causing them to gain mass and rotate extremely quickly, formingmillisecond pulsars. Furthermore, binary systems such as these continue toevolve, with many companions eventually becomingcompact objects such as white dwarfs or neutron stars themselves, though other possibilities include a complete destruction of the companion throughablation or collision.

The study of neutron star systems is central togravitational wave astronomy. Themerger of binary neutron stars produces gravitational waves and may be associated withkilonovae andshort-duration gamma-ray bursts. In 2017, theLIGO andVirgo interferometer sites observedGW170817, the first direct detection of gravitational waves from such an event.^[18] 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, theHulse–Taylor pulsar.

Anymain-sequence star with an initial mass of greater than 8 M_☉ (eight times the mass of theSun) 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 theChandrasekhar limit. Electron-degeneracy pressure is overcome, and the core collapses further, causing temperatures to rise to over5×10⁹ K (5 billion K). At these temperatures,photodisintegration (the breakdown of iron nuclei intoalpha particles due to high-energy gamma rays) occurs. As the temperature of the core continues to rise, electrons and protons combine to form neutrons viaelectron capture, releasing a flood ofneutrinos. When densities reach a nuclear density of4×10¹⁷ kg/m³, a combination ofstrong force repulsion and neutron degeneracy pressure halts the contraction.^[19] 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 asupernova and leaving behind a neutron star. However, if the remnant has a mass greater than about 3 M_☉, it instead becomes a black hole.^[20]

As the core of a massive star is compressed during aType II supernova or aType Ib or Type Ic supernova, and collapses into a neutron star, it retains most of itsangular momentum. Because it has only a tiny fraction of its parent's radius (sharply reducing itsmoment 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 ms to 30 s. The neutron star's density also gives it very highsurface gravity, with typical values ranging from10¹² to10¹³ m/s² (more than10¹¹ times that ofEarth).^[21] One measure of such immense gravity is the fact that neutron stars have anescape velocity of over half thespeed of light.^[22] The neutron star's gravity accelerates infalling matter to tremendous speed, andtidal forces near the surface can causespaghettification.^[22]

Theequation 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 adegenerate 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 becauseNewtonian gravity is no longer sufficient in those conditions. Effects such asquantum chromodynamics (QCD),superconductivity, andsuperfluidity 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.^[23]

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 thestrong force of thestandard 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 ofQCD 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 ofquantum 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, andLove numbers. 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.

Neutron stars have overall densities of3.7×10¹⁷ to5.9×10¹⁷ kg/m³ (2.6×10¹⁴ to4.1×10¹⁴ times the density of the Sun),^[a] which is comparable to the approximate density of an atomic nucleus of3×10¹⁷ kg/m³.^[24] The density increases with depth, varying from about1×10⁹ kg/m³ at the crust to an estimated6×10¹⁷ or8×10¹⁷ kg/m³ deeper inside.^[25] Pressure increases accordingly, from about3.2×10³¹ Pa (32 QPa) at the inner crust to1.6×10³⁴ Pa in the center.^[26]

A neutron star is so dense that one teaspoon (5milliliters) of its material would have a mass over5.5×10¹² kg, about 900 times the mass of theGreat Pyramid of Giza.^[b] The entire mass of the Earth at neutron star density would fit into a sphere 305 m in diameter, about the size of theArecibo Telescope.

In popular scientific writing, neutron stars are sometimes described as macroscopicatomic nuclei. Indeed, both states are composed ofnucleons, 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 thestrong interaction, whereas a neutron star is held together bygravity. The density of a nucleus is uniform, while neutron stars arepredicted to consist of multiple layers with varying compositions and densities.^[27]

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 fromLIGO,^[28] which is a gravitational wave observatory, andNICER,^[29] which is an X-ray telescope.

NICER's observations ofpulsars 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 pulsarPSR J0740+6620 was able to constrain the radius of a 1.4 solar mass neutron star to12.33+0.76
−0.8 km with 95% confidence.^[30] These mass-radius constraints, combined withchiral effective field theory calculations, tightens constraints on the neutron star equation of state.^[23]

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 ofbinary neutron star mergers. From these simulations, researchers can extractgravitational waveforms, 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. Pastnumerical 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 toLIGO detections.^[31] For example, the LIGO detection of the binary neutron star mergerGW170817 provided limits on the tidal deformability of the two neutron stars which dramatically reduced the family of allowed equations of state.^[32] Future gravitational wave signals with next generation detectors likeCosmic Explorer can impose further constraints.^[33]

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.^[34] There is also recent work on constraining the equation of state with the speed of sound through hydrodynamics.^[35]

TheTolman-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:^[36]

$${\displaystyle \frac{dp}{dr}=-\frac{Gϵ(r)M(r)}{c^2{r}^2}\left(1+\frac{p(r)}{ϵ(r)}\right)\left(1+\frac{4\pi r^{3}p(r)}{M(r)c^2}\right)\left(1-\frac{2GM(r)}{c^{2}r}\right)}$$ $${\displaystyle \frac{dM}{dr}=\frac{4\pi }{c^2}{r}^2ϵ(r)}$$ 

where${\displaystyle G}$  is the gravitational constant,${\displaystyle p(r)}$  is the pressure,${\displaystyle ϵ(r)}$  is the energy density (found from the equation of state), and${\displaystyle c}$  is the speed of light.

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, you 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 theTolman-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 wasPSR J0952-0607 which was2.35±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).^[37] 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.

There are three more properties of neutron stars that are dependent on the equation of state but can also be astronomically observed: themoment of inertia, thequadrupole moment, and theLove 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 totidal forces, 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.^[38]

The temperature inside a newly formed neutron star is from around10¹¹ to10¹² kelvin.^[25] However, the huge number ofneutrinos it emits carries away so much energy that the temperature of an isolated neutron star falls within a few years to around10⁶ kelvin.^[25] 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 usingRoman numerals (not to be confused with theYerkes 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 2 M_☉, and with higher cooling rates and possibly candidates forexotic stars.^[39]

The magnetic field strength on the surface of neutron stars ranges fromc. 10⁴ to10¹¹ tesla (T).^[40] These are orders of magnitude higher than in any other object: for comparison, a continuous 16 T field has been achieved in the laboratory and is sufficient to levitate a living frog due todiamagnetic 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.^[40]

The neutron stars known asmagnetars have the strongest magnetic fields, in the range of10⁸ to10¹¹ T,^[41] and have become the widely accepted hypothesis for neutron star typessoft gamma repeaters (SGRs)^[42] andanomalous X-ray pulsars (AXPs).^[43] The magneticenergy density of a10⁸ T field is extreme, greatly exceeding themass-energy density of ordinary matter.^[c] Fields of this strength are able topolarize the vacuum to the point that the vacuum becomesbirefringent. 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 causestarquakes, 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 seconds and which lasts for a few minutes.^[45]

The origins of the strong magnetic field are as yet unclear.^[40] One hypothesis is that of "flux freezing", or conservation of the originalmagnetic flux during the formation of the neutron star.^[40] 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 themagnetic 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.^[40]

The gravitational field at a neutron star's surface is about2×10¹¹ timesstronger than on Earth, at around2.0×10¹² m/s².^[47] Such a strong gravitational field acts as agravitational lens and bends the radiation emitted by the neutron star such that parts of the normally invisible rear surface become visible.^[46]If the radius of the neutron star is 3GM/c² or less, then the photons may betrapped 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,E =mc²). The energy comes from thegravitational 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.^[48] However, even before impact, thetidal force would causespaghettification, 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.^[49]

Neutron star relativistic equations of state describe the relation of radius vs. mass for various models.^[50] The most likely radii for a given neutron star mass are bracketed by models AP4 (smallest radius) and MS2 (largest radius).E_B is the ratio of gravitational binding energy mass equivalent to the observed neutron star gravitational mass ofM kilograms with radiusR meters,^[51]$${\displaystyle E_{\text{B}}=\frac{0.60\beta }{1-\frac{\beta }{2}}}$$ $${\displaystyle \beta =GM/R{c}^2}$$ Given current values

• ${\displaystyle G=6.67408\times {10}^{-11}{\text{m}}^3{\text{kg}}^{-1}{\text{s}}^{-2}}$ ^[52]
• ${\displaystyle c=2.99792458\times {10}^8\text{m}/\text{s}}$ ^[52]
• ${\displaystyle M_{\odot }=1.98855\times {10}^{30}\text{kg}}$ 

and star masses "M" commonly reported as multiples of one solar mass,$${\displaystyle M_x=\frac{M}{M_{\odot }}}$$ then the relativistic fractional binding energy of a neutron star is$${\displaystyle E_{\text{B}}=\frac{886.0M_x}{R_{\left[\text{in meters}\right]}-738.3M_x}}$$ 

A 2 M_☉ 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%.

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 ofneutron-star oscillations.Asteroseismology, a study applied to ordinary stars, can reveal the inner structure of neutron stars by analyzing observedspectra of stellar oscillations.^[21]

Current models indicate that matter at the surface of a neutron star is composed of ordinaryatomic nuclei crushed into a solid lattice with a sea ofelectrons flowing through the gaps between them. It is possible that the nuclei at the surface areiron, due to iron's highbinding energy per nucleon.^[53] It is also possible that heavy elements, such as iron, simply sink beneath the surface, leaving only light nuclei likehelium andhydrogen.^[53] If the surface temperature exceeds10⁶ 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 <10⁶ kelvins).^[53]

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.^[54][55]

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, theneutron drip becomes overwhelming, and the concentration of free neutrons increases rapidly.

After asupernova explosion of asupergiant star, neutron stars are born from the remnants. A neutron star is composed mostly ofneutrons (neutral particles) and contains a small fraction ofprotons (positively charged particles) andelectrons (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.^[56]

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.^[57]

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 thestrong 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.^[58]The composition of the superdense matter in the core remains uncertain. One model describes the core assuperfluidneutron-degenerate matter (mostly neutrons, with some protons and electrons). More exotic forms of matter are possible, including degeneratestrange matter (containingstrange quarks in addition toup anddown quarks), matter containing high-energypions andkaons in addition to neutrons,^[21] or ultra-densequark-degenerate matter.

Neutron stars are detected from theirelectromagnetic radiation. Neutron stars are usually observed topulseradio waves and other electromagnetic radiation, and neutron stars observed with pulses are called pulsars.

Pulsars' radiation is thought to be caused by particle acceleration near theirmagnetic poles, which need not be aligned with therotational axis of the neutron star. It is thought that a largeelectrostatic field builds up near the magnetic poles, leading toelectron emission.^[59] These electrons are magnetically accelerated along the field lines, leading tocurvature radiation, with the radiation being stronglypolarized towards the plane of curvature.^[59] In addition, high-energyphotons can interact with lower-energy photons and the magnetic field forelectron−positron pair production, which throughelectron–positron annihilation leads to further high-energy photons.^[59]

The radiation emanating from the magnetic poles of neutron stars can be described asmagnetospheric radiation, in reference to themagnetosphere of the neutron star.^[60] It is not to be confused withmagnetic dipole radiation, which is emitted because themagneticaxis is not aligned with the rotational axis, with a radiation frequency the same as the neutron star's rotational frequency.^[59]

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 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 starPSR J0901-4046, with spin properties distinct from the known neutron stars.^[61] It is unclear how its radio emission is generated, and it challenges the current understanding of how pulsars evolve.^[62]

In addition to pulsars, non-pulsating neutron stars have also been identified, although they may have minor periodic variation in luminosity.^[63][64] This seems to be a characteristic of the X-ray sources known asCentral Compact Objects insupernova remnants (CCOs in SNRs), which are thought to be young, radio-quiet isolated neutron stars.^[63]

In addition toradio emissions, neutron stars have also been identified in other parts of theelectromagnetic spectrum. This includesvisible light,near infrared,ultraviolet,X-rays, andgamma rays.^[60] Pulsars observed in X-rays are known asX-ray pulsars if accretion-powered, while those identified in visible light are known asoptical pulsars. The majority of neutron stars detected, including those identified in optical, X-ray, and gamma rays, also emit radio waves;^[65] theCrab Pulsar produces electromagnetic emissions across the spectrum.^[65] However, there exist neutron stars calledradio-quiet neutron stars, with no radio emissions detected.^[66]

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.

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 calledspin down. The rate at which a neutron star slows its rotation is usually constant and very small.

Theperiodic time (P) is therotational 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${\displaystyle \dot{P}}$  (P-dot), thederivative ofP with respect to time. It is defined as periodic time increase per unit time; it is adimensionless quantity, but can be given the units of s⋅s⁻¹ (seconds per second).^[59]

The spin-down rate (P-dot) of neutron stars usually falls within the range of10⁻²² to10⁻⁹ s⋅s⁻¹, with the shorter period (or faster rotating) observable neutron stars usually having smallerP-dot. As a neutron star ages, its rotation slows (asP 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.^[59]

P andP-dot allow minimum magnetic fields of neutron stars to be estimated.^[59]P andP-dot can be also used to calculate thecharacteristic age of a pulsar, but gives an estimate which is somewhat larger than the true age when it is applied to young pulsars.^[59]

P andP-dot can also be combined with neutron star'smoment of inertia to estimate a quantity calledspin-downluminosity, which is given the symbol${\displaystyle \dot{E}}$  (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 actualluminosity, the neutron stars are said to be "rotation powered".^[59][60] The observed luminosity of theCrab Pulsar is comparable to the spin-down luminosity, supporting the model that rotational kinetic energy powers the radiation from it.^[59] 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.^[67]

P andP-dot can also be plotted for neutron stars to create aP–P-dot diagram. It encodes a tremendous amount of information about the pulsar population and its properties, and has been likened to theHertzsprung–Russell diagram in its importance for neutron stars.^[59]

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 anoblate 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.^[68] A 2007 paper reported the detection of an X-ray burst oscillation, which provides an indirect measure of spin, of 1122 Hz from the neutron starXTE J1739-285,^[69] 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.

Sometimes a neutron star will undergo aglitch, a sudden small increase of its rotational speed or spin up.^[70] Glitches are thought to be the effect of astarquake—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 inmagnetars, with a resulting glitch, is the leading hypothesis for the gamma-ray sources known as soft gamma repeaters.^[42]

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.^[71][70]

An anti-glitch, a sudden small decrease in rotational speed, or spin down, of a neutron star has also been reported.^[72][73] It occurred in the magnetar1E 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.^[72][70]

At present, there are about 3,200 known neutron stars in theMilky Way and theMagellanic 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 km/s) to the newly formed neutron star.

Some of the closest known neutron stars are RX J1856.5−3754, which is about 400light-years from Earth, andPSR J0108−1431 about 424 light-years.^[74] RX J1856.5-3754 is a member of a close group of neutron stars calledThe Magnificent Seven. Another nearby neutron star that was detected transiting the backdrop of the constellation Ursa Minor has been nicknamedCalvera by its Canadian and American discoverers, after the villain in the 1960 filmThe Magnificent Seven. This rapidly moving object was discovered using theROSAT 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 theirblackbody radiation and gravitational effects on other stars.

About 5% of all known neutron stars are members of abinary system. The formation and evolution of binary neutron stars^[75] and double neutron stars^[76] can be a complex process. Neutron stars have been observed in binaries with ordinarymain-sequence stars,red giants, 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 ofgravitational waves.^[77][78]

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.^[79]

The distance between two neutron stars in a close binary system is observed to shrink asgravitational waves are emitted.^[80] 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 ofshort gamma-ray bursts. Strong evidence for this model came from the observation of akilonova associated with the short-duration gamma-ray burst GRB 130603B,^[81] and was finally confirmed by detection of gravitational waveGW170817 and shortGRB 170817A byLIGO,Virgo, and 70 observatories covering the electromagnetic spectrum observing the event.^{[82][83][84][85]} 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 ther-process can occur; this—as opposed tosupernova nucleosynthesis—may be responsible for the production of around half the isotopes inchemical elements beyondiron.^[86]

Neutron stars can hostexoplanets. These can be original,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 achthonian planet or a stellar object depending on interpretation. For pulsars, suchpulsar planets can be detected with thepulsar 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 planetsDraugr,Poltergeist andPhobetor around the pulsarLich, discovered in 1992–1994. Of these, Draugr is the smallest exoplanet ever detected, at a mass of twice that of the Moon. Another system isPSR B1620−26, where acircumbinary 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.

At the meeting of theAmerican Physical Society in December 1933 (the proceedings were published in January 1934),Walter Baade andFritz Zwicky proposed the existence of neutron stars,^[87][d] less than two years afterthe discovery of the neutron byJames Chadwick.^[90] In seeking an explanation for the origin of asupernova, 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, whenFranco 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 astronomerAntony Hewish and his graduate studentJocelyn 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 andSamuel Okoye discovered "an unusual source of high radio brightness temperature in theCrab Nebula".^[91] This source turned out to be the Crab Pulsar that resulted from the greatsupernova of 1054.

In 1967,Iosif Shklovsky examined the X-ray and optical observations ofScorpius X-1 and correctly concluded that the radiation comes from a neutron star at the stage ofaccretion.^[92]

In 1967, Jocelyn Bell Burnell and Antony Hewish discovered regular radio pulses fromPSR 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${\displaystyle P\approx 33}$  ms of theCrab pulsar usingArecibo Observatory.^[93][94] After this discovery, scientists concluded thatpulsars were rotatingneutron stars.^[95] Before that, many scientists believed that pulsars were pulsatingwhite 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 theconstellationCentaurus,Cen X-3.^[96] They interpreted this as resulting from a rotating hot neutron star. The energy source is gravitational and results from arain of gas falling onto the surface of theneutron star from acompanion star or theinterstellar medium.

In 1974,Antony Hewish was awarded theNobel Prize in Physics "for his decisive role in the discovery of pulsars" withoutJocelyn Bell who shared in the discovery.^[97]

In 1974,Joseph Taylor andRussell 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'sgeneral theory of relativity predicts that massive objects in short binary orbits should emitgravitational waves, 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 theNobel Prize in Physics for this discovery.^[98]

In 1982,Don Backer and colleagues discovered the first millisecond pulsar,PSR B1937+21.^[99] 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, untilPSR 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.^[100] 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 pulsarPSR J1614−2230 to be1.97±0.04 M_☉, usingShapiro delay.^[101] This was substantially higher than any previously measured neutron star mass (1.67 M_☉, seePSR J1903+0327), and places strong constraints on the interior composition of neutron stars.

In 2013,John Antoniadis and colleagues measured the mass ofPSR J0348+0432 to be2.01±0.04 M_☉, using white dwarf spectroscopy.^[102] This confirmed the existence of such massive stars using a different method. Furthermore, this allowed, for the first time, a test ofgeneral 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),^[103] leading to further discoveries about neutron stars.

In October 2018, astronomers reported thatGRB 150101B, agamma-ray burst event detected in 2015, may be directly related to the historic GW170817 and associated with themerger of two neutron stars. The similarities between the two events, in terms ofgamma ray,optical and x-ray emissions, as well as to the nature of the associated hostgalaxies, are "striking", suggesting the two separate events may both be the result of the merger of neutron stars, and both may be akilonova, which may be more common in the universe than previously understood, according to the researchers.^{[104][105][106][107]}

In July 2019, astronomers reported that a new method to determine theHubble 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.^[108][109] Their measurement of the Hubble constant is70.3+5.3
−5.0 (km/s)/Mpc.^[110]

A 2020 study byUniversity 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.^{[55][111][112]}

Using theJWST, astronomers have identified a neutron star within the remnants of theSupernova 1987Astellar explosion after seeking to do so for 37 years, according to a 23 February 2024Science 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.^[113]

There are a number of types of object that consist of or contain a neutron star:

• Isolated neutron star (INS):^{[60][63][114][115]} not in a binary system.
  • Rotation-powered pulsar (RPP or "radio pulsar"):^[63] neutron stars that emit directed pulses of radiation towards us at regular intervals (due to their strong magnetic fields).
    • Rotating radio transient (RRATs):^[63] 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).^[60]
    • Anomalous X-ray pulsar (AXP).^[60]
  • Radio-quiet neutron stars.
    • X-ray dim isolated neutron stars.^[63]
    • Central compact objects insupernova remnants (CCOs in SNRs): young, radio-quiet non-pulsating X-ray sources, thought to be Isolated Neutron Stars surrounded by supernova remnants.^[63]
• X-ray pulsars or "accretion-powered pulsars": a class ofX-ray binaries.
  • Low-mass X-ray binary pulsars: a class oflow-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.^[116]
        • "Black Widow" pulsar, a pulsar that falls under the "Spider Pulsar" if the companion has extremely low mass (less than 0.1 M_☉).
        • "Redback" pulsar, are if the companion is more massive.
      • Sub-millisecond pulsar.^[117]
    • 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 ofintermediate-mass X-ray binaries (IMXB), a pulsar with an intermediate mass star.
  • High-mass X-ray binary pulsars: a class ofhigh-mass X-ray binaries (HMXB), a pulsar with a massive star.
  • Binary pulsars: apulsar with abinary companion, often awhite dwarf or neutron star.
  • X-ray tertiary (theorized).^[118]

There are also a number of theorized compact stars with similar properties that are not actually neutron stars.

• Protoneutron star (PNS),^[119] a theorized intermediate–stage object that cools and contracts to form a neutron star or a black hole^[120]
• 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 ofquark matter, orstrange 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 ofpreon matter. As of 2018, there is no evidence for the existence ofpreons.

• Black Widow Pulsar – a millisecond pulsar that is very massive
• PSR J0952-0607 – the heaviest neutron star with2.35+0.17
  −0.17 M_☉, a type of Black Widow Pulsar^[8][121]
• LGM-1 (now known as PSR B1919+21) – the first recognized radio-pulsar. It was discovered byJocelyn 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 theChandra X-ray Observatory
• RX J1856.5−3754 – the closest neutron star
• 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,2.01±0.04 M_☉
• 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

• Neutron stars containing 500,000 Earth-masses in 25-kilometer-diameter (16 mi) sphere
• Neutron stars colliding
• Neutron star collision
•  
  Artist's impression of a neutron star bending light

• Hessels, Jason W. T; Ransom, Scott M; Stairs, Ingrid H; Freire, Paulo C. C; Kaspi, Victoria M; Camilo, Fernando (2003). "Neutron Stars for Undergraduates".American Journal of Physics.72 (2004):892–905.arXiv:nucl-th/0309041.Bibcode:2004AmJPh..72..892S.doi:10.1119/1.1703544.S2CID 27807404.
  • Silbar, Richard R; Reddy, Sanjay (2005). "Erratum: "Neutron stars for undergraduates" [Am. J. Phys. 72 (7), 892–905 (2004)]".American Journal of Physics.73 (3): 286.arXiv:nucl-th/0309041.Bibcode:2005AmJPh..73..286S.doi:10.1119/1.1852544.
• NASA on pulsars
• "NASA Sees Hidden Structure Of Neutron Star In Starquake". SpaceDaily.com. April 26, 2006
• "Mysterious X-ray sources may be lone neutron stars" David Shiga.New Scientist. 23 June 2006
• "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.
• "Neutron star clocked at mind-boggling velocity".New Scientist. A neutron star has been clocked traveling at more than 1500 kilometers per second.