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92-574: Once formed, neutron stars no longer actively generate heat and cool over time, but they may still evolve further through collisions or accretion . Most of the basic models for these objects imply that they are composed almost entirely of neutrons , as the extreme pressure causes the electrons and protons present in normal matter to combine into additional neutrons. These stars are partially supported against further collapse by neutron degeneracy pressure , just as white dwarfs are supported against collapse by electron degeneracy pressure . However, this

184-425: A black hole . The most massive neutron star detected so far, PSR J0952–0607 , is estimated to be 2.35 ± 0.17  M ☉ . 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

276-471: A certain confidence level. The temperature inside a newly formed neutron star is from around 10 to 10  kelvin . However, the huge number of neutrinos it emits carries away so much energy that the temperature of an isolated neutron star falls within a few years to around 10 kelvin . At this lower temperature, most of the light generated by a neutron star is in X-rays. Some researchers have proposed

368-412: A change in the observed rotational frequency of the pulsar. Hellings and Downs extended this idea in 1983 to an array of pulsars and found that a stochastic background of gravitational waves would produce a quadrupolar correlation between different pulsar pairs as a function of their angular separations on the sky. This work was limited in sensitivity by the precision and stability of the pulsar clocks in

460-399: A cluster of stars known as Messier 30 was discovered by astronomer Charles Messier . In the twentieth century, astronomers concluded that the cluster was approximately 13 billion years old. The Hubble Space Telescope resolved the individual stars of Messier 30. With this new technology, astronomers discovered that some stars, known as blue stragglers , appeared younger than other stars in

552-470: A companion star in a close binary system. For this reason, millisecond pulsars are sometimes called recycled pulsars . Millisecond pulsars are thought to be related to low-mass X-ray binary systems. It is thought that the X-rays in these systems are emitted by the accretion disk of a neutron star produced by the outer layers of a companion star that has overflowed its Roche lobe . The transfer of angular momentum from this accretion event can increase

644-545: A complete destruction of the companion through ablation or collision. The study of neutron star systems is central to gravitational wave astronomy. The merger of binary neutron stars produces gravitational waves and may be associated with kilonovae and short-duration gamma-ray bursts . In 2017, the LIGO and Virgo interferometer sites observed GW170817 , the first direct detection of gravitational waves from such an event. Prior to this, indirect evidence for gravitational waves

736-400: A far stronger magnetic field. However, this simple explanation does not fully explain magnetic field strengths of neutron stars. The gravitational field at a neutron star's surface is about 2 × 10 times stronger than on Earth , at around 2.0 × 10 m/s . Such a strong gravitational field acts as a gravitational lens and bends the radiation emitted by the neutron star such that parts of

828-411: 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

920-575: A neutron star classification system using Roman numerals (not to be confused with the 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 2  M ☉ , and with higher cooling rates and possibly candidates for exotic stars . The magnetic field strength on

1012-539: 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-rays . During this process, matter

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1104-493: A rate of c. 1500 rotations per second or more, and that at a rate of above about 1000 rotations per second they would lose energy by gravitational radiation faster than the accretion process would accelerate them. In early 2007 data from the Rossi X-ray Timing Explorer and INTEGRAL spacecraft discovered a neutron star XTE J1739-285 rotating at 1122 Hz. The result is not statistically significant, with

1196-411: A red giant. When two low-mass stars in a binary system merge, mass may be thrown off in the orbital plane of the merging stars, creating an excretion disk from which new planets can form. While the concept of stellar collision has been around for several generations of astronomers, only the development of new technology has made it possible for it to be more objectively studied. For example, in 1764,

1288-519: A significance level of only 3 sigma . While it is an interesting candidate for further observations, current results are inconclusive. Still, it is believed that gravitational radiation plays a role in slowing the rate of rotation. One X-ray pulsar that spins at 599 revolutions per second, IGR J00291+5934 , is a prime candidate for helping detect such waves in the future (most such X-ray pulsars only spin at around 300 rotations per second). Millisecond pulsars, which can be timed with high precision, have

1380-441: 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. 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 becomes overwhelming, and

1472-462: A sphere 305 m in diameter, about the size of the Arecibo Telescope . In popular scientific writing, neutron stars are sometimes described as macroscopic atomic nuclei . Indeed, both states are composed of nucleons , 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

1564-448: 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

1656-403: A stability comparable to atomic-clock -based time standards when averaged over decades. This also makes them very sensitive probes of their environments. For example, anything placed in orbit around them causes periodic Doppler shifts in their pulses' arrival times on Earth, which can then be analyzed to reveal the presence of the companion and, with enough data, provide precise measurements of

1748-518: A stellar merger in Scorpius (named V1309 Scorpii ), though it was not known to be the result of a stellar merger at the time. White dwarfs are the remnants of low-mass stars which, if they form a binary system with another star, can cause large stellar explosions known as type Ia supernovae. The normal route by which this happens involves a white dwarf drawing material off a main sequence or red giant star to form an accretion disc . Much more rarely,

1840-471: 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 ms to 30 s. The neutron star's density also gives it very high surface gravity , with typical values ranging from 10 to 10 m/s (more than 10 times that of Earth ). One measure of such immense gravity

1932-461: A type Ia supernova occurs when two white dwarfs orbit each other closely. Emission of gravitational waves causes the pair to spiral inward. When they finally merge, if their combined mass approaches or exceeds the Chandrasekhar limit , carbon fusion is ignited, raising the temperature. Since a white dwarf consists of degenerate matter , there is no safe equilibrium between thermal pressure and

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2024-507: 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) from Earth's surface. 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

2116-520: Is a gravitational wave observatory, and NICER , which is an X-ray telescope. NICER's observations of pulsars 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 12.33 +0.76 −0.8 km with 95% confidence. These mass-radius constraints, combined with chiral effective field theory calculations, tightens constraints on

2208-465: Is based on the current assumed maximum mass of neutron stars (~2 solar masses) and the minimum black hole mass (~5 solar masses). 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

2300-470: Is between one thousand and one million years old. 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. For comparison, the Sun has an effective surface temperature of 5,780 K. Neutron star material is remarkably dense : a normal-sized matchbox containing neutron-star material would have

2392-483: 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 pulsars . Furthermore, binary systems such as these continue to evolve , with many companions eventually becoming compact objects such as white dwarfs or neutron stars themselves, though other possibilities include

2484-451: 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 gas , it cannot be modeled strictly like one (as white dwarfs are) because of the extreme gravity. General relativity must be considered for

2576-512: Is not by itself sufficient to hold up an object beyond 0.7  M ☉ and repulsive nuclear forces increasingly contribute to supporting more massive neutron stars. If the remnant star has a mass exceeding the Tolman–Oppenheimer–Volkoff limit , which ranges from 2.2–2.9 M ☉ , the combination of degeneracy pressure and nuclear forces is insufficient to support the neutron star, causing it to collapse and form

2668-428: 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 of neutron-star oscillations . Asteroseismology , a study applied to ordinary stars, can reveal the inner structure of neutron stars by analyzing observed spectra of stellar oscillations. Current models indicate that matter at

2760-477: 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 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

2852-449: Is released in the supernova explosion from which it forms (from the law of mass–energy equivalence, E = mc ). 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. However, even before impact,

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2944-416: 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

3036-466: Is that of "flux freezing", or conservation of the original magnetic flux during the formation of the neutron star. 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

3128-454: Is the fact that neutron stars have an escape velocity of over half the speed of light . The neutron star's gravity accelerates infalling matter to tremendous speed, and tidal forces near the surface can cause spaghettification . 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

3220-429: 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

3312-451: Is to deform the star due to tidal 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

3404-470: Is very important when it comes to constraining the equation of state. Oppenheimer and Volkoff came up with the 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

3496-406: 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

3588-480: The Milky Way , and at a minimum several hundred million, a figure obtained by estimating the number of stars that have undergone supernova explosions. 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

3680-406: The pulsar timing array to gravitational waves in the early stages of the international effort. The five-year data release, analysis, and first NANOGrav limit on the stochastic gravitational wave background were described in 2013 by Demorest et al. It was followed by the nine-year and 11-year data releases in 2015 and 2018, respectively. Each further limited the gravitational wave background and, in

3772-442: The strong interaction , whereas a neutron star is held together by gravity . The density of a nucleus is uniform, while neutron stars are predicted to consist of multiple layers with varying compositions and densities. 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 , which

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3864-459: 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. Neutron star relativistic equations of state describe

3956-401: The universe can collide, whether they are "alive", meaning fusion is still active in the star, or "dead", with fusion no longer taking place. White dwarf stars, neutron stars , black holes , main sequence stars , giant stars , and supergiants are very different in type, mass, temperature, and radius, and accordingly produce different types of collisions and remnants. About half of all

4048-558: The Sun is 1 in 10 years. For comparison, the age of the universe is of the order 10 years. The likelihood of close encounters with the Sun is also small. The rate is estimated by the formula: where N is the number of encounters per million years that come within a radius D of the Sun in parsecs . For comparison, the mean radius of the Earth's orbit, 1 AU , is 4.82 × 10 parsecs . Our star will likely not be directly affected by such an event because there are no stellar clusters close enough to cause such interactions. An analysis of

4140-473: The array. Following the discovery of the first millisecond pulsar in 1982, Foster and Backer improved the sensitivity to gravitational waves by applying in 1990 the Hellings-Downs analysis to an array of highly stable millisecond pulsars. The advent of digital data acquisition systems, new radio telescopes and receiver systems, and the discoveries of many new millisecond pulsars advanced the sensitivity of

4232-457: The cluster. Astronomers then hypothesized that stars may have "collided", or "merged", giving them more fuel so they continued fusion while fellow stars around them started going out. While stellar collisions may occur very frequently in certain parts of the galaxy, the likelihood of a collision involving the Sun is very small. A probability calculation predicts the rate of stellar collisions involving

4324-502: 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 neutrons (neutral particles) and contains a small fraction of protons (positively charged particles) and electrons (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

4416-463: 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 5 × 10 K (5 billion K). At these temperatures, photodisintegration (the breakdown of iron nuclei into alpha particles due to high-energy gamma rays) occurs. As

4508-414: 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 3  M ☉ , it instead becomes a black hole. As the core of a massive star is compressed during a Type II supernova or a Type Ib or Type Ic supernova, and collapses into a neutron star, it retains most of its angular momentum . Because it has only

4600-408: The crust cause starquakes , 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. The origins of the strong magnetic field are as yet unclear. One hypothesis

4692-493: The crust to an estimated 6 × 10 or 8 × 10 kg/m deeper inside. Pressure increases accordingly, from about 3.2 × 10 Pa at the inner crust to 1.6 × 10 Pa in the center. A neutron star is so dense that one teaspoon (5 milliliters ) of its material would have a mass over 5.5 × 10 kg , about 900 times the mass of the Great Pyramid of Giza . The entire mass of the Earth at neutron star density would fit into

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4784-468: 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 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

4876-410: The dynamics of space-time itself. Pulsars are rapidly rotating, highly magnetized neutron stars formed during the supernova explosions of massive stars. They act as highly accurate clocks with a wealth of physical applications ranging from celestial mechanics, neutron star seismology, tests of strong-field gravity and Galactic astronomy. The proposal to use pulsars as gravitational wave detectors

4968-446: The eclipses of KIC 9832227 initially suggested that its orbital period was indeed shortening, and that the cores of the two stars would merge in 2022. However subsequent reanalysis found that one of the datasets used in the initial prediction contained a 12-hour timing error, leading to a spurious apparent shortening of the stars' orbital period. The mechanism behind binary star mergers is not yet fully understood, and remains one of

5060-467: 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

5152-447: 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

5244-430: 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

5336-399: 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

5428-462: The formation of either a heavier neutron star or a black hole, depending on whether the mass of the remnant exceeds the Tolman–Oppenheimer–Volkoff limit . This creates a magnetic field that is trillions of times stronger than that of Earth, in a matter of one or two milliseconds. Astronomers believe that this type of event is what creates short gamma-ray bursts and kilonovae . A gravitational wave event that occurred on 25 August 2017, GW170817 ,

5520-429: The gravitational constant, p ( r ) {\displaystyle p(r)}  is the pressure, ϵ ( r ) {\displaystyle \epsilon (r)}  is the energy density (found from the equation of state), and c {\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

5612-503: The gravitational wave signal that can be applied to LIGO detections. 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. Future gravitational wave signals with next generation detectors like Cosmic Explorer can impose further constraints. When nuclear physicists are trying to understand

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5704-430: 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. There is also recent work on constraining the equation of state with the speed of sound through hydrodynamics. The 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

5796-520: The main focuses of those researching KIC 9832227 and other contact binaries. Millisecond pulsar A millisecond pulsar ( MSP ) is a pulsar with a rotational period less than about 10 milliseconds . Millisecond pulsars have been detected in radio , X-ray , and gamma ray portions of the electromagnetic spectrum . The leading hypothesis for the origin of millisecond pulsars is that they are old, rapidly rotating neutron stars that have been spun up or "recycled" through accretion of matter from

5888-590: The nature of the other process remains a mystery. Many millisecond pulsars are found in globular clusters . This is consistent with the spin-up hypothesis of their formation, as the extremely high stellar density of these clusters implies a much higher likelihood of a pulsar having (or capturing) a giant companion star. Currently there are approximately 130 millisecond pulsars known in globular clusters. The globular cluster Terzan 5 contains 37 of these, followed by 47 Tucanae with 22 and M28 and M15 with 8 pulsars each. The first millisecond pulsar, PSR B1937+21 ,

5980-424: The neutron star equation of state because Newtonian gravity is no longer sufficient in those conditions. Effects such as 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

6072-477: The neutron star equation of state. 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 binary neutron star mergers . From these simulations, researchers can extract gravitational waveforms , thus studying

6164-1046: The neutron star observables: d p d r = − G ϵ ( r ) M ( r ) c 2 r 2 ( 1 + p ( r ) ϵ ( r ) ) ( 1 + 4 π r 3 p ( r ) M ( r ) c 2 ) ( 1 − 2 G M ( r ) c 2 r ) {\displaystyle {\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^{3}p(r)}{M(r)c^{2}}}\right)\left(1-{\frac {2GM(r)}{c^{2}r}}\right)} d M d r = 4 π c 2 r 2 ϵ ( r ) {\displaystyle {\frac {dM}{dr}}={\frac {4\pi }{c^{2}}}r^{2}\epsilon (r)} where G {\displaystyle G}  is

6256-401: The normally invisible rear surface become visible. If the radius of the neutron star is 3 GM / c or less, then the photons may be 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

6348-571: The only Earth-mass objects known outside of the Solar System . One of them, PSR B1257+12 D , has an even smaller mass, comparable to that of the Moon , and is still today the smallest-mass object known beyond the Solar System. Gravitational waves are an important prediction from Einstein's general theory of relativity and result from the bulk motion of matter, fluctuations during the early universe and

6440-404: The orbit and the object's mass. The technique is so sensitive that even objects as small as asteroids can be detected if they happen to orbit a millisecond pulsar. The first confirmed exoplanets , discovered several years before the first detections of exoplanets around "normal" solar-like stars, were found in orbit around a millisecond pulsar, PSR B1257+12 . These planets remained, for many years,

6532-486: 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. 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

6624-454: The periodicity of pulsars. The neutron stars known as magnetars have the strongest magnetic fields, in the range of 10 to 10 T , and have become the widely accepted hypothesis for neutron star types soft gamma repeaters (SGRs) and anomalous X-ray pulsars (AXPs). The magnetic energy density of a 10 T field is extreme, greatly exceeding the mass-energy density of ordinary matter. Fields of this strength are able to polarize

6716-510: 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 of 3.7 × 10 to 5.9 × 10 kg/m ( 2.6 × 10 to 4.1 × 10 times the density of the Sun), which is comparable to the approximate density of an atomic nucleus of 3 × 10 kg/m . The density increases with depth, varying from about 1 × 10 kg/m at

6808-906: The relation of radius vs. mass for various models. 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 of M kilograms with radius R meters, E B = 0.60 β 1 − β 2 {\displaystyle E_{\text{B}}={\frac {0.60\,\beta }{1-{\frac {\beta }{2}}}}} β   = G M / R c 2 {\displaystyle \beta \ =G\,M/R\,{c}^{2}} Given current values and star masses "M" commonly reported as multiples of one solar mass, M x = M M ⊙ {\displaystyle M_{x}={\frac {M}{M_{\odot }}}} then

6900-417: 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

6992-542: The relativistic fractional binding energy of a neutron star is E B = 886.0 M x R [ in meters ] − 738.3 M x {\displaystyle E_{\text{B}}={\frac {886.0\,M_{x}}{R_{\left[{\text{in meters}}\right]}-738.3\,M_{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

7084-469: The rotation rate of the pulsar to hundreds of times per second, as is observed in millisecond pulsars. There has been recent evidence that the standard evolutionary model fails to explain the evolution of all millisecond pulsars, especially young millisecond pulsars with relatively high magnetic fields, e.g. PSR B1937+21 . Bülent Kiziltan and S. E. Thorsett ( UCSC ) showed that different millisecond pulsars must form by at least two distinct processes. But

7176-438: The second case, techniques to precisely determine the barycenter of the solar system were refined. In 2020, the collaboration presented the 12.5-year data release, which included strong evidence for a power-law stochastic process with common strain amplitude and spectral index across all pulsars, but statistically inconclusive data for the critical Hellings-Downs quadrupolar spatial correlation. In June 2023, NANOGrav published

7268-531: 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. Stellar collision A stellar collision is the coming together of two stars caused by stellar dynamics within a star cluster , or by the orbital decay of a binary star due to stellar mass loss or gravitational radiation , or by other mechanisms not yet well understood. Any stars in

7360-503: The stars in the sky are part of binary systems, with two stars orbiting each other. Some binary stars orbit each other so closely that they share the same atmosphere, giving the system a peanut shape. While most such contact binary systems are stable, some do become unstable and either eject one partner or eventually merge. Astronomers predict that events of this type occur in the globular clusters of our galaxy about once every 10,000 years. On 2 September 2008 scientists first observed

7452-429: 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 force of the 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,

7544-417: The surface of a neutron star is composed of ordinary atomic nuclei crushed into a solid lattice with a sea of electrons 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. It is also possible that heavy elements, such as iron, simply sink beneath the surface, leaving only light nuclei like helium and hydrogen . If

7636-474: The surface of neutron stars ranges from c.   10 to 10   tesla (T). 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 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

7728-424: The surface temperature exceeds 10 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 < 10 kelvins ). 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

7820-425: The temperature of the core continues to rise, electrons and protons combine to form neutrons via electron capture , releasing a flood of neutrinos . When densities reach a nuclear density of 4 × 10 kg/m , a combination of strong force repulsion and neutron degeneracy pressure halts the contraction. The contracting outer envelope of the star is halted and rapidly flung outwards by a flux of neutrinos produced in

7912-431: 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

8004-535: The weight of overlying layers of the star. Because of this, runaway fusion reactions rapidly heat up the interior of the combined star and spread, causing a supernova explosion . In a matter of seconds, all of the white dwarf's mass is thrown into space. Neutron star mergers occur in a fashion similar to the rare type Ia supernovae resulting from merging white dwarfs. When two neutron stars orbit each other closely, they spiral inward as time passes due to gravitational radiation. When they meet, their merger leads to

8096-445: Was PSR J0952-0607 which was 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

8188-436: Was discovered in 1982 by Backer et al . Spinning roughly 641 times per second, it remains the second fastest-spinning millisecond pulsar of the approximately 200 that have been discovered. Pulsar PSR J1748-2446ad , discovered in 2004, is the fastest-spinning pulsar known, as of 2023, spinning 716 times per second. Current models of neutron star structure and evolution predict that pulsars would break apart if they spun at

8280-505: Was inferred by studying the gravity radiated from the orbital decay of a different type of (unmerged) binary neutron system, the Hulse–Taylor pulsar . Any main-sequence star with an initial mass of greater than 8  M ☉ (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

8372-420: Was originally made by Sazhin and Detweiler in the late 1970s. The idea is to treat the solar system barycenter and a distant pulsar as opposite ends of an imaginary arm in space. The pulsar acts as the reference clock at one end of the arm sending out regular signals which are monitored by an observer on the Earth. The effect of a passing gravitational wave would be to perturb the local space-time metric and cause

8464-403: Was reported on 16 October 2017 to be associated with the merger of two neutron stars in a distant galaxy , the first such merger to be observed via gravitational radiation. If a neutron star collides with red giant of sufficiently low mass and density, the merger is conjectured to produce a Thorne–Żytkow object , an hypothetical type of compact star containing a neutron star enveloped by

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