# Neutron star

Neutron star
Neutron stars crush half a million times more mass than Earth into a sphere no larger than Manhattan.

A neutron star is a type of stellar remnant that can result from the gravitational collapse of a massive star during a Type II, Type Ib or Type Ic supernova event. Such stars are composed almost entirely of neutrons, which are subatomic particles without electrical charge and with a slightly larger mass than protons. Neutron stars are very hot and are supported against further collapse by quantum degeneracy pressure due to the Pauli exclusion principle. This principle states that no two neutrons (or any other fermionic particles) can occupy the same place and quantum state simultaneously.

A typical neutron star has a mass between 1.35 and about 2.0 solar masses [1][2], with a corresponding radius of about 12 km if the Akmal-Pandharipande-Ravenhall equation of state (APR EOS) is used.[3][4] In contrast, the Sun's radius is about 60,000 times that. Neutron stars have overall densities predicted by the APR EOS of 3.7×1017 to 5.9×1017 kg/m3 (2.6×1014 to 4.1×1014 times the density of the Sun),[5] which compares with the approximate density of an atomic nucleus of 3×1017 kg/m3.[6] The neutron star's density varies from below 1×109 kg/m3 in the crust, increasing with depth to above 6×1017 or 8×1017 kg/m3 deeper inside (denser than an atomic nucleus).[7] This density is approximately equivalent to the mass of the entire human population compressed to the size of a sugar cube.[8]

In general, compact stars of less than 1.44 solar masses – the Chandrasekhar limit – are white dwarfs, and above 2 to 3 solar masses (the Tolman–Oppenheimer–Volkoff limit), a quark star might be created; however, this is uncertain. Gravitational collapse will usually occur on any compact star between 10 and 25 solar masses and produce a black hole.[9]

Neutron star collision.

## Formation

As the core of a massive star is compressed during a supernova, and collapses into a neutron star, it retains most of its angular momentum. Since it has only a tiny fraction of its parent's radius (and therefore its moment of inertia is sharply reduced), a neutron star is formed with very high rotation speed, and then gradually slows down. Neutron stars are known to have rotation periods between about 1.4 ms to 30 seconds. The neutron star's density also gives it very high surface gravity, up to 7×1012 m/s2 with typical values of a few ×1012 m/s2 (that is more than 1011 times of that of Earth). One measure of such immense gravity is the fact that neutron stars have an escape velocity of around 100,000 km/s, about a third the speed of light. Matter falling onto the surface of a neutron star would be accelerated to tremendous speed by the star's gravity. The force of impact would likely destroy the object's component atoms, rendering all its matter identical, in most respects, to the rest of the star.[citation needed]

## Properties

Gravitational light deflection at a neutron star. Due to relativistic light deflection more than half of the surface is visible (each chequered patch here represents 30 degrees by 30 degrees).[10] The mass of the star depicted here is 1 and its radius 4, in natural units[10] from a geometrized unit system such that it has double its Schwarzschild radius of 2.

The gravitational field at the star's surface is about 2×1011 times stronger than on Earth. Such a strong gravitational field acts as a gravitational lens and bends the radiation emitted by the star such that parts of the normally invisible rear surface become visible.[10]

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 the gravitational binding energy of a neutron star.

Neutron star relativistic equations of state provided by Jim Lattimer include a graph of radius vs. mass for various models.[11] The most likely radii for a given neutron star mass are bracketed by models AP4 (smallest radius) and MS2 (largest radius). BE is the ratio of gravitational binding energy mass equivalent to observed neutron star gravitational mass of "M" kilograms with radius "R" meters,[12]

$BE = \frac{0.60\,\beta}{1 - \frac{\beta}{2}}$      $\beta \ = G\,M/R\,{c}^{2}$

Given current values

$G = 6.6742\times10^{-11}\, m^3kg^{-1}sec^{-2}$ [13]
$c^2 = 8.98755\times10^{16}\, m^2sec^{-2}$
$M_{solar} = 1.98844\times10^{30}\, kg$

and star masses "M" commonly reported as multiples of one solar mass,

$M_x = \frac{M}{M_\odot}$

then the relativistic fractional binding energy of a neutron star is

$BE = \frac{885.975\,M_x}{R - 738.313\,M_x}$

A two solar mass 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%.

A neutron star is so dense that one teaspoon (5 milliliters) of its material would have a mass over 5.5×1012 kg, about 900 times the mass of the Great Pyramid of Giza.[14] The resulting force of gravity is so strong that if an object were to fall from a height of one meter it would only take one microsecond to hit the surface of the neutron star, and would do so at around 2000 kilometers per second, or 7.2 million kilometers per hour.[15]

The temperature inside a newly formed neutron star is from around 1011 to 1012 kelvin.[7] However, the huge number of neutrinos it emits carries away so much energy that the temperature falls within a few years to around 106 kelvin.[7] Even at 1 million kelvin, most of the light generated by a neutron star is in X-rays. In visible light, neutron stars probably radiate approximately the same energy in all parts of visible spectrum, and therefore appear white.

The equation of state for a neutron star is still not known. It is assumed that it differs significantly from that of a white dwarf, whose EOS is that of a degenerate gas which can be described in close agreement with special relativity. However, with a neutron star the increased effects of general relativity can no longer be ignored. Several EOS have been proposed (FPS, UU, APR, L, SLy, and others) and current research is still attempting to constrain the theories to make predictions of neutron star matter.[3][16] This means that the relation between density and mass is not fully known, and this causes uncertainties in radius estimates. For example, a 1.5 solar mass neutron star could have a radius of 10.7, 11.1, 12.1 or 15.1 kilometres (for EOS FPS, UU, APR or L respectively).[16] All EOS show that neutronium compresses with pressure.

## Structure

Cross-section of neutron star. Densities are in terms of ρ0 the saturation nuclear matter density, where nucleons begin to touch.

Current understanding of the structure of neutron stars is defined by existing mathematical models, but it might be possible to infer through studies of neutron-star oscillations. Similar to asteroseismology for ordinary stars, the inner structure might be derived by analyzing observed frequency spectra of stellar oscillations.[3]

On the basis of current models, the matter at 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.[17] It is also possible that heavy element cores, such as iron, simply drown beneath the surface, leaving only light nuclei like helium and hydrogen cores.[17] If the surface temperature exceeds 106 kelvin (as in the case of a young pulsar), the surface should be fluid instead of the solid phase observed in cooler neutron stars (temperature <106 kelvins).[17]

The "atmosphere" of the star is roughly one meter thick, and its dynamic is fully controlled by the star's magnetic field. Below the atmosphere one encounters a solid "crust". This crust is extremely hard and very smooth (with maximum surface irregularities of ~5 mm), because of the extreme gravitational field.[18]

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.

Proceeding deeper, one comes to a point called neutron drip where neutrons leak out of nuclei and become free neutrons. In this region, there are nuclei, free electrons, and free neutrons. The nuclei become smaller and smaller until the core is reached, by definition the point where they disappear altogether.

The composition of the superdense matter in the core remains uncertain. One model describes the core as superfluid neutron-degenerate matter (mostly neutrons, with some protons and electrons). More exotic forms of matter are possible, including degenerate strange matter (containing strange quarks in addition to up and down quarks), matter containing high-energy pions and kaons in addition to neutrons,[3] or ultra-dense quark-degenerate matter.

## History of discoveries

The first direct observation of a neutron star in visible light. The neutron star is RX J185635-3754.

In 1934 Walter Baade and Fritz Zwicky proposed the existence of the neutron star,[19][20] only a year after the discovery of the neutron by Sir James Chadwick.[21] In seeking an explanation for the origin of a supernova, they proposed that the neutron star is formed in a supernova. Supernovae are suddenly-appearing dying stars in the sky, whose luminosity in visible light outshine an entire galaxy for days to weeks. 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". If the central part of a massive star before its collapse contains (for example) 3 solar masses, then a neutron star of 2 solar masses can be formed. The binding energy E of such a neutron star, when expressed in mass units via the mass-energy equivalence formula E = mc2, is 1 solar mass. It is ultimately this energy that powers the supernova.

As demonstrated and cited in "Properties" section above, a two solar mass neutron star has a mass equivalent gravitational binding energy of no more than -18.7% (exothermic). A ~2.3 solar mass neutron star with ~10,000 meters radius is the large mass limit of the AP4 model. It would have a relative mass equivalent gravitational binding energy of 24.5%, half of claimed 50% mass equivalent of its observed gravitational mass in the preceding paragraph. Neutron star maximum binding energy under any circumstances cannot exceed 25.2% of its observed gravitational mass.[22]

In 1965, Antony Hewish and Samuel Okoye discovered "an unusual source of high radio brightness temperature in the Crab Nebula".[23] This source turned out to be the Crab Nebula neutron star that resulted from the great supernova of 1054.

In 1967, Iosif Shklovsky examined the X-ray and optical observations of Scorpius X-1 and correctly concluded that the radiation comes from a neutron star at the stage of accretion.[24]

In 1967, Jocelyn Bell and Antony Hewish discovered regular radio pulses from CP 1919. 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 1971, Riccardo Giacconi, Herbert Gursky, Ed Kellogg, R. Levinson, E. Schreier, and H. Tananbaum discovered 4.8 second pulsations in an X-ray source in the constellation Centaurus, Cen X-3. They interpreted this as resulting from a rotating hot neutron star. The energy source is gravitational and results from a rain of gas falling onto the surface of the neutron star from a companion star or the interstellar medium.

In 1974, Antony Hewish was awarded the Nobel Prize in Physics "for his decisive role in the discovery of pulsars" without Jocelyn Bell who shared in the discovery.

In 1974, Joseph Taylor and Russell Hulse discovered the first binary pulsar, PSR B1913+16, which consists of two neutron stars (one seen as a pulsar) orbiting around their center of mass. Einstein's general theory of relativity predicts that massive objects in short binary orbits should emit gravitational 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 the Nobel Prize in Physics for this discovery.

In 2010, Paul Demorest and colleagues measured the mass of the millisecond pulsar PSR J1614–2230 to be 1.97±0.04 solar masses, using Shapiro delay.[25] This is substantially higher than any other precisely measured neutron star mass (in the range 1.2-1.45 solar masses), and places strong constraints on the interior composition of neutron stars.

## Rotation

Neutron stars rotate extremely rapidly after their creation due to the conservation of angular momentum; like 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 several times a second; sometimes, the neutron star absorbs orbiting matter from a companion star, increasing the rotation to several hundred times per second, reshaping the neutron star into an oblate spheroid.

Over time, neutron stars slow down because their rotating magnetic fields radiate energy; older neutron stars may take several seconds for each revolution.

The rate at which a neutron star slows its rotation is usually constant and very small: the observed rates of decline are between 10−10 and 10−21 seconds for each rotation. Therefore, for a typical slow down rate of 10−15 seconds per rotation, a neutron star now rotating in 1 second will rotate in 1.000003 seconds after a century, or 1.03 seconds after 1 million years.

An artist's conception of a "starquake", or "stellar quake".

Sometimes a neutron star will spin up or undergo a glitch, a sudden small increase of its rotation speed. Glitches are thought to be the effect of a starquake - as the rotation of the star slows down, the shape becomes more spherical. Due to the stiffness of the 'neutron' crust, this happens as discrete events as the crust ruptures, similar to tectonic earthquakes. After the starquake, the star will have a smaller equatorial radius, and since angular momentum is conserved, rotational speed increases. 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 superfluid core of the star from one metastable energy state to a lower one.[26]

Neutron stars have been observed to "pulse" radio and x-ray emissions believed to be caused by particle acceleration near the magnetic poles, which need not be aligned with the rotation axis of the star. Through mechanisms not yet entirely understood, these particles produce coherent beams of radio emission. External viewers see these beams as pulses of radiation whenever the magnetic pole sweeps past the line of sight. The pulses come at the same rate as the rotation of the neutron star, and thus, appear periodic. Neutron stars which emit such pulses are called pulsars.

The most rapidly rotating neutron star currently known, PSR J1748-2446ad, rotates at 716 revolutions per second.[27] A recent paper reported the detection of an X-ray burst oscillation (an indirect measure of spin) at 1122 Hz from the neutron star XTE J1739-285.[28] However, at present this signal has only been seen once, and should be regarded as tentative until confirmed in another burst from this star.

## Population and distances

At present there are about 2000 known neutron stars in the Milky Way and the Magellanic Clouds, the majority of which have been detected as radio pulsars. The population of neutron stars is concentrated along the disk of the Milky Way although the spread perpendicular to the disk is fairly large. The reason for this spread is due to the asymmetry of the supernova explosion process, which can impart high speeds (400 km/s) to the newly created neutron star. One of the closest known neutron stars is PSR J0108-1431 at a distance of about 130 parsecs (or 424 light years).[29] Another nearby neutron star that was detected transiting the backdrop of the constellation Ursa Minor has been catalogued as 1RXS J141256.0+792204. This rapidly moving object, nicknamed by its Canadian and American discoverers "Calvera", was discovered using the ROSAT/Bright Source Catalog. Initial measurements placed its distance from earth at 200 to 1,000 light years away, with later claims at about 450 light-years.

## Binary neutron stars

About 5% of all neutron stars are members of a binary system. The formation and evolution scenario of binary neutron stars is a rather exotic and complicated process.[30] The companion stars may be either ordinary stars, 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. Such binaries are expected to be prime sources for emitting gravitational waves. Neutron stars in binary systems often emit X-rays which is caused by the heating of material (gas) accreted from the companion star. Material from the outer layers of a (bloated) companion star is sucked towards the neutron star as a result of its very strong gravitational field. As a result of this process binary neutron stars may also coalesce into black holes if the accretion of mass takes place under extreme conditions.[31]

## Subtypes

• Neutron star
• Protoneutron star (PNS), theorized.[32]
• Single pulsars–general term for neutron stars that emit directed pulses of radiation towards us at regular intervals (due to their strong magnetic fields).
• Binary pulsars
• Low-mass X-ray binaries (LMXB)
• Intermediate-mass X-ray binaries (IMXB)
• High-mass X-ray binaries (HMXB)
• Accretion-powered pulsar ("X-ray pulsar")
• 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.
• Millisecond pulsar (MSP) ("recycled pulsar")
• Sub-millisecond pulsar[33]
• Exotic star
• Quark star–currently a hypothetical type of neutron star composed of quark matter, or strange matter. As of 2008, 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 star is prevented by radiation pressure. As of 2010, there is no evidence for their existence.
• Preon star–currently a hypothetical type of neutron star composed of preon matter. As of 2008, there is no evidence for the existence of preons.

## Giant nucleus

A neutron star has some of the properties of an atomic nucleus, including density and being composed of nucleons. In popular scientific writing, neutron stars are therefore sometimes described as giant nuclei. However, in other respects, neutron stars and atomic nuclei are quite different. In particular, a nucleus is held together by the strong interaction, while a neutron star is held together by gravity. It is generally more useful to consider such objects as stars.

## Examples of neutron stars

• PSR J0108-1431 - closest neutron star
• LGM-1 - the first recognized radio-pulsar
• PSR B1257+12 - the first neutron star discovered with planets (a millisecond pulsar)
• SWIFT J1756.9-2508 - a millisecond pulsar with a stellar-type companion with planetary range mass (below brown dwarf)
• PSR B1509-58 source of the "Hand of God" photo shot by the Chandra X-ray Observatory.

## References

1. ^ Bulent Kiziltan (2011). Reassessing the Fundamentals: On the Evolution, Ages and Masses of Neutron Stars. Universal-Publishers. ISBN 1612337651.
2. ^ Bulent Kiziltan; Athanasios Kottas; Stephen E. Thorsett (2010). "The Neutron Star Mass Distribution". arXiv:1011.4291 [astro-ph.GA].
3. ^ a b c d Paweł Haensel, A Y Potekhin, D G Yakovlev (2007). Neutron Stars. Springer. ISBN 0387335439.
4. ^ A neutron star's density increases as its mass increases, and, for most equations of state (EOS), its radius decreases non-linearly. For example, EOS radius predictions for a 1.35 M star are: FPS 10.8 km, UU 11.1 km, APR 12.1 km, and L 14.9 km. For a more massive 2.1 M star, radius predictions are: FPS undefined, UU 10.5 km, APR 11.8 km, and L 15.1 km. (NASA mass radius graph)
5. ^ 3.7×1017 kg/m3 derives from mass 2.68 × 1030 kg / volume of star of radius 12 km; 5.9×1017 kg m-3 derives from mass 4.2×1030 kg per volume of star radius 11.9 km
6. ^   NB 3 × 1017 kg/m3 is 3×1014 g/cm3
7. ^ a b c "Introduction to neutron stars". Retrieved 2007-11-11.
8. ^
9. ^ [1], a ten stellar mass star will collapse into a black hole.
10. ^ a b c Zahn, Corvin (1990-10-09). "Tempolimit Lichtgeschwindigkeit" (in German). Retrieved 2009-10-09. "Durch die gravitative Lichtablenkung ist mehr als die Hälfte der Oberfläche sichtbar. Masse des Neutronensterns: 1, Radius des Neutronensterns: 4, ... dimensionslosen Einheiten (c, G = 1)"
11. ^ Neutron Star Masses and Radii, p. 9/20, bottom
12. ^ J. M. Lattimer and M. Prakash, "Neutron Star Structure and the Equation of State" Astrophysical J. 550(1) 426 (2001); http://arxiv.org/abs/astro-ph/0002232
13. ^ Measurement of Newton's Constant Using a Torsion Balance with Angular Acceleration Feedback , Phys. Rev. Lett. 85(14) 2869 (2000)
14. ^ The average density of material in a neutron star of radius 10 km is 1.1×1012 kg cm−3. Therefore, 5 ml of such material is 5.5×1012 kg, or 5 500 000 000 metric tons. This is about 15 times the total mass of the human world population. Alternatively, 5 ml from a neutron star of radius 20 km radius (average density 8.35×1010 kg cm−3) has a mass of about 400 million metric tons, or about the mass of all humans.
15. ^ Miscellaneous Facts
16. ^ a b NASA. Neutron Star Equation of State Science Retrieved 2011-09-26
17. ^ a b c V. S. Beskin (1999). "Radiopulsars". УФН. T.169, №11, p.1173-1174
18. ^ neutron star
19. ^ Baade, Walter and Zwicky, Fritz (1934). "Remarks on Super-Novae and Cosmic Rays". Phys. Rev. 46 (1): 76–77. Bibcode 1934PhRv...46...76B. doi:10.1103/PhysRev.46.76.2.
20. ^ Even before the discovery of neutron, in 1931, neutron stars were anticipated by Lev Landau, who wrote about stars where "atomic nuclei come in close contact, forming one gigantic nucleus" (published in 1932: Landau L.D.. "On the theory of stars". Phys. Z. Sowjetunion 1: 285–288. ). However, the widespread opinion that Landau predicted neutron stars proves to be wrong: for details, see P. Haensel, A. Y. Potekhin, & D. G. Yakovlev (2007). Neutron Stars 1: Equation of State and Structure (New York: Springer), page 2 http://adsabs.harvard.edu/abs/2007ASSL..326.....H
21. ^ Chadwick, James (1932). "On the possible existence of a neutron". Nature 129 (3252): 312. Bibcode 1932Natur.129Q.312C. doi:10.1038/129312a0.
22. ^ Lattimer; Prakash (2010). "What a Two Solar Mass Neutron Star Really Means". arXiv:1012.3208 [astro-ph.SR].
23. ^ Hewish and Okoye; Okoye, S. E. (1965). "Evidence of an unusual source of high radio brightness temperature in the Crab Nebula". Nature 207 (4992): 59. Bibcode 1965Natur.207...59H. doi:10.1038/207059a0.
24. ^ Shklovsky, I.S. (April 1967). "On the Nature of the Source of X-Ray Emission of SCO XR-1". Astrophys. J. 148 (1): L1–L4. Bibcode 1967ApJ...148L...1S. doi:10.1086/180001
25. ^ Demorest, PB; Pennucci, T; Ransom, SM; Roberts, MS; Hessels, JW (2010). "A two-solar-mass neutron star measured using Shapiro delay". Nature 467 (7319): 1081–1083. Bibcode 2010Natur.467.1081D. doi:10.1038/nature09466. PMID 20981094.
26. ^ Alpar, M Ali (January 1, 1998). "Pulsars, glitches and superfluids". Physicsworld.com.
27. ^ [astro-ph/0601337] A Radio Pulsar Spinning at 716 Hz
28. ^ University of Chicago Press - Millisecond Variability from XTE J1739285 - 10.1086/513270
29. ^ Posselt, B.; Neuhäuser, R.; Haberl, F. (March 2009). "Searching for substellar companions of young isolated neutron stars". Astronomy and Astrophysics 496 (2): 533–545. Bibcode 2009A&A...496..533P. doi:10.1051/0004-6361/200810156.
30. ^ Tauris & van den Heuvel (2006), in Compact Stellar X-ray Sources. Eds. Lewin and van der Klis, Cambridge University Press http://adsabs.harvard.edu/abs/2006csxs.book..623T
31. ^ Compact Stellar X-ray Sources (2006). Eds. Lewin and van der Klis, Cambridge University
32. ^ Neutrino-Driven Protoneutron Star Winds, Todd A. Thompson.
33. ^ Nakamura, T. (1989). "Binary Sub-Millisecond Pulsar and Rotating Core Collapse Model for SN1987A". Progress of Theoretical Physics 81 (5): 1006. Bibcode 1989PThPh..81.1006N. doi:10.1143/PTP.81.1006.
• "ASTROPHYSICS: ON OBSERVED PULSARS". scienceweek.com. Retrieved 6 August 2004.
• Norman K. Glendenning, R. Kippenhahn, I. Appenzeller, G. Borner, M. Harwit (2000). Compact Stars (2nd ed.).
• Kaaret; Prieskorn; in 't Zand; Brandt; Lund; Mereghetti; Gotz; Kuulkers et al. (2006). "Evidence for 1122 Hz X-Ray Burst Oscillations from the Neutron-Star X-Ray Transient XTE J1739-285". The Astrophysical Journal 657 (2): L97. arXiv:astro-ph/0611716. Bibcode 2007ApJ...657L..97K. doi:10.1086/513270.

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