A typical neutron star has a mass between 1.35 and about 2.1 solar masses, with a corresponding radius of about 12 km if the Akmal-Pandharipande-Ravenhall (APR) Equation of state is used. In contrast, the Sun's radius is about 600,000 times larger. Neutron stars have overall densities predicted by EOS APR of 3.7 (2.6 times Solar density) to 5.9 kg/m³ (4.1 times Solar density), which compares with the approximate density of an atomic nucleus of 3 kg/m³. The neutron star's density varies from below 1 kg/m³ in the crust increasing with depth to above 6 or 8 kg/m³ deeper inside.
In general, compact stars of less than 1.44 solar masses, the Chandrasekhar limit, are white dwarfs; above 2 to 3 solar masses (the Tolman-Oppenheimer-Volkoff limit), a quark star might be created, however this is uncertain. Gravitational collapse will always occur on any star over 5 solar masses, inevitably producing a black hole.
The gravitational field at the star's surface is about 2times stronger than on Earth. The escape velocity is about 100,000 km/s, which is about one third the speed of light. 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.
The gravitational binding energy of a two solar mass neutron star is equivalent to the total conversion of one solar mass to energy (From the law of mass-energy equivalence, E=mc2). That energy was released during the supernova explosion.
The temperature inside a newly formed Neutron star is from 100 thousand million to a million million Kelvin. However, the huge number of neutrinos it emits carries away so much energy that the temperature falls within a few years to only one million Kelvin.
The Equation of state (EOS) for a Neutron star is still not known as of 2008. 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 and L) and current research is still attempting to constrain the theories to make predictions of neutron star matter. 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). All EOS show that neutronium compresses with pressure.
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. A neutron star is so dense that one teaspoon (5 millilitre) of its material would have a mass over 5×1012 kg. On the basis of current models, the matter at the surface of a neutron star is composed of ordinary atomic nuclei as well as electrons. The "atmosphere" of the star is roughly one meter thick, below which 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. The crust would appear black because all radiation is focused around the X-ray spectrum.
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 free neutrons leak out of nuclei. 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 exact nature of the superdense matter in the core is still not well understood. While this theoretical substance is referred to as neutronium in science fiction and popular literature, the term "neutronium" is rarely used in scientific publications, due to ambiguity over its meaning. The term neutron-degenerate matter is sometimes used, though not universally as the term incorporates assumptions about the nature of neutron star core material. Neutron star core material could be a superfluid mixture of neutrons with a few protons and electrons, or it could incorporate high-energy particles like pions and kaons in addition to neutrons, or it could be composed of strange matter incorporating quarks heavier than up and down quarks, or it could be quark matter not bound into hadrons. (A compact star composed entirely of strange matter would be called a strange star.) However, so far, observations have neither indicated nor ruled out such exotic states of matter.
The neutron elementary particle was discovered in 1932 by Sir James Chadwick. By bombarding the hydrogens atoms in parafin with emissions from beryllium that was itself being bombarded with alpha particles, he demonstrated that these emissions contained a neutral particle that had about the same mass as a proton. In 1935 he was awarded the Nobel Prize in Physics for this discovery.
In 1933, Walter Baade and Fritz Zwicky proposed the existence of the neutron star, only a year after Chadwick's discovery of the neutron. 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 the optical might 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.
In 1965, Antony Hewish and Samuel Okoye discovered "an unusual source of high radio brightness temperature in the Crab Nebula". This source turned out to be the Crab Nebula neutron star that resulted from the great supernova of 1054 CE.
In 1967, Jocelyn Bell and Antony Hewish discovered regular radio pulses from the location of the Hewish and Okoye radio source. This pulsar was later interpreted as originating from an isolated, rotating neutron star. The energy source of the pulsar is the rotational energy of the neutron star. The largest number of known neutron stars are of this type (See Rotation-powered pulsar).
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 (See Accretion-powered pulsar).
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.
Sometimes a neutron star will spin up or undergo a glitch, a rapid and unexpected increase of its rotation speed (of the same, extremely small scale as the constant slowing down). 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.
Neutron stars may "pulse" due to particle acceleration near the magnetic poles, which are not 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. 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. However, at present this signal has only been seen once, and should be regarded as tentative until confirmed in another burst from this star.
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