A neutron star is a type of compact star remnant that can result from the gravitational collapse of a massive star during a Type II supernova, Type Ib and Ic supernovae event. Such stars are composed almost entirely of neutrons, which are subatomic particles without electrical charge and roughly the same mass as protons. Neutron stars are very hot and are supported against further collapse because of the Pauli exclusion principle. This principle states that no two neutrons (or any other fermionic particle) can occupy the same place and quantum state simultaneously.
A neutron star's density increases as its mass increases, and, for most Equations of State (EOS), its radius decreases in a non-linear way. 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.
In contrast, the Sun's radius is about 60,000 times that. Neutron stars have overall densities predicted by the APR EOS of to kg/m3 (or to times the density of the Sun), which compares with the approximate density of an atomic nucleus of kg/m3.
The neutron star's density varies from below kg/m3 in the crust increasing with depth to above kg/m3 or kg/m3 deeper inside.
This density is approximately equivalent to the mass of the entire human population compressed into the size of a sugar cube.
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 compact star over 5 solar masses, inevitably producing a black hole or explosion of the star.
History of discoveries
The neutron subatomic particle was discovered in 1932 by Sir James Chadwick.  By bombarding the hydrogen atoms in paraffin 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 1934, Walter Baade and Fritz Zwicky  proposed the existence of the neutron star, only a year after Chadwick's discovery of the neutron.
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).  However, the widespread opinion that Landau predicted neutron stars proves to be wrong. 
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 night 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.
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.
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 Samuel Okoye and Jocelyn Bell who shared in the discovery.
A neutron star has some of the properties of an atomic nucleus, including density, and being made 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 force or strong gravitation, 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.
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- "Mysterious X-ray sources may be lone neutron stars". New Scientist.
- "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.