A neutron star is the collapsed core of a large star which before collapse had a total of between 10 and 29 solar masses.
Neutron stars are the smallest and densest stars,
not counting hypothetical quark stars and strange stars. Typically,
neutron stars have a radius on the order of 10 kilometres and a mass between 1.4 and 2.16 solar masses.
They result from the supernova explosion of a massive star,
combined with gravitational collapse,
that compresses the core past the white dwarf star density to that of atomic nuclei. Once formed,
they no longer actively generate heat,
and cool over time, however,
they may still evolve further through collision or accretion.
Most of the basic models for these objects imply that neutron stars are composed almost entirely of neutrons,
the electrons and protons present in normal matter combine to produce neutrons at the conditions in a neutron star.
Neutron stars are supported against further collapse by neutron degeneracy pressure,
a phenomenon described by the Pauli exclusion principle,
just as white dwarfs are supported against collapse by electron degeneracy pressure.
If the remnant star has a mass greater than about 3 solar masses,
it continues collapsing to form a black hole.
Neutron stars that can be observed are very hot and typically have a surface temperature of around 600000 K. They are so dense that a normal-sized matchbox containing neutron-star material would have a mass of approximately 3 billion tonnes,
or a 0.5 cubic kilometre chunk of the Earth.
Their magnetic fields are between 108 and 1015 times as strong as that of the Earth.
The gravitational field at the neutron star's surface is about 2×1011 times that of the Earth.
As the star's core collapses,
its rotation rate increases as a result of conservation of angular momentum,
hence newly formed neutron stars rotate at up to several hundred times per second.
Some neutron stars emit beams of electromagnetic radiation that make them detectable as pulsars. Indeed,
the discovery of pulsars by Jocelyn Bell Burnell in 1967 was the first observational suggestion that neutron stars exist.
The radiation from pulsars is thought to be primarily emitted from regions near their magnetic poles.
If the magnetic poles do not coincide with the rotational axis of the neutron star,
the emission beam will sweep the sky,
and when seen from a distance,
if the observer is somewhere in the path of the beam,
it will appear as pulses of radiation coming from a fixed point in space.
The fastest-spinning neutron star known is PSR J1748-2446ad,
rotating at a rate of 716 times a second or 43,000 revolutions per minute,
giving a linear speed at the surface on the order of 0.24 c. There are thought to be around 100 million neutron stars in the Milky Way,
a figure obtained by estimating the number of stars that have undergone supernova explosions. However,
most are old and cold,
and neutron stars can only be easily detected in certain instances,
such as if they are a pulsar or part of a binary system.
Slow-rotating and non-accreting neutron stars are almost undetectable, however,
since the Hubble Space Telescope detection of RX J185635-3754,
a few nearby neutron stars that appear to emit only thermal radiation have been detected.
Soft gamma repeaters are conjectured to be a type of neutron star with very strong magnetic fields,
known as magnetars, or alternatively,
neutron stars with fossil disks around them.
Neutron stars in binary systems can undergo accretion which typically makes the system bright in X-rays while the material falling onto the neutron star can form hotspots that rotate in and out of view in identified X-ray pulsar systems. Additionally,
such accretion can "recycle" old pulsars and potentially cause them to gain mass and spin-up to very fast rotation rates,
forming the so-called millisecond pulsars.
These binary systems will continue to evolve,
and eventually the companions can become compact objects such as white dwarfs or neutron stars themselves,
though other possibilities include a complete destruction of the companion through ablation or merger.
The merger of binary neutron stars may be the source of short-duration gamma-ray bursts and are likely strong sources of gravitational waves. In 2017,
a direct detection of the gravitational waves from such an event was made,
and gravitational waves have also been indirectly detected in a system where two neutron stars orbit each other. 
