A neutron star is not actually a star at all. They are the remnant core of very massive, collapsed stars which have undergone a Type II supernova. They are extremely small for a celestial body, are composed purely of neutrons, and are incredibly dense (Chaisson, 2002). A typical neutron star is about 20 km in diameter, which is about the size of a terrestrial city, and their average densities can reach values as high as 1018 kg/m3, a density nearly a billion times that of a white dwarf (Chaisson, 2002). .
As stated above, neutron stars are believed to be left behind after a Type II supernova explosion. Exactly how they are formed is a complex process, and it is believed that during the moment of implosion in a massive star, just prior to the actual explosion, core electrons smash violently into protons, creating neutrons and neutrinos (Chaisson, 2002). At the very high pressures involved in this collapse, it is energetically favorable to combine protons and electrons to form neutrons plus neutrinos. The neutrinos subsequently leave the core at the speed of light, which accelerates the collapse of the neutron core. The core continues to contract until its particles come into contact and neutron degeneracy pressure causes the central portion of the core to rebound, violently expelling matter into space (Chaisson, 2002). The important aspect that should be noted here is that the shock wave which destroys the star does not begin at the very center of the collapsing core. The inner, "bouncing" region survives the shock wave, and the inner ball of neutrons is all that remains (Chaisson, 2002). The neutrons then settle down and form what astronomers term a "neutron star", with the neutron degeneracy pressure managing to oppose gravity. Since supernovas are known to occur about once every 30 years, and because most supernovae tend to create neutron stars as opposed to black holes, in the 10 billion year lifetime of the galaxy there have probably been from 108 to 109 neutron stars formed (Shu, 1982).