Neutron stars are the dense cinders of massive stars which have gone supernova and crushed the matter in their cores to densities of 10^14 grams/cc. At these densities, equal to that of nuclear matter, most of the protons and electrons have combined to create neutrons, so that the core is nearly 100% pure neutrons. The cinder is prevented from further gravitational collapse because neutrons are particles with 1/2-unit of quantum spin, and only two of these can exist in the same quantum state. This produces what is called Fermi Degeneracy Pressure which at these densities and neutron star masses, can be as strong as gravity, but a repulsive force.

Neutrons are composed of three quarks, which are also capable of generating the same kind of degeneracy pressure, but first you have to compress the neutron star to densities of 10^16 grams/cc or higher. This requires an amount of mass in the neutron star that puts it nearly at the black hole limit for its size...about 25 kilometers in radius or less. At these densities, the neutrons in the core of this object begin to dissolve into their constituent quarks, and so in the deep interior of the cinder you end up with a 'gas' of quarks. As you continue to crank up the density even higher, the quark-state encompasses more and more of the neutron star. The problem is that such 'quark stars' are nearly the same size as the black hole limit for the amount of mass and size, so when you factor-in the relativistic effects, quark stars are probably a very unstable and fleeting phase in the life of a very massive neutron star.

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