The term "Neutron stars" refers to stars that have collapsed to the point where the density is so great that the components of the atoms themselves (neutrons, protons and electrons ) fuse together to form electrically neutral neutrons. So there are no orbiting electrons - just free neutrons jammed together. This is why they are all the same density.
The protons, neutrons and electrons can't get any closer to each other. A regular star is 500,000 Km across and a neutron star is 20km (12miles) across. The gravity on the surface is 70 billion times stronger than earth gravity.
Neutron stars were all originally 1.4 to 3 times the size of our Sun. They exhausted their fuel and exploded into supernovas. The collapsed remnant left behind is a neutron star.
Stars bigger or smaller than this will not become neutron stars - which is another reason why Neutron stars are all the same density. (Larger stars become Black holes - smaller ones are likely to become White Dwarfs) As the original star (from originally 1.4 to 3 times our Sun's size) collapses under its own gravity the spin increases - just as a ballerina spins faster if she draws her limbs in towards her torso. Neutron stars will spin so fast they do a complete rotation in a millisecond or so.
We call these Pulsars if we can detect the radiation from their poles as they spin. Gravity is the force that collapses the stars and it is balanced by the forces keeping the atomic particles apart in the Neutronium soup. The two forces reach an equilibrium and the star become stable.
This Neutronim soup is the densest form of matter outside of a black hole. The particles are kept apart by degenerate Neutron pressure which is a result of Pauli's exclusion principle. This fundamental rule states that no two electrons can occupy the same quantum state at the same place and time.
There are about 2000 known neutron stars in our Milky Way Galaxy - the majority are pulsars.
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