Superfluidity of neutron stars

What Are Neutron Stars?

Stellar Evolution

Neutron stars are one of the many possible ends to the life of a star. All stars begin as space dust, usually in a giant cloud. Should perturbations in the density of cloud permit enough mass to be in a certain radius, the cloud will collapse. As the dust free-falls the dust will form a disk, most of which will end up in the star and the rest will form planets, moons, asteroids, and meteoroids. Then assuming that the dust cloud was massive enough, the core of the condensed cloud will ignite forming a main sequence star. This phase of stellar life is characterized by hydrogen burning via the pp-chain or CNO-cycle. Some stars (those of less than 0.7 solar masses) finish their lives here as the core contraction after the red giant phase cannot raise the temperature high enough to burn helium. These very low mass stars will become white dwarfs. The rest will then move on to helium burning in the phase known as the horizontal branch. After the helium shell burning the next mass cutoff occurs. Any star less than 8 solar masses will then turn into white dwarf as the core will not become hot enough to produce carbon. The stars that are still massive enough will then begin burning helium to carbon and oxygen, carbon to neon, neon and oxygen to silicon, and silicon to nickel (nickel will then beta decay to cobalt and cobalt then decays to iron). Once the star produces nickel it is doomed as it cannot gain any more energy by fusing elements together. Of course mass limits the exact stopping stage, but whatever the cause, when the burning does cease these stars explode.

The end state of any star occurs suddenly. Stars maintain a balance between the inward gravitational pressure and the outward energy pressure. But the star eventually cannot burn past a certain stage. The core of the star shrinks rapidly until the atoms squeeze next to each other as the electron clouds are what is holding the atoms apart. The outward pressure of this state, the white dwarf, is known as the electron degeneracy pressure. For larger mass stars, the core shrinks so rapidly that there is too much pressure it is then favorable for the protons and electrons to react to form neutrons. The reverberation from this rapid compression is the classical cause of the supernova explosion. This way the neutrons become degenerate and the star becomes a neutron star. If the mass then shrinks below the Schwarzschild radius, the star becomes a black hole. The Schwarzschild radius is given by:

$r_{s}=(3M/M_{\odot })km$

where M is the mass of the star and the M with the dot is the mass of the sun. Interestingly, after the red supergiant phase (after helium burning has ceased) the time it takes for the energy from the core to make it to the surface is 10,000 years. However, the rest of the star's life will last less than 1000 years. This means that the surface of the star has no idea that the star is dead until it explodes.

Properties of the Neutron Star

As mentioned before, a star with eight times the mass of the sun is eligible to be a neutron star. A white dwarf (which the sun will one day be) is usually about one hundredth the size of the sun, or about the size of the earth. Neutron stars are obviously much smaller than this. One can use a simple calculation to approximate the size of this star. From the statistical physics one has the following relations: