Friday, October 03, 2014

Degenerate Stars

Not talking Hollywood or Hip Hop here, but those stellar objects where electrons (or in neutron stars, neutrons) are compressed so highly that degeneracy pressures dominate the equation of state. Degeneracy pressure arises from the fact that fermions (particles with half integral spin) obey Fermi-Dirac statistics, which prohibits any two such particles from occupying the same quantum mechanical state.

When a star of a certain size has exhausted the hydrogen in its core, that core, unsupported by radiation and gas pressure contracts until the electrons are crowded enough to approach degeneracy and be supported by mainly degeneracy pressure, while hydrogen continues burning in a shell beyond the core, thus releasing more and more helium "ash" to accumulate in the core. Eventually, the temperature rises high enough (about 100 million K) to ignite helium burning in the core. This dumps a bunch of new energy into the core and rapidly heats it up.

For a main sequence star, temperature and pressure combine to act as a thermostat for the star, with a small increase in temperature increasing the pressure, thus expanding the star and decreasing energy generation, thus maintaining something like stability. For a purely degenerate Fermi gas, though, pressure is independent of temperature, so the onset of helium burning in a largely degenerate core has little expansionary effect, and the new energy source rapidly heats the core without much decrease in density, setting off a rapid chain reaction called the "helium flash." Of course the rapid heating bumps a bunch of electrons to higher energy levels, decreasing the degeneracy as fewer and fewer of the lowest energy levels are occupied, and eventually ordinary gas pressure dominates and the system returns to stability.