White DwarfsPerhaps 10 percent of the stars in our galaxy are believed to be white dwarfs.These
are stars in the final stages of their evolution with original masses that were less than
about 8 solar masses. After the nuclear reactions that provided it with energy run out
of fuel, such a star becomes unstable, swells to become a red giant, and eventually
throws off its outer layer. The remaining core then cools and contracts gravitationally
until its atoms collapse into nuclei and electrons packed closely together. A typical
white dwarf has a mass of two-thirds that of the sun but is only about the size of the
earth; a handful of its matter would weigh over a ton on the earth.
As a prospective white dwarf contracts, its volume Vdecreases and as a result the
Fermi energy Fof its electrons increases; see Eq. (9.56). When F exceeds kT, the
electrons form a degenerate gas. A reasonable estimate for the Fermi energy in a typical
white dwarf is 0.5 MeV. The nuclei present are much more massive than the electrons,
and because Fis inversely proportional to m, they continue to behave classically.
With the star’s nuclear reactions at an end, the nuclei cool down and come together
under the influence of gravitation. The electrons, however, cannot cool down since
most of the low-energy states available to them are already filled; the situation corre-
sponds to Fig. 9.6b. The electron gas becomes hotter and hotter as the star shrinks.
Even though the total electron mass is only a small fraction of the star’s mass, in time
it exerts enough pressure to stop the gravitational contraction. Thus the size of a white
dwarf is determined by a balance between the inward gravitational pull of its atomic
nuclei and the pressure of its degenerate electron gas.328 Chapter Nine
The Ring nebula in the constellation Lyra is a shell of gas moving outward from the
star at its center, which is in the process of becoming a white dwarf.bei48482_Ch09.qxd 1/22/02 8:46 PM Page 328