A burnt-out star is basically a gas of electrons and ions. As the
star collapses, its density increases, so the mean separation between its
constituent particles decreases. Eventually, the mean separation becomes
of order the de Broglie wavelength of the electrons, and the electron
gas becomes *degenerate*. Note, that the de Broglie wavelength of the
ions is much smaller than that of the electrons, so the ion gas remains
non-degenerate. Now, even at
zero temperature, a degenerate electron gas exerts a substantial pressure,
because the Pauli exclusion principle prevents the mean electron separation
from becoming significantly smaller than the typical
de Broglie wavelength (see the
previous section). Thus, it is possible for a burnt-out star to maintain
itself against complete collapse under gravity via the *degeneracy pressure*
of its constituent electrons. Such stars are termed *white-dwarfs*.
Let us investigate the physics of white-dwarfs in more detail.

The total energy of a white-dwarf star can be written

where is the gravitational constant, is the stellar mass, and is the stellar radius.

Let us assume that the electron gas is highly degenerate, which is
equivalent to taking the limit
. In this case, we know,
from the previous section, that the Fermi momentum can be written

(684) |

Here,

is the stellar volume, and is the total number of electrons contained in the star. Furthermore, the number of electron states contained in an annular radius of -space lying between radii and is

(687) |

where is the electron mass. It follows that

The interior of a white-dwarf star is composed of atoms like
and which contain equal numbers of protons, neutrons, and
electrons. Thus,

Equations (682), (683), (685), (686),
(689), and (690) can be combined to give

(691) |

(692) | |||

(693) |

The equilibrium radius of the star is that which

(694) |

(695) |

where is the solar radius, and is the solar mass. It follows that the radius of a typical solar mass white-dwarf is about 7000km: