White dwarfs

White dwarfs have low luminosities (∼ 10-4 - 1L⊙) but their photospheric temperatures (T ≃ 6000 – 2 × 104 K) are comparable to those of main-sequence stars. It follows that the radii of white dwarfs are small (≃ 109 cm). The masses and radii of several white dwarfs in binary systems have been determined. The white dwarfs Sirius B and 40 Eri B are known to have masses and radii equal to (M = 1.05 M⊙, R = 0.0074 R⊙) and (M = 0.48 M⊙, R = 0.0124 R⊙) respectively. Because the central densities of white dwarfs are high (≃ 106-109 g cm-3) and the temperatures of their isothermal cores relatively low (∼ 107 K), electrons are completely degenerate except in thin surface layers.

The structures of white dwarfs are determined by the equations of hydrostatic equilibrium (Equation (2.27)), mass conservation (Equation (2.28)) and the equation of state of an electron-degenerate gas described in Section 3.2. Unlike main-sequence stars the radii of white dwarfs decrease as a function of increasing mass and in addition there exists an upper limit to the mass of a white dwarf. This mass limit, which is known as the Chandrasekhar mass limit, depends on the electron molecular weight because the electron pressure increases as the number density of electrons increases. The calculated white dwarf mass limit Mc for uniform electron molecular weight μe is

Since most white dwarfs consist primarily of fully ionized 4He, 12C and 16O their electron molecular weight is μe = 2.