The additional pressure of white dwarf stars generated by net charges

Abstract

The upper-mass limit of a white dwarf star is predicted to be 1.44 ${M}_{\odot} $ based on an ideally degenerate Fermi electron gas at a temperature of absolute zero. However, more conditions should be considered, such as temperature and charge. In this research, first, we use the grand partition function in statistical mechanics to build expressions for the electron gas pressure and the particle number depending on temperature. At 1.16 × 107 K, there is a total of about 1.50 × 10−4 electrons exceeding the Fermi energy, and about 1.50 × 10−7 at 1.16 × 104 K. Because some of these Fermi electrons are extremely relativistic, some of them can escape the gravity and some return to the star after leaving. These two mechanisms result in a positively charged star and the net positive charges produce a repulsive force and pressure against gravity. The increased pressure is comparable to that of the Fermi electron gas at T = 0 when the star is charged at 1020 C. The net charges will decrease the mass density of the star but increase the upper-mass limit.