Authors: Ting-Hang Pei
Traditional explanation for the white dwarf star is based on the ideally degenerate Fermi electron gas to produce the pressure against gravity. This theory predicts the upper mass limit of the white dwarf star is 1.44 Mʘ although the Fermi electron gas is calculated at the temperature T of absolute zero. In this research, first considering the electron-electron interaction in the high-density Fermi electron gas at T=0 K, this interaction causes the pressure 2/137 time less than the original value. However, the pressure of the Fermi electron gas should have something to do with temperature at 10^7 K. Then we estimate the temperature effect using statistical mechanics and find the total pressure depends on temperature weakly at the given particle number N and volume V. According to this, the relationship between radius and mass of the white dwarf star is obtained and it mainly depends on temperature, electron mass, and proton mass. An unknown parameter δ=34.75 is calculated by using an example of a white dwarf star with the mass of our sun and the radius of Earth. This relationship is useful for estimating the inner temperature of a white dwarf star. The lowest limit of M/R^3 depends on neutron mass, electron mass, and temperature.
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