Production of Electron Pairs and the Theory of Stellar Structure

Abstract

IN the discussion of problems of stellar structure, only the deviations from the perfect gas laws arising from degeneracy due to the exclusion principle for the electrons have so far been considered. In fact, as has recently been shown by one of us¹, these deviations involve far-reaching limitations on the possible stellar configurations under given conditions. Thus, it can be deduced from the form of the equation of state of a degenerate gas, taking due account of relativity, that in order that degeneracy should develop in any part of a star, the ratio of gas pressure to total pressure at that point must satisfy the condition, and on the standard model, in which is assumed to be constant throughout the star, this implies the existence of a critical mass (&circdot; denoting the mass of the sun and the molecular weight) above which degeneracy cannot set in at all. A study of the equilibrium of completely degenerate gas spheres leads further to the result that there is an upper limit to the masses of such configuration; this affords the possibiliy, for stars of mass M₃, of a course of evolution leading to complete degeneracy through intermediate stages comparable to the observed white dwarf configurations.