Self-gravity Correction to the Chandrasekhar Limiting Mass of White Dwarfs

TL;DR

This paper investigates how including the star's self-gravity as an effective potential affects the Chandrasekhar mass limit of white dwarfs, using perturbation theory to refine the classical model.

Contribution

It introduces a novel correction to the Chandrasekhar limit by accounting for the star's self-gravity through quantum mechanical perturbation theory.

Findings

Self-gravity causes a non-trivial correction to the degeneracy pressure.

The correction is small but potentially significant for precise modeling.

Major observational implications remain unaffected.

Abstract

While computing the Fermi degeneracy pressure of electrons in a white dwarf star within the framework of hydrostatic equilibrium, we depart from the extant practice of treating the electrons as a free fermion gas, by including the effect of the star's self-gravity as an effective gravitational potential. By the star's self gravity, we mean the gravitational field due to the star itself, resulting from the mass of its constituent atoms, the mass of the atom being effectively the mass of the proton. Modifying the free particle Hamiltonian with this effective potential, we employ first order quantum mechanical perturbation theory to compute the degeneracy pressure, in order to study the effect of inclusion of this self-gravity of the star on the Chandrasekhar limiting mass. The final effect is found to be non-trivial, but perhaps a shade too small to alter any major observational result.