Quantum plasma modification of the Lane-Emden equation for stellar structure

TL;DR

This paper introduces a quantum plasma correction to the Lane-Emden equation, affecting white dwarf models by slightly reducing the Chandrasekhar mass and marginally increasing stellar radii.

Contribution

It derives a quantum-modified Lane-Emden equation incorporating quantum plasma effects in degenerate stars, providing new insights into stellar structure equations.

Findings

Quantum corrections slightly reduce the Chandrasekhar mass.

Quantum effects marginally increase white dwarf radii.

Derived an approximate solution for the quantum-modified equation.

Abstract

The proper quantum plasma treatment of the electron gas in degenerate stars such as white dwarfs provides an additional quantum contribution to the electron pressure. The additional pressure term modifies the equation for hydrostatic equilibrium, resulting in the quantum modified Lane-Emden equation for polytropic equation of states. The additional pressure term also modifies the expression for the limiting Chandrasekhar mass of white dwarfs. An approximate solution is derived of the quantum modified Lane-Emden equation for general polytropic indices, and it is demonstrated that the quantum corrections reduce the standard Chandrasekhar mass and enhance the white dwarf radius by negligibly small values only.