Newtonian polytropes for anisotropic matter: General framework and applications

TL;DR

This paper develops a general formalism for modeling anisotropic Newtonian stars using polytropic equations, deriving the Lane-Emden equation, and analyzing how pressure anisotropy affects stellar structure and mass limits.

Contribution

It introduces a comprehensive framework for anisotropic polytropic stars and demonstrates its application by calculating the Chandrasekhar mass variation due to anisotropy.

Findings

Anisotropy alters the stellar structure and mass limits.

Derived the Lane-Emden equation for anisotropic matter.

Showed how Chandrasekhar mass depends on pressure anisotropy.

Abstract

We set up the general formalism to model polytropic Newtonian stars with anisotropic pressure. We obtain the corresponding Lane-Emden equation. A heuristic model based on an ansatz to obtain anisotropic matter solutions from known solutions for isotropic matter is adopted to illustrate the effects of the pressure anisotropy on the structure of the star. In particular, we calculate the Chandrasekhar mass for a white dwarf. It is clearly displayed how the Chandrasekhar mass limit changes depending on the anisotropy. Prospective astrophysical applications of the proposed approach are discussed.