A Polytropic Approach to Semi-relativistic Isothermal Gas Spheres at Arbitrary Temperature

TL;DR

This paper establishes a mathematical link between polytropic models and semi-relativistic isothermal gas spheres at finite temperatures, using polynomial expansion and numerical analysis to explore their thermal properties.

Contribution

It introduces a novel relation between polytropic indices and temperature/chemical potential in semi-relativistic gas spheres, bridging models for fermions and bosons.

Findings

Polytropic index correlates with temperature and chemical potential.

A polynomial expansion technique reveals the relation between models.

Numerical analysis supports the correspondence between models.

Abstract

We use standard polynomial expansion technique to show the existence of a relation between polytropic model and the description of gas spheres at finite temperature. A numerical analysis is made concerning the obtained perturbative parameters. It is shown that there is a correspondence between polytropic and gas sphere thermal models for fermions and bosons. For instance, the polytropic index $n$ displays evident correlation with temperature and chemical potential.