A polytropic approach to semi-relativistic isothermal gas spheres at arbitrary temperature

We use the standard polynomial expansion technique to show the existence of a relation between the polytropic model and the description of gas spheres at finite temperature. A numerical analysis is performed 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. The behaviour of sample configurations is illustrated, considering neutrons as fermions and Z(0) bosons. Boson and fermion stars presented similar graphics for the parameters used in this model, but with very different temperature regimes.