RELATIVISTIC EFFECTS IN POLYTROPIC COMPACT STARS

We solve numerically the two first order differential equations obtained by Tooper for polytropic compact stars. These equations depend on the polytropic index n related to the adiabatic index Γ = 1 + 1/n and on a parameter σ that manifests the relativistic content of the polytropic equation of state (EOS). In this work we investigate the effect of increasing σ for two polytropic EOS: the case of a nonrelativistic Fermi gas (n = 1.5) and the relativistic one (n = 3.0). We show that for large values of σ, where the sound velocity is not small in comparison to the velocity of light, the matter density is more concentrated in the center of the star and as a consequence the star mass also is: this effect is quite strong in the case of the relativistic fermi gas.