Density dependent B parameter of relativistic stars with anisotropy in pseudo-spheroidal space-time

Abstract

We present a class of relativistic solutions for compact cold stars with strange matter in a pseudo-spheroidal space-time. Considering strange matter equation of state namely, $p = \frac{1}{3}(\rho -4B)$ , where $\rho $ , $p$ and $B$ are energy density, pressure and MIT Bag parameter respectively, stellar models are obtained. In the presence of anisotropy with a pseudo-spheroidal geometry described by Vaidya-Tikekar, metric stellar models are explored where the Bag parameter varies with the energy density ( $\rho $ ) inside the compact object. We determine the density dependence of $B$ at different anisotropy. It is noted that although $B$ varies with anisotropy inside the star, finally at the surface it attains a value which is independent of the anisotropy. The Bag parameter $B$ is found to increase with an increase in anisotropy for a given compactness factor $(M/b)$ and spheroidicity $\lambda $ . It is also noted that for a star with given mass and radius, the parameter $B$ increases with the increase in $\lambda $ and finally at large $\lambda $ , it attains a constant. The equation of state (EoS) obtained here from geometrical consideration with allowed ‘B’ value is found same to that one obtains from micro-physics. The stability of the stellar models for compact stars with anisotropy in hydrostatic equilibrium obtained here is also studied.