Gaussian Anisotropy In Strange Quark Stars

Abstract: In this paper for studying the anisotropic strange quark stars, we assume that the radial pressure inside the anisotropic star is a superposition of pressure in an isotropic case plus a Gaussian perturbation term. Considering a proportionality between electric charge density and the density of matter, we solve the TOV equation for different cases numerically. Our results indicate that anisotropy increases the maximum mass $M_{max}$ and also its corresponding radius $R$ for a typical strange quark star. According to our calculations, an anisotropy amplitude of $A=3\times10^{33}Nm^{-2}$ with a standard deviation of $\sigma=3\times10^{3}m$ leads to a neutron star of 1.97$M_{\odot}$. Furthermore, electric charge not only increases the maximum mass and its corresponding radius, but also raises up the anisotropy factor. We can see that the tangential pressure $p_{t}$ and anisotropy factor $\Delta$ unlike the radial pressure $p_{r}$ have a maximum on the surface and this maximum increases by adding electric charge effect. However, we show that anisotropy can be more effective than electric charge in rasing maximum mass of strange quark stars.