Relativistic core-envelope anisotropic fluid model of super dense stars

The objective of the present paper is to explore and study an anisotropic spherically symmetric core-envelope model of a super dense star in which core is outfitted with linear equation of state whereas the envelope is considered to be of quadratic equation of state. There is smooth matching between the three regions: the core, envelope and the Schwarzschild exterior metric. We investigate that all the physical and geometrical variables are realistic within the core as well as the envelope of the stellar object and continuous at the junction. Our model is shown to be physically plausible and validate with the intrinsic properties of the neutron star in Vela X-1, SMC X-4 and Her X-1. Further, We infer that with the increase of mass of star the core shrinks, which vindicates the dominating effect of gravity for higher mass astronomical objects.