Anisotropic stars with a modified polytropic equation of state

Abstract In this article, we have presented the anisotropic stars by taking a modified polytropic equation of state ( p r = k ρ 1+1/ n − α , where k and α are constants) in the framework of the Korkina-Orlyanskii spacetime. In this study, we have discussed four different models as: (A) n = 1 (Bose–Einstein Condensate (BEC) neutron liquid), (B) n = 2, (C) n = 3/2 (Non-relativistic neutron gas, (D) n = 3 (Ultra relativistic Fermi-gas). Moreover, we have tested several physical properties for each model. To compare the stiffness of these four models, we have plotted the M − R curves, M − I curves and compression modulus. As per the M − R curves, the equation of state can hold maximum mass when the polytropic index in 2 and minimum mass when n = 1 (BEC neutron liquid). Further, the ultra relativistic Fermi gas ( n = 3) can also hold more M max than its non-relativistic counter part ( n = 3/2). These results are further supported by the compression modulus. Lastly, to show its physical validity we have fitted six well known compact stars in M − R curve within their observational error bars.