Semi-empirical relation to understand matter properties at neutron star interiors

Abstract

The occurrence of quark matter at the center of neutron stars is still in debate. This study defines some semi-empirical parameters that try to quantify the presence and the amount of quark matter at star interiors. We find that one needs unusually accurate measurement to qualitatively deduce the occurrence of quark core at the center of stars by studying the compactness of a fast rotating star as a function of angular momentum. Nevertheless one can deduce the quark content of a static 1.4 solar mass star and extend it for a rotating star. The quark fractions in a star depend on the stiffness of the equation of state and the critical density for phase transition. As the phase transition from the neutron star to a hybrid star happens, the star shrinks, releasing significant energy. A massive neutron star usually collapses into a black hole if the phase transition happens at constant baryonic mass. Given a hadronic EoS, we have shown how one can have a critical mass of the neutron star and the corresponding maximum mass of the hybrid star for a given equation of state.