Properties of static limit and rotating equilibrium sequences of compact stars: Systematic correlations and constraints

We study the properties of nonrotating and rapidly rotating configurations of compact stars (CS) by employing a representative set of equations of state (EOSs). The chosen EOSs depend upon different dense matter models of compact stars. The empirical relationships of rotating equilibrium configurations and fixed frequency configurations with the some key properties of nonrotating sequences of compact stars are investigated. We find that the maximum gravitational mass of static limit CS ranges from 1.6Mo to 2.5Mo and their canonical radius R1.4 varies from 10 to 15 km, which is reasonably well within the available observational bounds for CS mass and radius R1.4. We show suitable parametric relationship between the combination of observable properties of static limit sequences with the observable properties uniformally rotating equilibrium configurations. It is found that the calculated values of Mmaxstat and R1.4 of nonrotating CSs have shown empirical relationship with ΩK. The suitable combination of R1.4 and ΩK is reasonably correlated with the value of δMB. Whereas any combination of ΩK with angular momentum J1122 or moment of inertia I1122 are weakly correlated with δMB.