Correlations in the properties of static and rapidly rotating compact stars

Correlations in the properties of the static compact stars (CSs) and the ones rotating with the highest observed frequency of 1122Hz are studied using a large set of equations of state (EOSs). These EOSs span various approaches and their chemical composition vary from the nucleons to hyperons and quarks in $\beta$-equilibrium. It is found that the properties of static CS, like, the maximum gravitational mass $M_{\rm max}^{\rm stat}$ and radius $R_{1.4}^{\rm stat}$ corresponding to t he canonical mass and supramassive or non-supramassive nature of the CS rotating at 1122 Hz are strongly correlated. In particular, only those EOSs yield the CS rotating at 1122Hz to be non-supramassive for which $\left (\frac{M_{\rm max}^{\rm stat}}{M_\odot}\right )^{1/2} \left (\frac{10{\rm km}}{R_{1.4}^{\rm stat}})^{3/2} $ is greater than unity. Suitable parametric form which can be used to split the $M_{\rm max}^{\rm stat}$ $-$ $R_{1.4}^{\rm stat}$ plane into the regions of different supramassive nature of the CS rotating at 1122Hz is presented. Currently measured maximum gravitational mass 1.76$M_\odot$ of PSR J0437-4715 suggests that the CS rotating at 1122Hz can be non-supramassive provided $R_{1.4}^{\rm stat} \leqslant 12.4$ km.