Exploring the universal relations with the correlation analysis of neutron star properties

Abstract

Motivated by finding a way to construct the universal relations between the neutron star properties and obtaining the application scope of the universal relations, the linear correlation properties between several properties of neutron stars are analyzed. Based on this, several existing universal relations are tested and several new universal relations are predicted. The results show that in the whole typical central density range of neutron stars, the better the linear correlation properties between the combinations of physical quantities are, the better the universality of the universal relations will be. It is shown that the quantities possessing desired linear correlation properties are the compactness $\ensuremath{\beta}$, moment of inertia $I$, gravitational redshift $z$ and gravitational binding energy ${E}_{g}$, etc. Based on the linear correlation analysis of the above acquired quantities, several existing universal relations about the dimensionless gravitational binding energy and several new universal relations about the dimensionless moment of inertia are tested and predicted respectively. Moreover, the moment of inertia of PSR $\mathrm{J}0030+0451$ can be constrained by the newly discovered universal relation. In conclusion, the linear correlation analysis of the neutron star properties is an effective and feasible method to explore the universal relations.