Universal relations for neutron stars: Selected recent works

Abstract

It is well known that the properties of a compact star in general depend on the equation-of-state (EOS) of the star. However, various approximately EOS-insensitive universal relations connecting different quantities of compact stars are known to exist. In this contribution, we discuss two selected recent works in the area of research of universal relations. We first discuss how taking the effect of elasticity into account in the calculation of the tidal deformability of compact stars with crystalline quark matter can break the universal I-Love relation originally discovered for non-rotating fluid compact stars. We then review two new universal relations discovered for the spacetime of a rapidly rotating neutron star that connect the orbital radius and frequency of the innermost stable circular orbit (ISCO) to the spin frequency and mass of the star. We also demonstrate how the ISCO universal relations can be applied to accreting neutron stars in low-mass X-ray binaries. In particular, the ISCO universal relations predict that the mass of the neutron star in the system 4U 0614+09 is 2.0M⊙, assuming that the observed highest kilohertz quasi-periodic oscillations in the system is due to the orbital motion at the ISCO, and also the spin frequency of the star as inferred from the X-ray burst oscillations detected by Swift can be confirmed in the future.