I-Love-$\langle c_s^2 \rangle$: Approximately universal relations for the average neutron star stiffness

Abstract

The accurate observations of neutron stars have deepened our knowledge of both general relativity and the properties of nuclear physics at large densities. Relating observations to the microphysics that govern these stars can sometimes be aided by approximate universal relations. One such relation connects the ratio of the central pressure to the central energy density and the compactness of the star, and it has been found to be insensitive to realistic models for the equation of state to a $\sim 10\%$ level. In this paper, we clarify the meaning of the microscopic quantity appearing in this relation, which is reinterpreted as the average of the speed of sound squared in the interior of a star, $\langle c_s^2 \rangle\!$. The physical origin of the quasi-universality of the $\langle c_s^2 \rangle - C$ relation is then investigated. Making use of post-Minkowskian expansions, we find it to be linked to the Newtonian limit of the structure equations, as well as to the fact that the equations of state that describe NSs are relatively stiff. The same post-Minkowskian approach is also applied to the relations between $\langle c_s^2 \rangle\!$, the moment of inertia, and the tidal deformability of a neutron star, arriving at similar conclusions.