Binding energy of compact stars and their non-radial oscillations

TL;DR

This paper explores a potential universal relation between the binding energy of compact stars and their non-radial oscillation frequencies, which could be useful for astrophysical measurements and tests of gravity.

Contribution

It identifies an empirical relation between oscillation frequencies and binding energy for hadronic stars, highlighting deviations with hybrid equations of state.

Findings

Empirical relation found for hadronic stars between oscillation frequency and binding energy.

Deviations observed when hybrid equations of state with phase transitions are included.

Potential for using oscillation data to infer stellar binding energy.

Abstract

In the past years, a significant effort has been made with the scope of determining correlations, involving compact star properties, that are independent of the nuclear equation of state. Such universal relations are of utmost importance as they allow for the imposition of constraints on stellar properties without directly measuring them and they may also serve as a probe of General Relativity. In the present study, we investigated the possible existence of a universal relation between the binding energy of compact stars and the frequency of their non-radial oscillations. The main motivation was related to the fact that both of the aforementioned quantities might be measured in the occurrence of a supernova explosion. Interestingly, we found that there is a empirical relation between the oscillation frequency and the binding energy for both $f$ and $p_1$ modes, assuming hadronic stellar matter. The inclusion of hybrid equations of state, incorporating sharp phase transitions, was shown to result into deviations from the aforementioned quasi-universal relation.