Thermodynamics of Hot Neutron Stars and Universal Relations

TL;DR

This paper explores how hot neutron star equations of state relate to universal properties like tidal deformability and binding energy, revealing limitations of universal relations at high temperatures and establishing new bounds based on gravitational wave data.

Contribution

It assesses the validity of universal relations for hot neutron stars and introduces a new relation connecting compactness, binding energy, and tidal deformability applicable to both cold and hot states.

Findings

Hot equations of state often violate universal relations.

Binding energy and tidal deformability show a universal trend for moderate masses.

New relation between compactness, binding energy, and tidal deformability is proposed.

Abstract

Over the last few years, the detection of gravitational waves from binary neutron star systems has rekindled our hopes for a deeper understanding of the unknown nature of ultradense matter. In particular, gravitational wave constraints on the tidal deformability of a neutron star can be translated into constraints on several neutron star properties using a set of universal relations. Apart from binary neutron star mergers, supernova explosions are also important candidates for the detection of multimessenger signals. Such observations may allow us to impose significant constraints on the binding energy of neutron stars. The purpose of the present study is twofold. Firstly, we investigate the agreement of finite temperature equations of state with established universal relations. Secondly, we examine the possible existence of a universal relation between the binding energy and the dimensionless tidal deformability, which are the bulk properties connected to the most promising sources for multimessenger signals. We find that hot equations of state are not always compatible with accepted universal relations. Therefore, the use of such expressions for probing general relativity or imposing constraints on the structure of neutron stars would be inconclusive (when thermal effects are present). Additionally, we show that the binding energy and the dimensionless tidal deformability exhibit a universal trend at least for moderate neutron star masses. The latter allows us to set bounds on the binding energy of a 1.4 $M_\odot$ neutron star using data from the GW170817 event. Finally, we provide a relation between the compactness, the binding energy and the dimensionless tidal deformability of a neutron star that is accurate for cold and hot isentropic equations of state.