Thermodynamics of Hot Neutron Stars and Universal Relations

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 ultra dense 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 not only independent on the employed equation of state but also holds when thermal effects are present.