Thermodynamics of Hot Neutron Stars and Universal Relations

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⊙ 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.

Universal relations and finite temperature neutron stars

“…As one can observe, the inclusion of temperature does not signifficanly affect the maximum mass of a neutron star. In contrast, the radius appears to be very sensitive to thermal effects [1,24]. In the case of isentropic EOSs, we can theoretically prove (using the generalized condition for thermal equilibrium in general relativity [24][25]) that the rescaled entropy is tighly connected to the binding energy of a neutron star.…”

“…In contrast, the radius appears to be very sensitive to thermal effects [1,24]. In the case of isentropic EOSs, we can theoretically prove (using the generalized condition for thermal equilibrium in general relativity [24][25]) that the rescaled entropy is tighly connected to the binding energy of a neutron star. Specifically, for constant entropy per nucleon, we can show that 𝑅𝐸 = (1 + 𝐸 𝑏 𝑀𝑐 2 ) 𝑒 𝛷(𝑅) , (6) where 𝑒 𝛷(𝑅) = √1 − 2𝐶 is the star's redshift [24].…”

“…In the case of isentropic EOSs, we can theoretically prove (using the generalized condition for thermal equilibrium in general relativity [24][25]) that the rescaled entropy is tighly connected to the binding energy of a neutron star. Specifically, for constant entropy per nucleon, we can show that 𝑅𝐸 = (1 + 𝐸 𝑏 𝑀𝑐 2 ) 𝑒 𝛷(𝑅) , (6) where 𝑒 𝛷(𝑅) = √1 − 2𝐶 is the star's redshift [24]. Therefore, we expect that the evaluation of the right hand side of Equation ( 6), for cold and hot isentropic EOSs, will produce the same results as in Figure 2(a).…”

Relativistic Brueckner–Hartree–Fock Calculations for Cold and Hot Neutron Stars

“…The vast majority of EOS models for neutron star matter, especially those calculated using a relativistic framework like the RBHF approximation, are done at zero temperature. However, finite-temperature EOS models are vital to understanding various astrophysical phenomena like core-collapse supernovae, binary neutron star mergers, and proto-neutron stars, as shown in the works of Moustakidis & Panos (2009), Oertel et al (2017), Carbone & Schwenk (2019), Chesler et al (2019), Schneider et al (2019, Koliogiannis & Moustakidis (2021), Wei et al (2021), andLaskos-Patkos et al (2022). In this work, we extend the RBHF approximation in full Dirac space to finite temperatures.…”

Tolman-Ehrenfest's criterion of thermal equilibrium extended to conformally static spacetimes

“…The criterion has inspired also a connection between gravitational fields and thermal transport in materials: thermal transport, understood as the linear response of a material to a temperature gradient, was mimicked by Luttinger as a counter-balancing weak gravitational field restoring thermal equilibrium in the presence of this gradient [9]. The Tolman-Ehrenfest criterion (1.2) is applied to neutron stars [10][11][12]; equilibrium with respect to simultaneous heat conduction and particle diffusion has been discussed in [13,15], together with the corresponding criterion in Weyl-integrable geometries [14].…”