Finite-temperature Extension for Cold Neutron Star Equations of State

Abstract

Observations of isolated neutron stars place constraints on the equation of state (EOS) of cold, neutron-rich matter, while nuclear physics experiments probe the EOS of hot, symmetric matter. Many dynamical phenomena, such as core-collapse supernovae, the formation and cooling of protoneutron stars, and neutron star mergers, lie between these two regimes and depend on the EOS at finite temperatures for matter with varying proton fractions. In this paper, we introduce a new framework to accurately calculate the thermal pressure of neutron-proton-electron matter at arbitrary density, temperature, and proton fraction. This framework can be expressed using a set of five physicallymotivated parameters that span a narrow range of values for realistic EOS and are able to capture the leading-order effects of degenerate matter on the thermal pressure. We base two of these parameters on a new approximation of the Dirac effective mass, with which we reproduce the thermal pressure to within 30% for a variety of realistic EOS at densities of interest. Three additional parameters, based on the behavior of the symmetry energy near the nuclear saturation density, allow for the extrapolation of any cold EOS in β-equilibrium to arbitrary proton fractions. Our model thus allows a user to extend any cold nucleonic EOS, including piecewise-polytropes, to arbitrary temperature and proton fraction, for use in calculations and numerical simulations of astrophysical phenomena. We find that our formalism is able to reproduce realistic finite-temperature EOS with errors of 20% and offers a 1 − 3 orders-of-magnitude improvement over existing ideal-fluid models.

Coalescence of black hole–neutron star binaries

“…where T and Y e are the temperature and the electron fraction, respectively (see, e.g., Lattimer and Swesty 1991;Shen et al 1998;Hempel et al 2012;Steiner et al 2013;Banik et al 2014, see also Raithel et al 2019 for a detailed analytic approach to augment zero-temperature equations of state in a similar manner to Eq. ( 36)).…”

Numerical relativity simulations of prompt collapse mergers: threshold mass and phenomenological constraints on neutron star properties after GW170817

“…Finally we include thermal effects in the zero temperature EOS models (BA, H3, H4, ALF2, and piecewise polytropic EOSs from subset (b), GRW1 and GRW2) by adding a thermal contribution with adiabatic index Γ th = 1.7 following, e.g., Refs. [10,[51][52][53], see [54,55] for an alternative approach.…”

Finite-temperature infinite matter with effective-field-theory-inspired energy-density functionals

“…For this reason, different approaches have been recently employed to extend to finite temperatures the EOS of cold and homogeneous nuclear matter [41,42].…”