Self-consistent treatment of thermal effects in neutron-star postmerger remnants: Observational implications for third-generation gravitational-wave detectors

We assess the impact of accurate, self-consistent modeling of thermal effects in neutron-star merger remnants in the context of third-generation gravitational-wave detectors. This is done through the usage, in Bayesian model selection experiments, of numerical-relativity simulations of binary neutron star (BNS) mergers modeled through (i) nuclear, finite-temperature (or ``tabulated'') equations of state (EOSs), and (ii) their simplifed piecewise (or ``hybrid'') representation using seven or ten polytropic pieces. These cover four different EOSs, namely SLy4, DD2, HShen and LS220. Our analyses make direct use of the Newman-Penrose scalar ${\ensuremath{\psi}}_{4}$ outputted by numerical simulations. Considering a detector network formed by three Cosmic Explorers, we show that differences in the gravitational-wave emission predicted by the two models are detectable with a natural logarithmic Bayes factor $\mathrm{log}\mathcal{B}\ensuremath{\ge}5$ at average distances of ${d}_{L}\ensuremath{\simeq}50\text{ }\text{ }\mathrm{Mpc}$, reaching ${d}_{L}\ensuremath{\simeq}100\text{ }\text{ }\mathrm{Mpc}$ for source inclinations $\ensuremath{\iota}\ensuremath{\le}0.8$, regardless of the EOS. This impact is most pronounced for the HShen EOS. For low inclinations, only the DD2 EOS prevents the detectability of such modeling differences at ${d}_{L}\ensuremath{\simeq}150\text{ }\text{ }\mathrm{Mpc}$. Our results suggest that the usage a self-consistent treatment of thermal effects is crucial for third-generation gravitational-wave detectors.