On the treatment of thermal effects in the equation of state on neutron star merger remnants

TL;DR

This paper assesses how different treatments of finite-temperature effects in the EOS (fully tabulated vs hybrid) influence long-term binary neutron star merger remnants, focusing on HMNS dynamics, convective stability, and post-merger gravitational-wave spectra up to $150\,\mathrm{ms}$. Using four finite-temperature tabulated EOS and corresponding hybrid representations, the authors perform NR simulations to compare density evolution, GW mode content ($f_{\max}$, $f_{2,i}$, $f_2$), and the excitation of inertial modes, aided by Ledoux and Solberg-Høiland criteria. They find that tabulated EOS generally yield more accurate thermal descriptions, delaying collapse in some soft EOS cases and shifting mode frequencies, while inertial modes persist in both representations but with EOS-dependent differences in growth and sustainment. The results underscore the necessity of precise thermal modeling for interpreting post-merger GW signals and for neutron-star asteroseismology, especially for third-generation detectors, and point to future work incorporating magnetic fields and neutrino cooling.

Abstract

We present results from long-term, numerical-relativity simulations of binary neutron star mergers modeled using both, fully tabulated, finite-temperature, equations of state and their corresponding hybrid representations. The simulations extend up to 150 ms which allows us to assess the role of the treatment of finite-temperature effects on the dynamics of the hypermassive neutron star remnant. Our study focuses on the analysis of the spectra of the post-merger gravitational-wave signals and on how these are affected by the treatment of thermal effects in the two EOS representations. Our simulations highlight distinct differences in the GW frequency evolution related to the thermal modeling of the EOS, demonstrating that deviations from established quasi-universal relations become significant at late post-merger phases. Furthermore, we investigate the stability of the HMNS against convection. Employing both the Ledoux criterion, necessary condition for the development of convective instabilities, and the Solberg-Høiland criterion, a generalized criterion for axisymmetric perturbations based on a combined analysis of the Brunt-Väisälä frequency and of the epicyclic frequency, we show that differential rotation and thermal stratification in the HMNS give rise to local (yet sustained) convective patterns that persist beyond 100 ms after merger. Those convective patterns, while substantially different between tabulated and hybrid EOS treatments, trigger the the excitation of inertial modes with frequencies smaller than those attained by the fundamental quadrupolar mode, and are potentially within reach of third-generation GW detectors. The late-time excitation of inertial modes, previously reported in studies based on hybrid EOS, is fully supported by the tabulated, finite-temperature EOS simulations presented here, which account for thermal effects in a more consistent way.

Figures (26)

• Figure 1: Gravitational mass vs circumferential radius for several EOSs along with some current observational constraints: the mass measurements of two high-mass pulsars and the observational constraints (within $95\%$ confidence levels) from NICER/XMM-Newton and LIGO-Virgo, along with the constraints from nuclear physics experiments, modeled through a Typel-Wolter density-dependent relativistic mean-field functional (within $99\%$ confidence levels) from prasanta (cyan region). The black curves represent the thermal, tabulated EOSs employed in this work, while the gray curves correspond to cold EOSs doi:10.1146compose. The red points indicate the specific models used in our study.
• Figure 2: From left to right the panels depict the pressure $P$ in log scale, adiabatic index $\Gamma$ and relativistic sound speed $c_\mathrm{s,r}^2$ against the barion density (in cgs units), for the LS220 EOS at the lowest available temperature of $T=0.01$ MeV in $\beta$-equilibrium. Black dots indicate tabulated points while red lines show the piecewise polytropic representation of the EOS. Vertical dashed lines mark the six breakpoints obtained from the regression code Pilgrim2021.
• Figure 3: Gravitational mass versus circumferential radius for spherically symmetric NSs built with all EOSs of our sample. Solid lines represent tabulated EOS configurations and dashed lines piecewise polytropic approximations. Red dots mark NS configurations with a baryon mass of $1.4\,M_\odot$.
• Figure 4: Dependence on the number of pieces of the gravitational mass versus circumferential radius curves for spherically symmetric NSs for all EOSs. In each panel, solid colored lines indicate the number of pieces of the piecewise polytropic representation while the solid black line represents the tabulated version of the corresponding EOS. The red dots indicate configurations with baryon mass $M_0=1.4 M_\odot$.
• Figure 5: Merger and early post-merger evolution of the maximum density (normalized by its initial value) for all four EOSs. Black solid lines indicate tabulated EOSs, red solid lines the $7-$pieces hybrid EOS, and green solid lines the $10-$pieces hybrid EOSs. Time is given with respect to the time of merger.