Impact of thermal effects on prompt-collapse binary neutron star mergers

TL;DR

The paper investigates how finite-temperature effects in the nuclear EoS influence the threshold for prompt collapse in equal-mass binary neutron star mergers. By applying the $M^*$ finite-temperature framework to two cold EoSs (soft and stiff) and exploring four thermal prescriptions, the authors determine $M_{\rm thresh}$ via bisection in full general relativity and analyze bounce-collapse dynamics near threshold. The key finding is that $M_{\rm thresh}$ is insensitive to realistic thermal variations at sub-percent accuracy, though thermal effects modestly affect core-bounce heating, dynamical ejecta, and remnant disk mass, with a notable exception showing up as a ~60% increase in ejecta for a stiff EoS under one thermal treatment. These results imply that constraints on tidal deformability from prompt-collapse scenarios are robust to thermal uncertainties, while ejecta-based constraints from events like GW170817 could still be influenced by thermal physics, motivating further study of asymmetric mergers and neutrino effects in this context.

Abstract

The fate of the remnant following the merger of two neutron stars initially on quasicircular orbits depends primarily on the mass of the initial neutron stars, the mass ratio, and the still-uncertain dense-matter equation of state (EoS). Previous works studying the threshold mass for prompt collapse to a black hole have primarily focused on the uncertainties in the zero-temperature EoS, which are parametrized by a macroscopic quantity such as the characteristic neutron star radius. However, prompt collapse can take place either with or without a core bounce during the merger. In the bounce-collapse scenario, shocks can produce additional thermal support, potentially altering the threshold for collapse. In this work, we investigate the impact of the uncertainties in the finite-temperature part of the nuclear EoS on the threshold mass for prompt collapse in equal mass mergers. Using two cold EoSs, combined with four parametrizations of the finite-temperature part of the EoS, we find that the threshold mass is insensitive to realistic variations of the thermal prescription, at sub-percent accuracy. We report on the thermal properties and ejecta of mergers with masses just above the threshold mass, i.e., which experience a single core-bounce before collapsing. During the bounce, the thermal pressure can reach )(1-10)% of the cold pressure at supranuclear densities, depending on the thermal treatment, leading to modest differences in the dynamical ejecta that are launched and in the remnant disk mass as a result.

Figures (22)

• Figure 1: Top: Mass-radius curves for the two EoSs considered in this work. The markers indicate the masses included in our series of equal-mass BNS merger simulations. Bottom: Pressure as a function of density, relative to the nuclear saturation density ($\rho_{\rm sat}=2.7 \times 10^{14}$g/cm$^3$), for the same models.
• Figure 2: Minimum lapse for the seven evolutions with the $R_{1.4}\approx10.6$ km cold EoS and the Case I thermal treatment. The colors indicate the binary mass for each evolution (corresponding to the gravitational mass at infinite orbital separation). The vertical dotted lines indicate the time at which the apparent horizon is first found. The largest mass that undergoes a single core bounce ($M_{\rm sub}$=$2.75M_{\odot}$) is emphasized here with the thick orange line.
• Figure 3: Top: Minimum lapse for the bounce-collapse evolutions ($M_{\rm sub}$=2.75$M_{\odot}$), with the $R_{1.4}\approx10.6$ km cold EoS and the four different thermal treatments. The markers indicate the times of the the onset of the bounce, the end of the bounce, and one time on the way to collapse, for reference. The vertical dotted lines indicate the time at which the apparent horizon is first found. Bottom: Compression ratio for the same evolutions, showing the maximum rest-mass density relative to the initial rest-mass density.
• Figure 4: Top: Plus-polarized gravitational wave strain for the $\ell=m=2$ mode from the bounce-collapse ($M_{\rm sub}$) evolutions, with the $R_{1.4}\approx10.6$ km cold EoS. Bottom: Total amplitude of the $\ell=m=2$ mode of the GW strain, $h=h_+ - i h_{\times}$. The strain is plotted relative to the retarded time, and has been scaled to a distance of 40 Mpc. The vertical dashed lines indicate the coordinate time of the onset of the bounce (corresponding to the filled squares in Fig. \ref{['fig:lapse_Mthr_R10']}).
• Figure 5: 2D snapshots at times corresponding to the onset of the bounce, the end of the bounce, and one time on the way to collapse for the $M_{\rm sub}$ evolution, evolved with the $R_{1.4}\approx10.6$ km cold EoS and Thermal Case II. The top row shows the rest-mass density, $\rho_0$, relative to the nuclear saturation density, $\rho_{\rm sat}$. The bottom row shows the thermal pressure, relative to the cold pressure. In both rows, the blue lines indicate contours of constant rest-mass density, corresponding to 2, 3, 4, and 5$\times \rho_{\rm sat}$.