Systematics of prompt black-hole formation in neutron star mergers

Abstract

This study addresses the collapse behavior of neutron star (NS) mergers expressed through the binary threshold mass ${M}_{\text{thres}}$ for prompt black-hole (BH) formation, which we determine by relativistic hydrodynamical simulations for a set of 40 equation of state (EOS) models of NS matter. ${M}_{\text{thres}}$ can be well described by various fit formulas involving stellar parameters of nonrotating NSs, which are employed to characterize the EOS models. Using these relations we compute which constraints on NS radii and the tidal deformability are set by current and future merger detections that reveal information about the merger product. We systematically investigate the impact of the binary mass ratio $q={M}_{1}/{M}_{2}$ and assemble various fits, which make different assumptions about a-priori knowledge. This includes fit formulas for ${M}_{\text{thres}}$ for a fixed mass ratio or a range of $q$ if this parameter is not known very well. Also, we construct relations describing the threshold to prompt collapse for different classes of candidate EOSs, which for instance do or do not include models with a phase transition to quark matter. In particular, we find fit formulas for ${M}_{\text{thres}}$ including an explicit $q$ dependence, which are valid in a broad range of $0.7\ensuremath{\le}q\ensuremath{\le}1$ and which are nearly as tight as relations for fixed mass ratios. For most EOS models except for some extreme cases the threshold mass of asymmetric mergers is equal or smaller than the one of equal-mass binaries. Generally, the impact of the binary mass asymmetry on ${M}_{\text{thres}}$ becomes stronger with more extreme mass ratios, while ${M}_{\text{thres}}$ is approximately constant for small deviations from $q=1$, i.e., for $0.85\ensuremath{\le}q\ensuremath{\le}1$. The magnitude of the reduction of ${M}_{\text{thres}}$ with the binary mass asymmetry follows a systematic EOS dependence. We also describe in more detail that a phase transition to deconfined quark matter can leave a characteristic imprint on the collapse behavior of NS mergers. The occurrence of quark matter can reduce the stability of the remnant and thus the threshold mass relative to a purely hadronic reference model. Comparing specifically the threshold mass and the combined tidal deformability ${\stackrel{\texttildelow{}}{\mathrm{\ensuremath{\Lambda}}}}_{\text{thres}}$ of a system with ${M}_{\text{thres}}$ can yield peculiar combinations of those two quantities, where ${M}_{\text{thres}}$ is particularly small in relation to ${\stackrel{\texttildelow{}}{\mathrm{\ensuremath{\Lambda}}}}_{\text{thres}}$. Since no purely hadronic EOS can yield such a combination of ${M}_{\text{thres}}$ and ${\stackrel{\texttildelow{}}{\mathrm{\ensuremath{\Lambda}}}}_{\text{thres}}$, a combined measurement or a constraint on both quantities can indicate the onset of quark deconfinement. Finally, we point out new univariate relations between ${M}_{\text{thres}}$ and stellar properties of high-mass NSs, which can be employed for direct EOS constraints or consistency checks in combination with other measurements.