Careless Whispers: A population of sub-threshold post-merger gravitational waves constrains the hot nuclear equation of state

TL;DR

The paper develops a Bayesian population method to extract information about the hot nuclear equation of state from sub-threshold post-merger gravitational waves of binary neutron star mergers. By estimating the post-merger remnant fraction $\xi$ and linking it with the inspiral-derived remnant-mass distribution, the authors constrain the maximum hot neutron-star mass $M_{\rm max}$ and, via $M_{\rm max}=\chi M_{\rm TOV}$, the Tolman-Oppenheimer-Volkoff mass $M_{\rm TOV}$. Through simulated 3G detector data and NRPMw_pmonly post-merger waveforms, they show that ~25–35 events can yield 11–20% fractional uncertainty on $M_{\rm max}$ (and 12–21% on $M_{\rm TOV}$), improving with larger populations to ~11–21% on $M_{\rm max}$. The approach complements cold-EoS constraints and provides a pathway to probe the thermal aspects of dense matter with next-generation gravitational-wave observatories.

Abstract

We show how to coherently combine information from a population of sub-threshold, gravitational-wave binary neutron star post-merger remnants. Although no individual event in our synthetic population can be claimed as a confident detection, we show how to statistically determine the fraction of merger events that promptly collapse to form a black hole, compared to those for which a neutron star survives the merger for at least tens of milliseconds. This fraction, when combined with information about the neutron star mass distribution gleaned from the inspiral portion of the signals, provides an indirect measure of the neutron star maximum mass. Using conservative measures of the post-merger waveforms, we show that 50-70 events with binary neutron star inspiral measurements can be combined to give an $11-20\%$ fractional uncertainty on the maximum mass of rapidly rotating, hot neutron stars, which can potentially be turned into a $12-21\%$ fractional constraint on the Tolman-Oppenheimer-Volkoff mass. We discuss how this measure of the hot nuclear equation of state can be combined with information of cold neutron stars to see the effect of temperature on physics in the densest regions of the Universe.

Figures (10)

• Figure 1: Prior probability distributions used in this work. We assume a bimodal remnant mass distribution calculated from the expected distribution of merging binary neutron star pairs with masses drawn independently from the observed neutron star population (top panel; green histogram). We choose uniform priors on $M_\mathrm{TOV}$ (top panel; purple filled histogram) and $M_\mathrm{Max} = 1.5M_\mathrm{TOV}$ (top panel; purple hollow histogram). The bottom panel shows the resultant $\xi$ prior for a given fixed value of $M_\mathrm{Max}$,calculated using Eq. \ref{['eq:XiPrior']}. There is a lower and upper bound on the prior distribution of $\xi$ as some of the neutron star remnant masses always lie above or below the limits our prior on $M_\mathrm{Max}$.
• Figure 2: Masses of simulated binary neutron star signals used in this work. Dashed lines show different values of $M_\mathrm{Max}$ used to evaluate the robustness of the technique. The dotted line shows $m_1 = m_2$. The colourbar indicates the network SNR of the injected signals. For each $M_\mathrm{Max} = [3.1, 3.25, 3.5]\,\mathrm{M_\odot}$, the fraction of data segments that contain injected signals is $\xi = [0.56, 0.70, 0.84]$.
• Figure 3: Distribution of luminosity distances and network postmerger SNRs for our injected signal population. Luminosity distances are drawn such that they are uniform in co-moving volume. The size of each point indicates the relative total mass of each binary neutron star system. More massive systems, and face-on systems ($\cos\iota\simeq\pm1$, represented by higher color saturations) produce signals with larger amplitudes, allowing them to attain considerable SNR out to larger luminosity distances.
• Figure 4: Distribution of $90\%$ credible-interval sky-localization uncertainties $d\Omega_{90}$ computed for the inspiral portion of our signals. The majority of signals are localized to under $5\deg^2$, justifying our use of delta-function priors for our post-merger analyses.
• Figure 5: Posterior probability distributions on $M_\mathrm{tot}$, mass ratio $q = m_1/m_2$ and tidal deformabilities $\Lambda_1, \Lambda_2$ for a post-merger signal with $\mathrm{SNR=3.7}$. In this case, $M_\mathrm{tot}$ can be recovered well, however the posterior distributions of other parameters do not have strong predictive power.