Needle in a Bayes Stack: a Hierarchical Bayesian Method for Constraining the Neutron Star Equation of State with an Ensemble of Binary Neutron Star Post-merger Remnants

Binary neutron star (BNS) post-merger gravitational-wave emission can occur in the aftermath of a BNS merger -- provided the system avoids prompt collapse to a black hole -- as a quasistable hypermassive remnant experiences quadrupolar oscillations and non-axisymmetric deformations. The post-merger gravitational-wave spectrum possesses a characteristic peak frequency that has been shown to be dependent on the binary chirp mass and the neutron star equation of state (EoS), rendering post-merger gravitational waves a powerful tool for constraining neutron star composition. Unfortunately, the BNS post-merger signal is emitted at high ($\gtrsim 1.5$ kHz) frequencies, where ground-based gravitational wave detectors suffer from reduced sensitivity. It is therefore unlikely that post-merger signals will be detected with sufficient signal-to-noise ratio (SNR) until the advent of next-generation detectors. However, by employing empirical relations derived from numerical relativity simulations, we can combine information across an ensemble of BNS mergers, allowing us to obtain EoS constraints with many low-SNR signals. We present a hierarchical Bayesian method for deriving constraints on $R_{1.6}$, the radius of a 1.6$\mathrm{M_{\odot}}$ neutron star, through an ensemble analysis of binary neutron star mergers. We apply this method to simulations of the next two LIGO-Virgo-KAGRA observing runs, O4 and O5, as well as an extended 4-year run at A+ sensitivity, demonstrating the potential of our approach to yield EoS information from the post-merger signal with current-generation detectors. The A+ 4-year scenario is predicted to improve the constraint on $R_{1.6}$ from the currently available multimessenger-based 95\% credible interval (C.I.) uncertainty of $R_{1.6}=12.07^{+0.98}_{-0.77}$ km to $R_{1.6}=11.91^{+0.80}_{-0.56}$ km, a 22% reduction of the 95% C.I. width.