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 occurs in the aftermath of a BNS merger as an unstable 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 unlikely to be detected with sufficient signal-to-noise ratio (SNR) for this purpose 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 in the low-SNR limit. We present a hierarchical Bayesian method for deriving constraints on the neutron star EoS through an ensemble analysis of binary neutron star mergers and discuss the prospects of our analysis as applied to realistic simulations of BNS observations with current-generation gravitational wave detectors.