Sub-threshold post-merger gravitational waves can constrain the hot nuclear equation of state

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 by providing indirect evidence for first-order phase transitions in neutron star interiors.