Evidence for a maximum mass cut-off in the neutron star mass distribution and constraints on the equation of state

We infer the mass distribution of neutron stars in binary systems using a flexible Gaussian mixture model and use Bayesian model selection to explore evidence for multi-modality and a sharp cut-off in the mass distribution. We find overwhelming evidence for a bimodal distribution, in agreement with previous literature, and report for the first time positive evidence for a sharp cut-off at a maximum neutron star mass. We measure the maximum mass to be 2. 0M_ 2M_ neutron stars, our inference of mₘax is able to distinguish between models at odds ratios of up to 12: 1, whilst under a flexible piecewise polytropic equation of state model our maximum mass measurement improves constraints on the pressure at 3-7 the nuclear saturation density by 30-50\% compared to simply requiring mₘax> 2M_. We obtain a lower bound on the maximum sound speed attained inside the neutron star of cₛᵐax > 0. 63c (99. 8\%), ruling out cₛᵐax < c/3 at high significance. Our constraints on the maximum neutron star mass strengthen the case for neutron star-neutron star mergers as the primary source of short gamma-ray bursts.