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_ < mₘax < 2.2M_ (68%), 2.0M_ < mₘax< 2.6M_ (90%), and evidence for a cut-off is robust against the choice of model for the mass distribution and to removing the most extreme (highest mass) neutron stars from the dataset. If this sharp cut-off is interpreted as the maximum stable neutron star mass allowed by the equation of state of dense matter, our measurement puts constraints on the equation of state. For a set of realistic equations of state that support >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.