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

Abstract

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 $2.0M_\odot < m_\mathrm{max} < 2.2M_\odot$ (68\%), $2.0M_\odot < m_\mathrm{max}< 2.6M_\odot$ (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 $>2M_\odot$ neutron stars, our inference of $m_\mathrm{max}$ 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 $3-7\times$ the nuclear saturation density by $\sim 30-50\%$ compared to simply requiring $m_\mathrm{max}> 2M_\odot$. We obtain a lower bound on the maximum sound speed attained inside the neutron star of $c_s^\mathrm{max} > 0.63c$ (99.8\%), ruling out $c_s^\mathrm{max} < c/\sqrt{3}$ 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.