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 multimodality 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 2.0 M_⊙ < m_max < 2.2 M_⊙ (68 per cent), 2.0 M_⊙ < m_max < 2.6 M_⊙ (90 per cent), 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 data set. 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 >2 M_⊙ neutron stars, our inference of m_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× the nuclear saturation density by ∼ 30-50 per cent compared to simply requiring m_max > 2 M_⊙. We obtain a lower bound on the maximum sound speed attained inside the neutron star of c_ s^max > 0.63c (99.8 per cent), ruling out c_ s^max < 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.