Effect of Differential Rotation on the Maximum Mass of Neutron Stars: Realistic Nuclear Equations of State

The merger of binary neutron stars is likely to lead to differentially rotating remnants. In this paper, we survey several cold nuclear equations of state (EOSs) and numerically construct models of differentially rotating neutron stars in general relativity. For each EOS we tabulate maximum allowed masses as a function of the degree of differential rotation. We also determine effective polytropic indices, and compare the maximum allowed masses with those for the corresponding polytropes. We consistently find larger mass increases for the polytropes, but even for the nuclear EOSs we typically find maximum masses 50% higher than the corresponding values for nonrotating (TOV) stars. We evaluate our findings for the six observed binary neutron star (pulsar) systems, including the recently discovered binary pulsar J0737-3039. For each EOS we determine whether their merger will automatically lead to prompt collapse to a black hole, or whether the remnant can be supported against collapse by uniform rotation (possibly as a supramassive star) or differential rotation (possibly as a hypermassive star). For hypermassive stars, delayed collapse to a black hole is likely. For the most recent EOSs we survey the merger remnants can all be supported by rotation against prompt collapse, but their actual fate will depend on the nonequilibrium dynamics of the coalescence event. Gravitational wave observations of coalescing binary neutron stars may be able to distinguish these outcomes -- no, delayed or prompt collapse -- and thereby constrain possible EOSs.