Stability of hypermassive neutron stars with post-merger-like rotation and entropy profiles

Binary neutron star mergers produce massive, hot, rapidly differentially rotating neutron star remnants; electromagnetic and gravitational wave signals associated with the subsequent evolution depend on the stability of these remnants. The stability of relativistic stars has previously been studied for uniform rotation and a class of differential rotation with monotonic angular velocity profiles. The stability of those equilibria to axisymmetric perturbations was found to respect a turning point criterion: along a constant angular momentum sequence, the onset of unstable stars is found at a maximum density less than but close to the density of maximum mass. We test this turning point criterion for non-monotonic angular velocity profiles and non-isentropic entropy profiles, both chosen to more realistically model post-merger equilibria. Stability is assessed by evolving perturbed equilibria in 2D using the Spectral Einstein Code. We present tests of the code's new capability for axisymmetric metric evolution. We confirm the turning point theorem and determine the region of our rotation law parameter space that provides the highest maximum mass for a given angular momentum.