  The merger of two neutron stars leaves behind a rapidly spinning hypermassive
object whose survival is believed to depend on the maximum mass supported by
the nuclear equation of state, angular momentum redistribution by
(magneto-)rotational instabilities, and spindown by gravitational waves. The
high temperatures (~5-40 MeV) prevailing in the merger remnant may provide
thermal pressure support that could increase its maximum mass and, thus, its
life on a neutrino-cooling timescale. We investigate the role of thermal
pressure support in hypermassive merger remnants by computing sequences of
spherically-symmetric and axisymmetric uniformly and differentially rotating
equilibrium solutions to the general-relativistic stellar structure equations.
Using a set of finite-temperature nuclear equations of state, we find that hot
maximum-mass critically spinning configurations generally do not support larger
baryonic masses than their cold counterparts. However, subcritically spinning
configurations with mean density of less than a few times nuclear saturation
density yield a significantly thermally enhanced mass. Even without decreasing
the maximum mass, cooling and other forms of energy loss can drive the remnant
to an unstable state. We infer secular instability by identifying approximate
energy turning points in equilibrium sequences of constant baryonic mass
parametrized by maximum density. Energy loss carries the remnant along the
direction of decreasing gravitational mass and higher density until instability
triggers collapse. Since configurations with more thermal pressure support are
less compact and thus begin their evolution at a lower maximum density, they
remain stable for longer periods after merger.
