  The threshold mass for prompt collapse in binary neutron star mergers was
empirically found to depend on the stellar properties of the maximum-mass
non-rotating neutron star model. Here we present a semi-analytic derivation of
this empirical relation which suggests that it is rather insensitive to thermal
effects, to deviations from axisymmetry and to the exact rotation law in merger
remnants. We utilize axisymmetric, cold equilibrium models with differential
rotation and determine the threshold mass for collapse from the comparison
between an empirical relation that describes the angular momentum in the
remnant for a given total binary mass and the sequence of rotating equilibrium
models at the threshold to collapse (the latter assumed to be near the turning
point of fixed-angular-momentum sequences). In spite of the various simplifying
assumptions, the empirical relation for prompt collapse is reproduced with good
accuracy, which demonstrates its robustness. We discuss implications of our
methodology and results for understanding other empirical relations satisfied
by neutron-star merger remnants that have been discovered by numerical
simulations and that play a key role in constraining the high-density equation
of state through gravitational-wave observations.

High Energy Astrophysical Phenomena;Solar and Stellar Astrophysics;General Relativity and Quantum Cosmology