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The threshold mass for prompt collapse in binary neutron star mergers wasempirically found to depend on the stellar properties of the maximum-massnon-rotating neutron star model. Here we present a semi-analytic derivation ofthis empirical relation which suggests that it is rather insensitive to thermaleffects, to deviations from axisymmetry and to the exact rotation law in mergerremnants. We utilize axisymmetric, cold equilibrium models with differentialrotation and determine the threshold mass for collapse from the comparisonbetween an empirical relation that describes the angular momentum in theremnant for a given total binary mass and the sequence of rotating equilibriummodels at the threshold to collapse (the latter assumed to be near the turningpoint of fixed-angular-momentum sequences). In spite of the various simplifyingassumptions, the empirical relation for prompt collapse is reproduced with goodaccuracy, which demonstrates its robustness. We discuss implications of ourmethodology and results for understanding other empirical relations satisfiedby neutron-star merger remnants that have been discovered by numericalsimulations and that play a key role in constraining the high-density equationof state through gravitational-wave observations.

Semi-analytic derivation of the threshold mass for prompt collapse in binary neutron star mergers