Quasi-universal behaviour of the threshold mass in unequal-mass, spinning binary neutron-star mergers

The lifetime of the remnant produced by the merger of two neutron stars can provide a wealth of information on the equation of state of nuclear matter and on the processes leading to the electromagnetic counterpart. Hence, it is essential to determine when this lifetime is the shortest, corresponding to when the remnant has a mass equal to the threshold mass, $M_{\rm th}$, to prompt collapse to a black hole. We report on the results of more than 360 simulations of merging neutron-star binaries covering 40 different configurations differing in mass ratio and spin of the primary. Using this data, we have derived a quasi-universal relation for $M_{\rm th}$ and expressed its dependence on the mass ratio and spin of the binary. The new expression recovers the results of Koeppel et al for equal-mass, irrotational binaries and reveals that $M_{\rm th}$ can increase (decrease) by $5\%~(10\%)$ for binaries that have spins aligned (anti-aligned) with the orbital angular momentum and provides evidence for a non-monotonic dependence of $M_{\rm th}$ on the mass asymmetry in the system. Finally, we extend to unequal-masses and spinning binaries the lower limits that can be set on the stellar radii once a neutron-star binary is detected, illustrating how the merger of an unequal-mass, rapidly spinning binary can significantly constrain the allowed values of the stellar radii.