Black hole-neutron star binaries with high spins and large mass asymmetries: I. Properties of quasi-equilibrium sequences

Black hole - neutron star (BHNS) mergers are a promising target of current gravitational-wave (GW) and electromagnetic (EM) searches, being the putative origin of ultra-relativistic jets, gamma-ray emission, and r-process nucleosynthesis. However, the possibility of any EM emission accompanying a GW detection crucially depends on the amount of baryonic mass left after the coalescence, i.e. whether the neutron star (NS) undergoes a `tidal disruption' or `plunges' into the black hole (BH) while remaining essentially intact. As the first of a series of two papers, we here report the most systematic investigation to date of quasi-equilibrium sequences of initial data across a range of stellar compactnesses $\mathcal{C}$, mass ratios $q$, BH spins $\chi_{_{\rm BH}}$, and equations of state satisfying all present observational constraints. Using an improved version of the elliptic initial-data solver FUKA, we have computed more than $1000$ individual configurations and estimated the onset of mass-shedding or the crossing of the innermost stable circular orbit in terms of the corresponding characteristic orbital angular velocities $\Omega_{_{\rm MS}}$ and $\Omega_{_{\rm ISCO}}$ as a function of $\mathcal{C}, q$, and $\chi_{_{\rm BH}}$. To the best of our knowledge, this is the first time that the dependence of these frequencies on the BH spin is investigated. In turn, by setting $\Omega_{_{\rm MS}} = \Omega_{_{\rm ISCO}}$ it is possible to determine the separatrix between the `tidal disruption' or `plunge' scenarios as a function of the fundamental parameters of these systems, namely, $q, \mathcal{C}$, and $\chi_{_{\rm BH}}$. Finally, we present a novel analysis of quantities related to the tidal forces in the initial data and discuss their dependence on spin and separation.