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We study the merger of black hole (BH)-neutron star (NS) binaries with avariety of BH spins aligned or anti-aligned with the orbital angular momentum,and with the mass ratio in the range MBH/MNS = 2--5, where MBH and MNS are themass of the BH and NS, respectively. We model NS matter by systematicallyparametrized piecewise polytropic equations of state. The initial condition iscomputed in the puncture framework adopting an isolated horizon framework toestimate the BH spin and assuming an irrotational velocity field for the fluidinside the NS. Dynamical simulations are performed in full general relativityby an adaptive mesh refinement code, SACRA. The treatment of hydrodynamicequations and estimation of the disk mass are improved. We find that the NS istidally disrupted irrespective of the mass ratio when the BH has a moderatelylarge prograde spin, whereas only binaries with low mass ratios, MBH/MNS <~ 3or small compactnesses of the NSs, bring the tidal disruption when the BH spinis zero or retrograde. The mass of the remnant disk is accordingly large as >~0.1 Msun, which is required by central engines of short gamma-ray bursts, ifthe BH spin is prograde. Information of the tidal disruption is reflected in aclear relation between the compactness of the NS and an appropriately defined"cutoff frequency" in the gravitational-wave spectrum, above which the spectrumdamps exponentially. We find that the tidal disruption of the NS and excitationof the quasinormal mode of the remnant BH occur in a compatible manner in highmass-ratio binaries with the prograde BH spin. The correlation between thecompactness and the cutoff frequency still holds for such cases. It is alsosuggested by extrapolation that the merger of an extremely spinning BH and anirrotational NS binary does not lead to formation of an overspinning BH.

Gravitational waves from spinning black hole-neutron star binaries: dependence on black hole spins and on neutron star equations of state