- In the final phase of BH-NS binaries, the NS is either tidally disrupted or swallowed by the companion BH. For a typical compactness of the NS, , with zero BH spin, tidal disruption occurs outside the ISCO only for a small mass ratio of . For the case in which tidal disruption occurs, the final remnant is a BH surrounded by a disk of relatively small mass (say ).
- The effects associated with BH spin enhance the possibilities for tidal disruption and for disk formation. Even for a moderately large spin , the criterion of tidal disruption for the mass ratio is relaxed to , for, e.g., . In addition the effects of BH spin increase the mass of a remnant disk surrounding a BH to for a typical NS of mass with and [109]. For a favorable condition, such as and , the disk mass may be [74].
- For a binary composed of a high-spin BH with high mass ratio, the disk, if it is formed, has a spread structure. However, the simulations so far (in which detailed microphysical effects such as neutrino wind are not taken into account) have not shown any evidence that a fraction of NS material escapes from the system.
- The final merger process is well reflected in gravitational waveforms. Up to now, it has been found that there are at least three types of gravitational waveform. (i) For the case in which tidal disruption occurs far outside the ISCO, the amplitude of gravitational waves steeply damps in the middle of the late inspiral phase, and ringdown gravitational waves associated with a QNM of the remnant BH are not seen clearly. This type is referred to as type-I. For the case in which tidal disruption does not occur outside the ISCO, ringdown gravitational waves associated with a QNM of the remnant BH are clearly seen in the final phase of the gravitational-wave signal. This type is referred to as type-II. For the case in which tidal disruption occurs near the ISCO, there are two possibilities. One is that the amplitude of the gravitational waves steeply damps and the ringdown signal of a QNM is not seen clearly. This is the case that the mass ratio (and thus BH mass) is small, and the resulting type of the gravitational waveform is type-I. For a large value of (for a high BH mass), the disrupted material falls into the BH from a narrow region of the BH surface. In such cases, both the feature of steep damping associated with tidal disruption and ringdown gravitational waves associated with a QNM are seen. This type is referred to as type-III.
- Reflecting that there are three types of gravitational waveforms, the gravitational-wave spectrum is also classified into three types. For type-I and type-III, the gravitational-wave spectrum is characterized by the cutoff frequency associated with tidal disruption. For a given set of masses of BH and NS, and BH spin, the cutoff frequency is determined by the EOS of the NS. Thus, if the cutoff frequencies are determined for a detected signal of gravitational waves, the EOS of the NS will be constrained. The cutoff frequency is higher than 1 kHz (e.g., Equation (8)). The frequency is lower for a NS of larger radii or for a rapidly spinning BH with a large BH mass. In particular, for a binary composed of a high-spin BH, the effective amplitude at is enhanced by the spin-orbit coupling effect. This effect is favorable for detecting a gravitational-wave signal at the cutoff frequency by advanced detectors.

There are several issues to be solved for the near future. First, more realistic modeling of NS is required because numerical studies have been performed with quite simple EOS and microphysics up till now. For more realistic modeling of BH-NS binaries (in particular for modeling formation and evolution processes of a disk surrounding a BH), more physical EOS should be taken into account; we have to take into account finite-temperature EOS, neutrino process, and magnetic fields (accurately evolving magnetic field configurations). Second, there is still a wide range of the parameter space that has not been studied. In particular, binaries of high BH spin () have not been studied yet. For the case in which BH spin is close to unity, the NS may be tidally disrupted even for a high mass ratio ; cf. Equation (12). This possibility has not been explored yet. For such a high-mass binary, tidal disruption occurs at a relatively-low gravitational-wave frequency 1 kHz. This is favorable for observing the tidal-disruption event by gravitational-wave detectors, and thus, this deserves intense study. Recent work by Liu et al. [130] indicated it feasible to perform a simulation with a high spin using a simple prescription (see also [133]). A simulation with such a high spin will be done in a few years. Third, only one study has been done for the merger process of the binaries in which the BH spin and orbital angular momentum vectors misalign. In particular, any study of gravitational waveforms has not been done for this case. This is also an issue to be explored. Finally, it is necessary to optimize simulation codes to efficiently and accurately perform a large number of longterm simulations for a wide range of parameter space. This is required for preparing template sets of gravitational waves that are used for gravitational-wave data analysis. Work along this line has recently begun in 2010 [153, 110], and in the next several years, it will be encouraged because the preparation of theoretical templates is an urgent task for advanced gravitational-wave detectors.

Living Rev. Relativity 14, (2011), 6
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