3.8 Summary and issues for the near future

The inspiral and merger of BH-NS binaries are among promising sources for kilometer size laser-interferometric gravitational-waves detectors. The merger remnant is also a possible candidate for the progenitor of the central engine of SGRB. BH-NS binaries are also invaluable experimental fields for studying high-density nuclear matter through astronomical observations. To derive accurate gravitational waveforms in the late inspiral and merger phases, and to explore the compact-binary-merger hypothesis for the central engine of SGRB, the numerical simulation in full general relativity, taking into account realistic physics, is the unique approach. We review the progress and current status of numerical simulations for BH-NS binaries, and summarize the current understanding obtained from numerical results. The following is a summary as of June 2011:

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 (a > 0.9) 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 Q ∼ 20; cf. Equation (12View Equation). 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 a ∼ 0.99 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.

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