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:
- 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.