1.5 Non-relativistic simulation for the merger
The other important task is to clarify the evolution process in the last inspiral and merger
phases. For this purpose, the numerical simulation is the unique approach because (at least)
non-linear hydrodynamics including related physics has to be solved. The merger process of BH-NS
binaries was first studied in the framework of Newtonian or pseudo-Newtonian gravity by several
groups [95
, 124
, 123
, 121
, 122
, 171
, 169
, 174
]. These works have qualitatively clarified the tidal
disruption process, the subsequent formation process of a BH-disk system, properties of the remnant
accretion disk, gravitational waveforms emitted during the merger, and a fraction of matter ejected from the
system. Earlier work [95
, 124, 123, 121, 122, 171
] was performed modeling BH by a point mass of
Newtonian gravity. Because of the absence of the ISCO around the point mass in Newtonian gravity, the
gravity in the vicinity of the BH was even qualitatively different from that in reality. They conclude that
the NS might be tidally disrupted even in an orbit very close to the BH (well inside a radius of
, which is unrealistic), and consequently, a massive remnant disk with mass larger than
might be formed around the BH, irrespective of the mass ratio and the internal velocity field of
the NS. In subsequent work [169
, 174
], the general-relativistic gravity of the BH was partly
mimicked employing the Paczyński–Wiita potential for the point mass [152]. In this work, it
was found that massive disk formation with mass larger than
was possible only for
a binary system composed of a low-mass BH or of a spinning BH for the case that the BH
mass is not low [174
]. These properties are qualitatively in agreement with those derived in
recent fully general-relativistic simulations, and thus, for qualitatively or semi-qualitatively
understanding the nature of the BH-NS merger, the pseudo-Newtonian simulation is shown to be
helpful. In recent years, approximately general relativistic simulations were also performed by two
groups [64, 65, 164]. The derived qualitative features in the merger of BH-NS binaries agree with
those from pseudo-Newtonian studies as well as by the general relativistic studies described in
Section 3.
Simulations in [95
] were carried out incorporating detailed microphysical processes such as
finite-temperature EOS and neutrino emission employing a neutrino leakage scheme. The neutrino
luminosity from the BH-disk system formed in their simulations was found to be 1053 – 1054 ergs/s for the
first 10 – 20 ms after the formation of the disks. This was the result for the case in which a hot
and massive disk (of temperature
10 MeV and mass
) is formed. The high
neutrino luminosity is encouraging for driving a SGRB via neutrino-antineutrino pair annihilation
process. As remarked upon above, the massive disk formation in their model parameters would
unlikely if general relativistic effects had been correctly taken into account. The high temperature
also does not agree with a latest fully general relativistic result in which the simulation was
performed with a similar EOS [57
]. However, the results of [95
] suggested for the first time
that if such a massive disk was indeed formed, the resulting BH-disk system was a promising
candidate for the central engine of SGRB. Also, their technique for handling the neutrino emission
process becomes a useful guideline for detailed numerical studies in full general relativity (e.g.,
[183
, 185
]).