In the first phase, all groups employed the -law EOS in the form
with the
special value of
, for which the initial condition is prepared by using the polytropic EOS
. In this EOS, physical parameters are non-dimensional quantities such as mass ratio,
, and compactness of the NS,
, because
can be freely
chosen. Since 2009, several more plausible EOS have been employed by the KT and CCCW
groups.
The early work of the KT group was done with the -law EOS for
and for a wide
range of
and
;
and
. Since 2009, the KT group has
employed a piecewise polytropic EOS [167, 150] with a wide variety of EOS parameters (see
Table 4). Simulations have been systematically performed employing this EOS for a wide range of
[107
, 109
];
,
, and
. (Here, the
negative value of the spin implies that the BH spin and orbital angular momentum vector are
anti-parallel.)
The simulations of the UIUC group were performed employing the -law EOS with
. The
UIUC group has chosen in total nine parameter sets for (
,
,
) as follows;
, and
,
, and
, and
and
. Simulations were performed for the relatively small
value of NS compactness.
The CCCW group performed simulations employing two types of EOS; -law EOS with
and
, and Shen’s EOS, which is a tabulated EOS derived in a relativistic mean field
theory [188, 189]. They focused on special parameter sets of
as
and
,
and
, and
and
. In their latest work, they focused on the case
and
, paying particular attention to the dependence of the merger process
on the EOS and on the misalignment angle of the BH spin and orbital angular momentum
axes.
The LBPLI group has performed one simulation to date, using the -law EOS with
, and with
(
,
,
) = (5, 0.5, 0.1) [41
]. In their first work, the compactness was chosen to be small and not
very realistic. In this simulation, magnetic fields in the ideal magnetohydrodynamics MHD
approximation were incorporated, but they did not play an important role. The AEI group
has performed simulations using
-law EOS with
, and with
,
, and
[154
].
To summarize, the total number of simulations is still small, although a systematic survey is required to
fully understand the complete picture of the coalescence of BH-NS binaries. In particular, many simulations
were performed in a not very realistic setting using a simple -law EOS and small values of
. As
mentioned in Section 1, tidal disruption is more subject to the less compact NS, and hence, it should be
in particular cautioned that a simulation with unphysically-small values of compactness may
lead to an incorrect conclusion that tidal disruption and subsequent disk formation are easily
achieved.
Nevertheless, the simulations performed so far have clarified a basic picture for the merger process of BH-NS binaries, the properties for the remnant, gravitational waveforms, and gravitational-wave spectrum. In the following, we summarize our current understanding of these topics based on work to date.
http://www.livingreviews.org/lrr-2011-6 |
Living Rev. Relativity 14, (2011), 6
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