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Prog. Theor. Phys. Vol. 111 No. 6 (2004) pp. 781-805
An Improved Template Space for Gravitational Ringing of Black Holes
Hiroyuki Nakano,1
Hirotaka Takahashi,2,3,4
Hideyuki Tagoshi3,5 and
Misao Sasaki4
1Department of Mathematics and Physics, Osaka City University,
Osaka 558-8585, Japan
2Department of Physics, Niigata University,
Niigata 950-2181, Japan
3Department of Earth and Space Science, Osaka University,
Toyonaka 560-0043, Japan
4Yukawa Institute for Theoretical Physics, Kyoto University,
Kyoto 606-8502, Japan
5Theoretical Astrophysics, California Institute of Technology,
Pasadena, CA 91125, USA
(Received March 17, 2004)
Abstract:
A black hole has characteristic quasi-normal modes
that are excited when it is formed or when the geometry is
perturbed. The state of a black hole when the quasi-normal modes
are excited is called `gravitational ringing',
and detections of it constitute a direct
confirmation of the existence of black holes.
To detect it, a method based on matched filtering needs to be
developed. Generically, matched filtering requires a large
number of templates, because one has to ensure the proper match
of a real gravitational wave
with one of template waveforms to keep the detection efficiency
as high as possible. On the other hand, the number of templates must
be kept as small as possible due to limits in computational capability.
In a previous paper, assuming that the gravitational ringing is
dominated by the least-damped (fundamental) mode with the smallest
imaginary part of the frequency, we constructed an efficient method for
tiling the template space. However, the dependence of the template
space metric on the initial phase of the wave was not taken into
account. This dependence arises because of an unavoidable mismatch
between the parameters of the signal waveform and those given discretely
in the template space.
In this paper, we properly take this dependence into account
and present an improved, efficient search method for the gravitational
ringing of black holes.
URL :
http://ptp.ipap.jp/link?PTP/111/781/
DOI : 10.1143/PTP.111.781
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