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キーワード:
General Relativity and Quantum Cosmology, gr-qc
要旨:
With recent advances in post-Newtonian (PN) theory and numerical relativity
(NR) it has become possible to construct inspiral-merger-ringdown gravitational
waveforms from coalescing compact binaries by combining both descriptions into
one complete hybrid signal. It is important to estimate the error of such
waveforms. Previous studies have identified the PN contribution as the dominant
source of error, which can be reduced by incorporating longer NR simulations.
There are two outstanding issues that make it difficult to determine the
minimum simulation length necessary to produce suitably accurate hybrids: (1)
the relevant criteria for a signal search is the mismatch between the true
waveform and a set of model waveforms, optimized over all waveforms in the
model. For discrete hybrids this optimization is not possible. (2) these
calculations require that NR waveforms already exist, while ideally we would
like to know the necessary length before performing the simulation. Here we
overcome these difficulties by developing a general procedure that allows us to
estimate hybrid mismatch errors without numerical data, and to optimize them
over all physical parameters. Using this procedure we find that, contrary to
some earlier studies, ~10 NR orbits before merger allow for the construction of
waveform families that are accurate enough for detection in a broad range of
parameters, only excluding highly spinning, unequal-mass systems. Nonspinning
binaries, even with high mass-ratio (>20) are well modeled for astrophysically
reasonable component masses. In addition, the parameter bias is only of the
order of 1% for total mass and symmetric mass-ratio and less than 0.1 for the
dimensionless spin magnitude. We take the view that similar NR waveform lengths
will remain the state of the art in the Advanced detector era, and begin to
assess the limits of the science that can be done with them.
