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General Relativity and Quantum Cosmology, gr-qc
Abstract:
The two-body dynamics in general relativity has been solved perturbatively
using the post-Newtonian (PN) approximation. The evolution of the orbital phase
and the emitted gravitational radiation are now known to a rather high order up
to O(v^8), v being the characteristic velocity of the binary. The orbital
evolution, however, cannot be specified uniquely due to the inherent freedom in
the choice of parameter used in the PN expansion as well as the method pursued
in solving the relevant differential equations. The goal of this paper is to
determine the (dis)agreement between different PN waveform families in the
context of initial and advanced gravitational-wave detectors. The waveforms
employed in our analysis are those that are currently used by Initial
LIGO/Virgo, that is the time-domain PN models TaylorT1, TaylorT2, TaylorT3,
TaylorT4 and TaylorEt, the effective one-body (EOB) model, and the
Fourier-domain representation TaylorF2. We examine the overlaps of these models
with one another and with the prototype effective one-body model (calibrated to
numerical relativity simulations, as currently used by initial LIGO) for a
number of different binaries at 2PN, 3PN and 3.5PN orders to quantify their
differences and to help us decide whether there exist preferred families that
are the most appropriate as search templates. We conclude that as long as the
total mass remains less than a certain upper limit M_crit, all template
families at 3.5PN order (except TaylorT3 and TaylorEt) are equally good for the
purpose of detection. The value of M_crit is found to be ~ 12M_Sun for Initial,
Enhanced and Advanced LIGO. From a purely computational point of view we
recommend that 3.5PN TaylorF2 be used below Mcrit and EOB calibrated to
numerical relativity simulations be used for total binary mass M > Mcrit.
