Comparison of post-Newtonian templates for compact binary inspiral signals in gravitational-wave detectors

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 $\mathcal{O}({v}^{8})$, $v$ 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, the Fourier-domain representation TaylorF2 (or stationary phase approximant), and the effective-one-body model, and two more recent models, TaylorT4 and TaylorEt. For these models we examine their overlaps with one another for a number of different binaries at 2PN, 3PN, and 3.5PN orders to quantify their differences. We then study the overlaps of these families with the prototype effective-one-body family, currently used by Initial LIGO, calibrated to numerical-relativity simulations to help us decide whether there exist preferred families, in terms of detectability and computational cost, that are the most appropriate as search templates. We conclude that as long as the total mass remains less than a certain upper limit ${M}_{\mathrm{crit}}$, all template families at 3.5PN order (except TaylorT3 and TaylorEt) are equally good for the purpose of detection. The value of ${M}_{\mathrm{crit}}$ is found to be $\ensuremath{\sim}12{M}_{\ensuremath{\bigodot}}$ for Initial, Enhanced, and Advanced LIGO. From a purely computational point of view, we recommend that 3.5PN TaylorF2 be used below ${M}_{\mathrm{crit}}$ and that the effective-one-body model calibrated to numerical-relativity simulations be used for total binary mass $M>{M}_{\mathrm{crit}}$.