Complete waveform model for compact binaries on eccentric orbits

Abstract

We present a time domain waveform model that describes the inspiral, merger and ringdown of compact binary systems whose components are nonspinning, and which evolve on orbits with low to moderate eccentricity. The inspiral evolution is described using third-order post-Newtonian equations both for the equations of motion of the binary, and its far-zone radiation field. This latter component also includes instantaneous, tails and tails-of-tails contributions, and a contribution due to nonlinear memory. This framework reduces to the post-Newtonian approximant TaylorT4 at third postNewtonian order in the zero-eccentricity limit. To improve phase accuracy, we also incorporate higher-order post-Newtonian corrections for the energy flux of quasicircular binaries and gravitational self-force corrections to the binding energy of compact binaries. This enhanced prescription for the inspiral evolution is combined with a fully analytical prescription for the merger-ringdown evolution constructed using a catalog of numerical relativity simulations. We show that this inspiral-mergerringdown waveform model reproduces the effective-one-body model of Ref. [Y. Pan et al., Phys. Rev. D 89, 061501 (2014).] for quasicircular black hole binaries with mass ratios between 1 to 15 in the zero-eccentricity limit over a wide range of the parameter space under consideration. Using a set of eccentric numerical relativity simulations, not used during calibration, we show that our new eccentric model reproduces the true features of eccentric compact binary coalescence throughout merger. We use this model to show that the gravitational-wave transients GW150914 and GW151226 can be effectively recovered with template banks of quasicircular, spin-aligned waveforms if the eccentricity e 0 of these systems when they enter the aLIGO band at a gravitational-wave frequency of 14 Hz satisfies e GW150914 0 ≤ 0.15 and e GW151226 0 ≤ 0.1. We also find that varying the spin combinations of the quasicircular, spin-aligned template waveforms does not improve the recovery of nonspinning, eccentric signals when e 0 ≥ 0.1. This suggests that these two signal manifolds are predominantly orthogonal.

Waveform model for an eccentric binary black hole based on the effective-one-body-numerical-relativity formalism

“…9. Overall the two waveforms show very good consistence which corresponds to the result of fitting factor 0.95 respect to advanced LIGO got in [34]. But we can still see some amplitude difference near merger, and some phase difference when the evolution time becomes longer.…”

“…Our basic idea is decomposing the waveform into quasicircular part and eccentric part. The strategy is following [34]. We treat the eccentric part as perturbation by assuming that the eccentricity is small.…”

“…This is the method taken by ax-model [34]. Similar to the idea we taken to treat the waveform in the above sub-section A, we divide the energy flux into two parts which correspond to the circular part and the non-circular correction part.…”

“…In principle the mass and the spin may be affected by the eccentricity. But here we neglect such dependence on the eccentricity as [34] based on the assumption that the eccentricity is small for the cases considered in current work. We specify the mass and the spin of the final black hole following [68,69] …”

Gravitational wave source localization for eccentric binary coalesce with a ground-based detector network

“…Recently, there are several waveform models for an eccentric binary have been constructed [30][31][32][33][34][35]. In particular, the enhanced post-circular (EPC) model [32,36] is one of such models.…”