High-accuracy comparison of numerical relativity simulations with post-Newtonian expansions

Abstract

Numerical simulations of 15 orbits of an equal-mass binary black-hole system are presented. Gravitational waveforms from these simulations, covering more than 30 cycles and ending about 1.5 cycles before merger, are compared with those from quasicircular zero-spin post-Newtonian (PN) formulae. The cumulative phase uncertainty of these comparisons is about 0.05 radians, dominated by effects arising from the small residual spins of the black holes and the small residual orbital eccentricity in the simulations. Matching numerical results to PN waveforms early in the run yields excellent agreement (within 0.05 radians) over the first 15 cycles, thus validating the numerical simulation and establishing a regime where PN theory is accurate. In the last 15 cycles to merger, however, generic time-domain Taylor approximants build up phase differences of several radians. But, apparently by coincidence, one specific post-Newtonian approximant, TaylorT4 at 3.5PN order, agrees much better with the numerical simulations, with accumulated phase differences of less than 0.05 radians over the 30-cycle waveform. Gravitational-wave amplitude comparisons are also done between numerical simulations and postNewtonian, and the agreement depends on the post-Newtonian order of the amplitude expansion: the amplitude difference is about 6%-7% for zeroth order and becomes smaller for increasing order. A newly derived 3.0PN amplitude correction improves agreement significantly ( < 1% amplitude difference throughout most of the run, increasing to 4% near merger) over the previously known 2.5PN amplitude terms.

Sources of Gravitational Waves: Theory and Observations

“…To incorporate possible systematics present in PN approximants, those template families either extended the binary parameter space to unphysical regions or incorporated higher-order physical effects, so that they could reach higher overlaps with both PN approximants and EOB waveforms. Eventually, after the NR breakthrough in 2005, PN approximants started to be compared to highly accurate NR waveforms [340,341] and also to EOB waveforms calibrated to NR waveforms [299]. It was found that for M > ∼ 10-15M , non-quasi-circular effects cannot be neglected and templates that include inspiral, merger and ringdown should be employed to avoid a large loss in the detection rate [299].…”

Measuring orbital eccentricity and periastron advance in quasicircular black hole simulations

“…We will primarily analyze the 16 orbit long inspiral simulation of an equal-mass, nonspinning black-hole binary presented in Ref. [14] (specifically, the run labeled 30c-1). This run with eccentricity of about 6 Â 10 À5 is used to compute the eccentricity data in Figs.…”

“…We extract the ðl; mÞ ¼ ð2; 2Þ mode of the gravitational wave using the Newman-Penrose scalar É 4 and define the wave phase ðtÞ as [14] É 22 4 ðr; tÞ ¼ Aðr; tÞe Ài ðr;tÞ :…”

“…In Section II, we compare these approaches, as well as some new ones, on the 15-orbit inspiral presented by Boyle et al [14] and on the data of a new simulation of an eccentric (e ¼ 0:05) nonspinning equal-mass binary black hole. Next, by measuring the extrema in the eccentricity estimator, we estimate in Sec.…”

“…The late stage of the inspiral, corresponding to the final few orbits and merger of the binary, is highly dynamical and involves strong gravitational fields, and it must be handled by numerical relativity. Breakthroughs in numerical relativity have allowed a system of two inspiraling black holes to be evolved through merger and the ringdown of the remnant black hole [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15].…”