Effective-one-body waveforms calibrated to numerical relativity simulations: Coalescence of nonprecessing, spinning, equal-mass black holes

Abstract

We present the first attempt at calibrating the effective-one-body (EOB) model to accurate numerical relativity simulations of spinning, nonprecessing black-hole binaries. Aligning the EOB and numerical waveforms at low frequency over a time interval of 1000M, we first estimate the phase and amplitude errors in the numerical waveforms and then minimize the difference between numerical and EOB waveforms by calibrating a handful of EOB-adjustable parameters. In the equal-mass, spin aligned case, we find that phase and fractional amplitude differences between the numerical and EOB ð2; 2Þ mode can be reduced to 0.01 radian and 1%, respectively, over the entire inspiral waveforms. In the equal-mass, spin antialigned case, these differences can be reduced to 0.13 radian and 1% during inspiral and plunge, and to 0.4 radian and 10% during merger and ringdown. The waveform agreement is within numerical errors in the spin aligned case while slightly over numerical errors in the spin antialigned case. Using Enhanced LIGO and Advanced LIGO noise curves, we find that the overlap between the EOB and the numerical ð2; 2Þ mode, maximized over the initial phase and time of arrival, is larger than 0.999 for binaries with total mass 30M -200M . In addition to the leading ð2; 2Þ mode, we compare four subleading modes. We find good amplitude and frequency agreements between the EOB and numerical modes for both spin configurations considered, except for the ð3; 2Þ mode in the spin antialigned case. We believe that the larger difference in the ð3; 2Þ mode is due to the lack of knowledge of post-Newtonian spin effects in the higher modes.

Mergers of black-hole binaries with aligned spins: Waveform characteristics

“…These would be an alternative to the timedomain effective-one-body (EOB) templates of [82][83][84], and the frequency-domain "phenomenological" templates of [18,19], similar to ringdown searches currently being applied to LIGO data [78][79][80][81]. In future work we plan to investigate the quality of this model, or its extensions, for a broader variety of mergers, including precessing and eccentric configurations.…”

Catalog of 174 Binary Black Hole Simulations for Gravitational Wave Astronomy

“…Independent validation of existing analytical waveform models: Many waveform models [49,[71][72][73][74][75] are calibrated against numerical relativity simulations-but usually only with a small number of short (typically < 10 orbits) simulations. The new simulations here enable tests of these models at many different points in parameter space and covering more cycles.…”

Sources of Gravitational Waves: Theory and Observations

“…As a consequence, higher-order PN terms (in particular, the test-particle limit terms) are included in the gravitational modes h m [277,292,346]. Since PN corrections are not yet fully known in the twobody dynamics, higher-order PN terms are included in the EOB dynamics with arbitrary coefficients [302,[346][347][348][349][350][351][352][353][354], which are then calibrated by minimising the phase and amplitude difference between EOB and NR waveforms aligned at low frequency. Those coefficients have been denoted adjustable or flexible parameters.…”