Effective-one-body waveforms calibrated to numerical relativity simulations: coalescence of non-precessing, spinning, equal-mass black holes

摘要

We present the first attempt at calibrating the effective-one-body (EOB)model to accurate numerical-relativity simulations of spinning, non-precessingblack-hole binaries. Aligning the EOB and numerical waveforms at low frequencyover a time interval of 1000M, we first estimate the phase and amplitude errorsin the numerical waveforms and then minimize the difference between numericaland EOB waveforms by calibrating a handful of EOB-adjustable parameters. In theequal-mass, spin aligned case, we find that phase and fractional amplitudedifferences between the numerical and EOB (2,2) mode can be reduced to 0.01radians and 1%, respectively, over the entire inspiral waveforms. In theequal-mass, spin anti-aligned case, these differences can be reduced to 0.13radians and 1% during inspiral and plunge, and to 0.4 radians and 10% duringmerger and ringdown. The waveform agreement is within numerical errors in thespin aligned case while slightly over numerical errors in the spin anti-alignedcase. Using Enhanced LIGO and Advanced LIGO noise curves, we find that theoverlap between the EOB and the numerical (2,2) mode, maximized over theinitial phase and time of arrival, is larger than 0.999 for binaries with totalmass 30-200Ms. In addition to the leading (2,2) mode, we compare foursubleading modes. We find good amplitude and frequency agreements between theEOB and numerical modes for both spin configurations considered, except for the(3,2) mode in the spin anti-aligned case. We believe that the larger differencein the (3,2) mode is due to the lack of knowledge of post-Newtonian spineffects in the higher modes.