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General Relativity and Quantum Cosmology, gr-qc
Abstract:
We calibrate an effective-one-body (EOB) model to numerical-relativity
simulations of mass ratios 1, 2, 3, 4, and 6, by maximizing phase and amplitude
agreement of the leading (2,2) mode and of the subleading modes (2,1), (3,3),
(4,4) and (5,5). Aligning the calibrated EOB waveforms and the numerical
waveforms at low frequency, the phase difference of the (2,2) mode between
model and numerical simulation remains below 0.1 rad throughout the evolution
for all mass ratios considered. The fractional amplitude difference at peak
amplitude of the (2,2) mode is 2% and grows to 12% during the ringdown. Using
the Advanced LIGO noise curve we study the effectualness and measurement
accuracy of the EOB model, and stress the relevance of modeling the
higher-order modes for parameter estimation. We find that the effectualness,
measured by the mismatch, between the EOB and numerical-relativity
polarizations which include only the (2,2) mode is smaller than 0.2% for
binaries with total mass 20-200 Msun and mass ratios 1, 2, 3, 4, and 6. When
numerical-relativity polarizations contain the strongest seven modes, and
stellar-mass black holes with masses less than 50Msun are considered, the
mismatch for mass ratio 6 (1) can be as high as 5% (0.2%) when only the EOB
(2,2) mode is included, and an upper bound of the mismatch is 0.5% (0.07%) when
all the four subleading EOB modes calibrated in this paper are taken into
account. For binaries with intermediate-mass black holes with masses greater
than 50Msun the mismatches are larger. We also determine for which
signal-to-noise ratios the EOB model developed here can be used to measure
binary parameters with systematic biases smaller than statistical errors due to
detector noise.
