Energetics and phasing of nonprecessing spinning coalescing black hole binaries

Abstract

We present an improved numerical relativity (NR) calibration of the new effective-one-body (EOB) model for coalescing nonprecessing spinning black hole binaries recently introduced by Damour and Nagar [Phys. Rev. D 90, 044018 (2014)]. We do so by comparing the EOB predictions to both the phasing and the energetics provided by two independent sets of NR data covering mass ratios 1 ≤ q ≤ 9.989 and dimensionless spin range −0.95 ≤ χ ≤ +0.994. One set of data is a subset of the Simulating eXtreme Spacetimes (SXS) catalog of public waveforms; the other set consists of new simulations obtained with the Llama code plus Cauchy characteristic evolution. We present the first systematic computation of the gauge-invariant relation between the binding energy and the total angular momentum, E_b (j), for a large sample of, spin-aligned, SXS and Llama data. The dynamics of the EOB model presented here involves only two free functional parameters, one [a^c_6 (ν)] entering the nonspinning sector, as a 5PN effective correction to the interaction potential, and one [c_3 (a_1, a_2, ν)] in the spinning sector, as an effective next-to-next-to-next-to-leading order correction to the spin-orbit coupling. These parameters are determined [together with a third functional parameter Δt_(NQC) (χ) entering the waveform] by comparing the EOB phasing with the SXS phasing, the consistency of the energetics being checked afterwards. The quality of the analytical model for gravitational wave data analysis purposes is assessed by computing the EOB/NR faithfulness. Over the NR data sample and when varying the total mass between 20 and 200 M⊙ the EOB/NR unfaithfulness (integrated over the NR frequency range) is found to vary between 99.493% and 99.984% with a median value of 99.944%.

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