Energetics and phasing of nonprecessing spinning coalescing black hole binaries

TL;DR

This paper improves an effective-one-body model for nonprecessing spinning black hole binaries by calibrating it against extensive numerical relativity data, achieving high faithfulness for gravitational wave analysis.

Contribution

It introduces a refined EOB model with only two free parameters, calibrated against new and existing NR data, and systematically computes the energy-angular momentum relation for spin-aligned binaries.

Findings

EOB/NR unfaithfulness ranges from 0.016% to 0.507%.

The model accurately reproduces NR phasing and energetics.

First systematic computation of the gauge-invariant energy-angular momentum relation for large spin-aligned data.

Abstract

We present an improved numerical relativity (NR) calibration of the new effective-one-body (EOB) model for coalescing non precessing spinning black hole binaries recently introduced by Damour and Nagar [Physical Review 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 $1\leq q \leq 9.989$ and dimensionless spin range $-0.95\leq \chi\leq +0.994$. 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 ($a_6^c(\nu)$) entering the non spinning sector, as a 5PN effective correction to the interaction potential, and one ($c_3(\tilde{a}_1,\tilde{a}_2,\nu))$ 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 $\Delta t_{\rm NQC}(\chi)$ 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~$M_\odot$ 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 $99.944\%$.