Prototype effective-one-body model for nonprecessing spinning inspiral-merger-ringdown waveforms

Abstract

This paper presents a tunable effective-one-body (EOB) model for black-hole (BH) binaries of arbitrary mass-ratio and aligned spins. This new EOB model incorporates recent results of smallmass-ratio simulations based on Teukolsky's perturbative formalism. The free parameters of the model are calibrated to numerical-relativity simulations of non-spinning BH-BH systems of five different mass-ratios and to equal-mass non-precessing BH-BH systems with dimensionless BH spins χi ≃ ±0.44. The present analysis focuses on the orbital dynamics of the resulting EOB model, and on the dominant (ℓ,m)=(2,2) gravitational-wave mode. The calibrated EOB model can generate inspiral-merger-ringdown waveforms for non-precessing, spinning BH binaries with any mass ratio and with individual BH spins −1 ≤ χi 0.7. Extremizing only over time and phase shifts, the calibrated EOB model has overlaps larger than 0.997 with each of the seven numerical-relativity waveforms for total masses between 20M⊙ and 200M⊙, using the Advanced LIGO noise curve. We compare the calibrated EOB model with two additional equal-mass highly spinning (χi ≃ −0.95, +0.97) numerical-relativity waveforms, which were not used during calibration. We find that the calibrated model has overlap larger than 0.995 with the simulation with nearly extremal anti-aligned spins. Extension of this model to black holes with aligned spins χi 0.7 requires improvements of our modeling of the plunge dynamics and inclusion of higher-order PN spin terms in the gravitational-wave modes and radiation-reaction force.

Approaching the Post-Newtonian Regime with Numerical Relativity: A Compact-Object Binary Simulation Spanning 350 Gravitational-Wave Cycles

“…energy fluxes of those EOBNR models [23,45,46] do not impact the low-frequency part of the waveforms but affect (in a minor way) only the last stages of the inspiral and the merger. The unfaithfulness of the time-and frequencydomain inspiral-only PN Taylor approximants varies between 0.1% and 10% depending on the binary's total mass and the PN approximant used.…”

“…We consider the following analytical waveform models from the LIGO Algorithm Library (LAL): the inspiral-only PN Taylor approximants [44] in the time domain (Taylor-T1, T2, T4) and in the frequency domain , an inspiral EOB model (obtained from Ref. [23] by dropping any NR information, thus, uncalibrated), the IMR EOBNR models that were obtained by calibrating the EOB model to NR simulations [23,45,46] (denoted in LAL as EOBNRv2, SEOBNRv1, and SEOBNRv2), and the IMR phenomenological models that were built combining PN and NR results [20,21] (denoted in LAL as PhenomB and PhenomC). All the timedomain IMR waveforms are tapered using a Planck windowing function [47] both at the beginning and at the end.…”

Sources of Gravitational Waves: Theory and Observations

“…Subsequent studies carried out with highly accurate NR waveforms revealed the necessity of including higher-order PN terms in the EOB dynamics, energy flux and waveforms if the goal is to develop highly accurate templates for aLIGO/AdV searches. 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.…”

Comparing gravitational waveform extrapolation to Cauchy-characteristic extraction in binary black hole simulations

“…Assuming first-order convergence in phase, we estimate the phase error in the r2 waveform using Richardson extrapolation to be 3 · ∆φ 12 . Similarly, assuming secondorder convergence, we estimate the (relative) amplitude error to be 9/7 · ∆A 12 .…”

“…However, because these simulations are computationally expensive, analytical or phenomenological models of GW emission are required in order to densely cover the parameter space. Because these models must be calibrated using results from numerical simulations [7][8][9][10][11][12], it is essential that accurate waveforms from numerical simulations are available. Moreover, it is crucial that the uncertainties in these numerical waveforms are well understood.…”