An improved effective-one-body model of spinning, nonprecessing binary black holes for the era of gravitational-wave astrophysics with advanced detectors

TL;DR

The paper addresses the need for highly accurate gravitational-wave templates for spinning, nonprecessing binary black holes by developing SEOBNRv4, an improved effective-one-body waveform model calibrated to an extensive NR and perturbative-waveform set. It combines a refined conservative dynamics with a PN-informed inspiral-plunge description, and a phenomenological merger-ringdown attuned to NR and Teukolsky inputs, augmented by a fast reduced-order surrogate for data-analysis workloads. The model achieves faithfulness above $0.99$ to the NR catalog across most of parameter space, though regions with very large mass ratios and spins require longer NR coverage for robust extrapolation; a thorough NQC treatment and RD fitting underpin this accuracy. The SEOBNRv4_ROM further enables rapid waveform generation suitable for large-scale template banks and Bayesian analyses, marking a significant advance for LIGO/Virgo data analysis in the O2 and future observing runs.

Abstract

We improve the accuracy of the effective-one-body (EOB) waveforms that were employed during the first observing run of Advanced LIGO for binaries of spinning, nonprecessing black holes by calibrating them to a set of 141 numerical-relativity (NR) waveforms. The NR simulations expand the domain of calibration towards larger mass ratios and spins, as compared to the previous EOBNR model. Merger-ringdown waveforms computed in black-hole perturbation theory for Kerr spins close to extremal provide additional inputs to the calibration. For the inspiral-plunge phase, we use a Markov-chain Monte Carlo algorithm to efficiently explore the calibration space. For the merger-ringdown phase, we fit the NR signals with phenomenological formulae. After extrapolation of the calibrated model to arbitrary mass ratios and spins, the (dominant-mode) EOBNR waveforms have faithfulness --- at design Advanced-LIGO sensitivity --- above $99\%$ against all the NR waveforms, including 16 additional waveforms used for validation, when maximizing only on initial phase and time. This implies a negligible loss in event rate due to modeling for these binary configurations. We find that future NR simulations at mass ratios $\gtrsim 4$ and double spin $\gtrsim 0.8$ will be crucial to resolve discrepancies between different ways of extrapolating waveform models. We also find that some of the NR simulations that already exist in such region of parameter space are too short to constrain the low-frequency portion of the models. Finally, we build a reduced-order version of the EOBNR model to speed up waveform generation by orders of magnitude, thus enabling intensive data-analysis applications during the upcoming observation runs of Advanced LIGO.

Figures (15)

• Figure 1: Numerical-relativity Mroue:2013xnaChu:2015kftKumar:2015thaLovelace:2010neScheel:2014inaHusa:2015iqa and Teukolsky Taracchini:2014zpa waveforms used for calibration and validation of the EOBNR waveform model. We project the 3D parameter space of spinning, nonprecessing waveforms using the symmetric mass ratio $\nu$ and two BH spin combinations: $\chi_{\textrm{eff}}\equiv (m_1 \chi_1+m_2 \chi_2)/M$ and $\chi_{\textrm{A}} \equiv (\chi_1 - \chi_2)/2$. We note the better coverage of the large, positive $\chi_{\textrm{eff}}$ region and of the $\chi_{\textrm{A}}$ dimension in the NR catalog used to calibrate the EOBNR model of this paper (SEOBNRv4) with respect to the one used in the EOBNR model of Ref. Taracchini:2013rva (SEOBNRv2). Red triangles indicate NR waveforms used for validation of the calibration.
• Figure 2: Unfaithfulness of the EOBNR model of Ref. Taracchini:2013rva (SEOBNRv2) (left panel) and the EOBNR model of this paper (SEOBNRv4) (right panel) against the NR catalog for total masses $10\,M_\odot \leq M \leq 200\,M_\odot$, using the Advanced LIGO design zero-detuned high-power noise PSD and a low-frequency cutoff equal to the initial geometric frequency of each NR run. In the left panel, the cases where the maximum unfaithfulness is $>3\%$ are highlighted in color and labeled by $( q,\chi_1,\chi_2)$. In the right panel, the cases that were not used in the calibration are highlighted with colors and 6 cases whose parameters lie close to the boundary of our calibration domain are singled out in the legend. We note that the new EOBNR model (SEOBNRv4) has unfaithfulness below 1% against the whole NR catalog.
• Figure 3: Distribution of minimum faithfulness of the old EOBNR model (SEOBNRv2) Taracchini:2013rva and new EOBNR model (SEOBNRv4) against the NR catalog. The total mass range considered is $10\,M_\odot \leq M \leq 200\,M_\odot$. The calculations are done with the Advanced LIGO design zero-detuned high-power noise PSD and a low-frequency cutoff corresponding to the initial geometric frequency of each NR simulation.
• Figure 4: Waveform comparison in the time domain between the (dominant mode) EOBNR waveform of this paper (SEOBNRv4) (dashed red) and the NR waveform (solid blue) for a BBH with $(q,\chi_1,\chi_2) = (3,0.85, 0.85)$. The waveforms are phase aligned and time shifted at low frequency (the alignment window is indicated by the vertical dashed lines). The phase evolution throughout late inspiral, merger and ringdown is well reproduced, as well as the time to merger.
• Figure 5: Faithfulness of the EOBNR model of this paper (SEOBNRv4) against the previous EOBNR model (SEOBNRv2) Taracchini:2013rva (top row) and the phenomenological inspiral-merger-ringdown model (IMRPhenomD) Khan:2015jqa (bottom row) for $2\times 10^5$ random spinning, nonprecessing BBHs with $4\,M_{\odot} \leq M \leq 200\, M_{\odot}$ using the Advanced LIGO O1 noise PSD and a low-frequency cutoff of 25 Hz. Here $\chi_{\textrm{eff}}\equiv (m_1 \chi_1+m_2 \chi_2)/M$ and $\chi_{\textrm{A}} \equiv (\chi_1 - \chi_2)/2$. Points with faithfulness above 97% are not shown. Points with faithfulness $\leq 73\%$ are in red. We note that the biggest changes introduced by the new calibration occur for large, positive $\chi_{\textrm{eff}}$ and positive $\chi_{\textrm{A}}$. The new EOBNR model is most different from the phenomenological model in the large-$q$, large-$\chi_{\textrm{eff}}$ region, where both models are extrapolated away from the available NR simulations.