BOB the (Waveform) Builder: Optimizing Analytical Black-Hole Binary Merger Waveforms

TL;DR

The paper introduces Backwards-One-Body (BOB), an analytic merger-ringdown framework based on null geodesics at the remnant light ring, with the amplitude evolution $A = A_p\,\text{sech}\left(\frac{t-t_p}{\tau}\right)$ and $\tau=\gamma^{-1}$. It demonstrates that BOB most accurately models the gravitational-wave news $\mathcal{N}$ (and often $\Psi_4$), achieving accuracy competitive with calibrated EOB and NR surrogate models while requiring minimal NR tuning, and derives an analytic link between the peak amplitude and the fundamental QNM amplitude $\mathcal{A}_{220}$. The work investigates several flavors of BOB, including a minimally tuned variant using only remnant properties $(M_f,\chi_f)$ and a universal $\Omega_0$ fit, and provides methods to obtain the strain $h$ from $\mathcal{N}$ via a controlled asymptotic expansion. It highlights BOB’s ability to robustly describe the merger-ringdown across parameter space, its role as a testbed for QNM extraction, and its potential to complement NR catalogs and IMR waveform approaches, including a companion gwBOB package for practical usage. The findings underscore BOB’s value for independent NR validation, strong-field physics insight, and future IMR integration, with extensions to higher modes and precession anticipated.

Abstract

The Backwards-One-Body (BOB) model provides a fully analytical and physically motivated description of the merger-ringdown gravitational radiation emanating from a black hole binary merger. We perform a comprehensive validation of BOB for the dominant $(2,2)$ mode of quasi-circular and non-precessing systems, assessing its accuracy against numerical relativity (NR) simulations, state-of-the-art waveform models, and a sum of quasinormal modes. We demonstrate that BOB most accurately describes the gravitational wave news, achieving accuracy comparable to highly-calibrated Effective-One-Body and NR surrogate models. Because BOB is minimally tuned to NR catalogs, it retains a high level of accuracy in regions of the parameter space sparsely covered by current NR catalogs. BOB yields an analytic link between the amplitude of the fundamental quasinormal mode and the peak amplitude of the News, which we verify to within the errors of a surrogate ringdown model. We identify a flavor of BOB that requires only the remnant mass and spin, yet matches the accuracy of models that fit a sum of many overtones. Lastly, we show that BOB accurately models both the mass and current quadrupole waves for superkick configurations, contrary to a claim in the literature, and explain why that study was not actually implementing BOB as it has been defined. Our findings establish BOB as a powerful tool for gravitational wave analysis, for providing independent tests of NR-calibrated models, and for better understanding the underlying physics of the merger. We provide a companion python package, gwBOB, allowing for the easy construction of various flavors of BOB and comparison to NR waveforms.

Figures (25)

• Figure 1: Comparison of BOB and a NR waveform for the imaginary part of the $(2,2)$ mode of the News for an SXS simulation SXS:BBH:0305sxs_cat1 with parameters similar to GW150914 gw150914.
• Figure 2: $\Omega_0$ values obtained from a least squares fit of NR frequency data to the respective BOB frequency evolution.
• Figure 3: $\mathcal{N}$ mismatch between BOB and NR for the $(2,2)$ mode for all quasi-circular and non-precessing systems in the SXS catalog as a function of the initial parameters of the binary.
• Figure 4: $\mathcal{N}$ mismatch between BOB and NR for the $(2,2)$ mode for all quasi-circular and non-precessing systems in the SXS catalog as a function of the remnant parameters of the system.
• Figure 5: BOB mismatch for the $(2,2)$ mode against the corresponding NR gravitational wave quantity. While BOB can successfully model both $\mathcal{N}$ and $\Psi_4$ directly, it does not accurately model $h$ directly, indicating that the most accurate way to obtain $h$ is to integrate BOB.