Hybrid model for inspiral-merger-ringdown gravitational waveforms from comparable-mass, nonspinning binary black holes

TL;DR

This paper advances the hybrid PN–black-hole perturbation approach for modeling inspiral-merger-ringdown gravitational waves from nonspinning comparable-mass BBHs by introducing three key phenomenological modifications: (i) employing an EOB-driven boundary trajectory that continues through merger and is smoothly blended with a late-time Kerr-inspired path, (ii) adjusting the boundary data via two PN-like coefficients to better calibrate amplitude and late-inspiral behavior, and (iii) replacing the exterior potential with a modified Poschl-Teller form tuned to match the remnant BH's least-damped QNM. The authors calibrate these parameters against NR surrogate waveforms for mass ratios corresponding to $q=1$ to $q=8$ (equivalently, $0.25 \ge \nu \ge 0.1$), achieving a waveform accuracy of about $10^{-3}$ in the $L^2$-norm and enabling rapid generation of IMR waveforms. The work provides a physically interpretable spacetime-dynamics picture while delivering a practical, fast alternative to full NR for data-analysis pipelines, and it opens pathways to extensions to spinning binaries and beyond-GR theories. The combination of EOB-inspired boundary dynamics, a tunable exterior potential, and PN-informed boundary data yields a versatile framework with potential broad applicability in GW astronomy and tests of gravity.

Abstract

Gravitational waves from comparable-mass binary-black-hole mergers are often described in terms of three stages: inspiral, merger and ringdown. Post-Newtonian and black-hole perturbation theories are used to model the inspiral and ringdown parts of the waveform, respectively, while the merger phase has been modeled most accurately using numerical relativity (NR). Nevertheless, there have been several approaches used to model the merger phase using analytical methods. In this paper, we adapt a hybrid approximation method that applies post-Newtonian and black-hole perturbation theories at the same times in different spatial regions of a binary-black-hole waveform (and which are matched at a boundary region with prescribed dynamics). Prior work with the hybrid method used leading post-Newtonian theory and the perturbation theory of nonrotating black holes, which led to errors during the late inspiral and disagreement with the dominant quasinormal-mode frequency extracted from NR simulations during the ringdown. To obtain a better match with NR waveforms of binary-black-hole mergers, we made several phenomenological modifications to the hybrid method. Specifically, to better capture the inspiral dynamics, we use the effective-one-body method for modeling the trajectory of the boundary between the two spatial regions. The waveform is determined by evolving a Regge-Wheeler-Zerilli-type equation for an effective black-hole perturbation theory problem with a modified Poschl-Teller potential. By tuning the potential to match the dominant quasinormal-mode frequency of the remnant black hole and also optimizing the boundary data on the matching region, we could match NR waveforms from nonspinning, comparable-mass binary black holes with mass ratios between one and eight, with a relative error of order $10^{-3}$.

Figures (7)

• Figure 1: Comparison of the hybrid-method and NR waveforms: The red dashed curve shows the hybrid waveform, while the blue solid curves depict the NR waveform for the symmetric mass ratio $\nu = 1/10$ (where $\nu$ and $rh^{2,2}/M$ are defined in the text). The left panel shows the waveform during the inspiral stage, and the right one shows the waveform during the merger and ringdown stages. More details about how the hybrid waveform was computed will be given in the subsequent sections of this paper.
• Figure 2: Trajectory of the matching shell in the Kerr $r_*$ coordinate for an equal mass-ratio BBH. In both panels, the trajectory corresponds to an equal-mass BBH system. In the top panel, the orange dash-dotted curve shows full trajectory after EOB and LT trajectories are smoothly blended. In the bottom panel, the solid blue curve shows the trajectory obtained from solving the EOB equations of motion. It stops at a time $t_\mathrm{st}$, which we have defined to be $t_\mathrm{st} = 0$. The maroon dashed line is the late-time trajectory, which is constructed to be the tangent to the EOB trajectory when it reaches a slope of $-1/2$.
• Figure 3: The modified Poschl-Teller potential for an equal mass system. The full mPT potential is shown as a dotted orange curve. It is constructed from a PT potential, the dashed purple curve, which is shown at all values of $r_*$. The potential that is a polynomial in $1/r$ at $r \geq r_\mathrm{lr}$, which we label as the "Centrifugal" potential, is shown as a solid blue curve. The red vertical line shows where the matching between the two potentials takes place at $r_\mathrm{lr}$.
• Figure 4: Calibrated modified Poschl-Teller potential for different mass ratios. Specifically, the solid blue curve represents the mPT potential for $\nu = 1/4$ (equal mass), the dashed purple curve is for $\nu = 1/6$, the dash-dotted orange is for $\nu = 1/8$ and the red dotted curve represents $\nu = 1/10$. As described in more detail the text of Sec. \ref{['sec:ModifiedPT']}, the potential decreases in amplitude and width as the symmetric mass ratio decreases.
• Figure 5: Comparison of the hybrid-method and NR waveforms: In both panels, the red dashed curves are the waveform produced by the hybrid method, and the solid blue curves are the NR waveforms. The top and bottom panels correspond to waveforms for mass ratios $\nu=1/4$ and $\nu=19/100$, respectively. The right side of each panel zooms in on the merger and ringdown stages of the waveform, which change on a shorter timescale than that of the inspiral shown on the left.