Highly accurate simulations of asymmetric black-hole scattering and cross validation of effective-one-body models

TL;DR

This work delivers the first large set of highly accurate NR scattering simulations for unbound BBHs using SpEC (60 runs, up to mass ratio $q=10$ and spin-aligned configurations), enabling precise measurements of scattering angles and cross-code validation with ETK. It demonstrates that PM-based closed-form EOB models SEOB-PM and $w_{\rm EOB}$ generally reproduce NR results within $\lesssim 5\%$, while evolution EOB models SEOBNRv5 and TEOBResumS-Dalí show mixed performance across spins and energies, with TEOBResumS-Dalí particularly sensitive to high energies and spin. A key result is the first NR-based measurement of disparate scattering angles arising from asymmetric GW emission, and the authors introduce asymmetric SEOB-PM variants to predict the individual BH angles, revealing only small asymmetries at current accuracies but highlighting the need for higher-PM information near the separatrix. The study also emphasizes the potential of using NR-derived scattering angles to calibrate bound EOB dynamics, guides future high-energy scattering investigations, and provides public NR data to support broader NR and modeling efforts. The findings reinforce the value of scattering observables as robust, gauge-invariant inputs for refining gravitational-wave waveform models and understanding strong-field two-body dynamics.

Abstract

The study of unbound binary-black-hole encounters provides a gauge-invariant approach to exploring strong-field gravitational interactions in two-body systems, which can subsequently inform waveform models for bound orbits. In this work, we present 60 new highly accurate numerical relativity (NR) simulations of black-hole scattering, generated using the Spectral Einstein Code (SpEC). Our simulations include 14 spin-aligned configurations, as well as 16 configurations with unequal masses, up to a mass ratio of 10. We perform the first direct comparison of scattering angles computed using different NR codes, finding good agreement. We compare our NR scattering angle results to the post-Minkowskian (PM)-based effective-one-body (EOB) closed-form models SEOB-PM and $w_{\rm EOB}$, finding less than 5% deviation except near the scatter-capture separatrix. Comparisons with the post-Newtonian-based EOB evolution models SEOBNRv5 and TEOBResumS-Dalí reveal that the former agrees within 8% accuracy with non-spinning NR results across most parameter ranges, whereas the latter matches similarly at lower energies but diverges significantly at higher energies. Both evolution EOB models exhibit increased deviations for spinning systems, predicting a notably different location of the capture separatrix compared to NR. Our key result is the first measurement of disparate scattering angles from NR simulations due to asymmetric gravitational-wave emission. We compare these results to SEOB-PM models constructed to calculate the scattering angle of a single black hole in asymmetric systems.

Figures (12)

• Figure 1: Coordinate trajectories of two unbound BHs for a variety of initial conditions. Upper: Non-spinning BHs with $\gamma=1.02$, $\ell = 4.8$, and mass ratios $q=1$ ( left) and $q=10$ ( right). Lower: Equal mass BHs with $\gamma=1.226$, $\ell = 5.18$, and equal parallel spins $\chi_+=-0.25$ ( left) and equal magnitude, anti-parallel spins $\chi_-=0.6$ ( right). See Eqs. (\ref{['eq:qDef']}), (\ref{['eq:gammaDef']}), (\ref{['eq:ellDef']}), and (\ref{['eq:chipmDef']}) for definitions of $q$, $\gamma$, $\ell$, and $\chi_\pm$, respectively.
• Figure 2: Spacetime diagram of a $q=3$SpEC scattering simulation. The solid blue and orange lines show the trajectories of the large and small BHs, respectively. The dashed lines represent the junk radiation emanating from the BH of the matching color, and the black discs show when the junk from one BH reaches the other. In the red-shaded region, encompassing the propagation of junk radiation, AMR is inactive and the red dotted line shows when AMR is turned on. The line $t_{\rm branch}$ marks the start of the lower resolution runs. We show the value of the outer boundary of the computational domain, $R_{\rm bdry}$ for reference.
• Figure 3: Parameter space coverage of simulations: 'SpEC$q\!=\!1,\chi_i\!=\!0$' indicates equal-mass, non-spinning simulations presented here, and the large open circles denote sequences of SpEC simulations of unequal masses (up to $q\!=\!10$), or with non-zero spins (up to $\chi_i\!=\!0.60$). The grey solid lines show contours of constant scattering angle generated using SEOB-4PM, delineated by a fit of the scatter-capture separatrix (red dashed line) Kankani:2024may. For context, the plot also shows parameters of equal-mass, non-spinning BBH scattering simulations performed with ETKDamour:2014afaHopper:2022rwoRettegno:2023ghrSwain:2024ngs and GRA++Albanesi:2024xus. Ref. Swain:2024ngs also presents simulations extending up to $\gamma=1.96$, which are not shown on this plot.
• Figure 4: Calculation of the asymptotic scattering angle. The left panel shows the extrapolated outgoing angle obtained by fits over varying intervals $[d_{\rm out}, 350M]$. The Keplerian fit Eq. (\ref{['eq:KeplerFit']}) yields more stable results than the polynomial fit Eq. (\ref{['eq:PolyFit']}). The right panel indicates the asymptotic scattering angle calculated from both fits in the left panel, and our choice of error bar. Both panels show three different resolutions (Lev1 through Lev3), which all give consistent results.
• Figure 5: Comparison of scattering angle extracted from SpEC and ETKSwain:2024ngs simulations. All simulations start as equal mass, non-spinning binaries with $\Gamma = 1.02264$. The top panel shows the relative scattering angle as a function of the initial angular momentum. The bottom panel shows the relative difference between the two codes. The SpEC values lie on $\delta\theta=0$ with the error bars being the errors of the upper panel rescaled by the value of the angle. These errors are too small to be resolved on this scale, but are resolved in the inset, which shows a zoom-in of the six largest $\ell$ values. The blue shaded region on the lower plot demonstrates the expected difference in the angle due to a $\pm 10^{-5}$ difference in the initial energy. The vertical dotted lines show the first confirmed capture from each code.