Adding equatorial-asymmetric effects for spin-precessing binaries into the SEOBNRv5PHM waveform model

Abstract

Gravitational waves from spin-precessing binaries exhibit equatorial asymmetries absent in non-precessing systems, leading to net linear momentum emission and contributing to the remnant's recoil. This effect, recently incorporated into only a few waveform models, is crucial for accurate recoil predictions and improved parameter estimation. We present an upgrade to the SEOBNRv5PHM model -- SEOBNRv5PHM_w/asym -- which includes equatorial asymmetric contributions to the l=m<=4 waveform modes in the co-precessing frame. The model combines post-Newtonian inputs with calibrated amplitude and phase corrections and a phenomenological merger-ringdown description, tuned against 1523 quasi-circular spin-precessing numerical relativity waveforms and single-spin precessing test-body plunging-geodesic waveforms. We find that SEOBNRv5PHM_w/asym improves the agreement with NR waveforms across inclinations, with median unfaithfulness reduced by up to 50% compared to SEOBNRv5PHM, and achieves 30-60% lower unfaithfulness than IMRPhenomXPNR and 76-80% lower than TEOBResumS_Dali. The model significantly improves the prediction of the recoil velocity, reducing the median relative error with numerical relativity from 70% to 1%. Bayesian inference on synthetic injections demonstrates improved recovery of spin orientations and mass parameters, and a reanalysis of GW200129 shows a threefold increase in the spin-precessing Bayes factor, highlighting the importance of these effects for interpreting spin-precessing events.

Figures (22)

• Figure 1: Distribution of the unfaithfulness between symmetrized spin-precessing NR waveforms (NRSym) from the SXS catalog and two alternatives: the original NR waveforms (with antisymmetric components) (NR, blue), and the SEOBNRv5PHM model without antisymmetric modes (orange). The unfaithfulness is computed mode by mode.
• Figure 2: Comparison of PN and NR antisymmetric modes for an example case with parameters $q=2$, $\chi_{1,\perp}=\chi_{2,\perp}=0.85$ (SXS:BBH:1207). Top row: amplitude of the antisymmetric modes. Bottom row: wave-frequency of the antisymmetric modes in the co-rotating frame. Solid colored lines denoted NR results, and dashed lines PN results. Solid black line in the bottom panel denotes the PN orbital frequency.
• Figure 3: Waveform reconstruction comparison for an example NR simulation SXS:BBH:0963 (with parameters $q=1$,$\chi_{1,\perp}=\chi_{2,\perp}=0.8$). Top: real part of the co-precessing antisymmetric (2,2) mode; middle: absolute value of the co-precessing antisymmetric (2,2) mode; bottom: phase derivative of the co-precessing antisymmetric (2,2) mode. The NR simulation is shown in blue. The orange curve corresponds to the evaluation of $h_{22}^{\rm asym,PN}$, while the dotted green curve has an additional amplitude correction factor and non-quasi-circular correction for the phase. The attachment time is shown as a vertical dashed black line, and after that time the green curve corresponds to the merger-ringdown model described in Sec.\ref{['sec:mrd_antisym']}.
• Figure 4: Comparison of symmetric and antisymmetric $\ell=m$ (with $\ell\leq 4$) modes for the NR simulation SXS:BBH:1216 (with parameters $q=2$, $\chi_{1,\perp}=0.85$, $\chi_{\rm{eff}}=-0.25$). Top panel: amplitude of the modes. Bottom panel: wave-frequency of the modes. Solid lines denote symmetric modes, and dashed lines antisymmetric modes.
• Figure 5: Histogram of the maximum SNR-weighted averaged unfaithfulness with the NR SXS dataset across a total mass range $[20,300]\,M_{\odot}$, for four source inclinations $\iota_s = \{0,\pi/6,\pi/3,\pi/2\}$. Vertical dashed lines mark the median of each distribution.