Adding equatorial-asymmetric effects for spin-precessing binaries into the seobnrv5phm waveform model

Gravitational waves from spin-precessing binaries exhibit equatorial asymmetries absent in nonprecessing 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 v5 model— <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mrow> <a:msub> <a:mrow> <a:mi mathsize="small">SEOBNRv</a:mi> <a:mn>5</a:mn> <a:mi mathsize="small">PHM</a:mi> </a:mrow> <a:mrow> <a:mi mathvariant="normal">w</a:mi> <a:mo>/</a:mo> <a:mi>asym</a:mi> </a:mrow> </a:msub> </a:mrow> </a:math> —which includes equatorial asymmetric contributions to the <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"> <f:mo>ℓ</f:mo> <f:mo>=</f:mo> <f:mi>m</f:mi> <f:mo>≤</f:mo> <f:mn>4</f:mn> </f:math> 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 quasicircular spin-precessing numerical relativity waveforms and single-spin-precessing test-body plunging-geodesic waveforms. We find that <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"> <h:mrow> <h:msub> <h:mrow> <h:mi mathsize="small">SEOBNRv</h:mi> <h:mn>5</h:mn> <h:mi mathsize="small">PHM</h:mi> </h:mrow> <h:mrow> <h:mi mathvariant="normal">w</h:mi> <h:mo>/</h:mo> <h:mi>asym</h:mi> </h:mrow> </h:msub> </h:mrow> </h:math> improves the agreement with numerical relativity waveforms across inclinations, with median unfaithfulness reduced by up to 50% compared to v5, and achieves 30%–60% lower unfaithfulness than henom and 76%–80% lower than esum_ali. 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.