Inconsistency in retrograde-spin treatment
I think I found an inconsistency in how retrograde-spin cases are treated in SEOBNRv5PHM:
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SEOBNRv5PHM uses the HBR fit for precessing final spin. This fit returns the magnitude of the spin, not the signed spin like the corresponding aligned-spin fit.
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To account for this SEOBNRv5PHM takes inspiration from IMRPhenomTPHM https://git.ligo.org/lscsoft/lalsuite/-/blob/master/lalsimulation/lib/LALSimIMRPhenomTPHM_EulerAngles.c#L1271 and takes the sign from the non-precessing fit with chi1_LN, chi2_LN to distinguish prograde- and retrograde-spin cases, before computing the QNMs. See https://git.ligo.org/waveforms/software/pyseobnr/-/blob/main/pyseobnr/eob/dynamics/postadiabatic_C_prec.pyx?ref_type=heads#L101
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For the post-merger extension of the Euler angles, one also multiplies the precession rate by -1 for retrograde-spin cases (inspired by the implementation of SEOBNRv4PHM https://git.ligo.org/lscsoft/lalsuite/-/blob/master/lalsimulation/lib/LALSimIMRSpinPrecEOBv4P.c?ref_type=heads#L3955, see here https://git.ligo.org/waveforms/software/pyseobnr/-/blob/main/pyseobnr/eob/utils/utils_precession_opt.py?ref_type=heads#L526). However in this case the distinction between prograde and retrograde spins uses Jhat dot Lhat at the attachment time, which is not equivalent to what is done for the final spin. The difference is especially relevant for systems close to transitional precession at merger.
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In SEOBNRv4PHM the sign of Jhat dot Lhat is used in both cases (see https://git.ligo.org/waveforms/reviews/seobnrv4p/-/wikis/Aligned-spin-limit). The motivation of flip in the precession rate was to preserve the sign of the derivative of the Euler angles when the QNMs change sign. A change of sign in the derivative is unphysical as this would correspond to the dominant direction of emission starting to precess in the opposite direction before vs after the merger and this can currently happen in SEOBNRv5PHM.
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A possible fix is to use Jhat dot Lhat to consistently flip sign (as in SEONRv4PHM). See this Fig. for an example of the difference (for the case considered in https://git.ligo.org/waveforms/reviews/seobnrv4p/-/wikis/Aligned-spin-limit with q=6, chi_1 =(-0.0131941810847,0.0676539715676,-0.646272606477), chi_2 = (0.,0.,0.) ). In practice the difference in the waveform is very small in this case.
This change affects ~1.5% of cases (taking 10000 points uniform in q between 1 and 100 and isotropic in spins) - mostly for negative chi1z.
