Investigating the effect of in-plane spin directions for Precessing BBH systems

Morphology of coalescing BBH waveforms are affected by its spins. Waveform models built for inference of source parameters have several in-built approximations. In current precessing IMRPhenom and SEOBNR waveform models, systems with the same spin magnitude but varying orientation of spins projected on the orbital plane are effectively mapped to the same system (bar an overall phase change) and the asymmetry due to precession between the $+m$ and $-m$ modes is not modelled. In this study, we investigate the validity of these approximations by generating numerical relativity (NR) simulations of single-spin NR systems with varying in-plane spin directions (including several superkick configurations) and provide an estimate of the SNR at which the effect of varying in-plane spin directions would be measurable. This is done computing the match between these waveforms and using these match values to estimate the distinguishability SNR. We also use NR waveforms with different spin magnitudes to compare the measurability of spin magnitude vs. in-plane spin direction. We find that the in-plane spin direction could be measurable at SNRs accessible by current generation detectors, with the distinguishability SNR of varying in-plane spins comparable to or lower than varying the in-plane spin magnitude. We then remove the mode-asymmetry content from the waveforms and find that, i) removing mode-asymmetry increases the SNR at which in-plane spin direction can be measured and ii) not modelling mode-asymmetry will lead to measurement biases. The SNRs that we see at which the in-plane spins would be measurable and at which mode-asymmetric content impacts the measurements are the SNRs at which precession would be measurable, and we therefore conclude that modelling in-plane spin direction and mode-asymmetry effects is necessary for unbiassed measurements of precession.