  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.
