Rarity of precession and higher-order multipoles in gravitational waves from merging binary black holes

The latest binary black hole population estimates argue for a subpopulation of unequal component mass binaries with spins that are likely small but isotropically distributed. This implies a nonzero probability of detecting spin-induced orbital precession and higher order multipole moments in the observed gravitational-wave signals. In this work we directly calculate the probability for precession and higher-order multipoles in each significant gravitational-wave candidate observed by the LIGO-Virgo-KAGRA collaborations. We find that only one event shows substantial evidence for precession: GW200129_065458, and two events show substantial evidence for higher-order multipoles: GW190412 and GW190814; any evidence for precession and higher-order multipole moments in other gravitational-wave signals is consistent with random fluctuations caused by noise. We then compare our observations with expectations from population models, and confirm that current population estimates from the LIGO-Virgo-KAGRA collaborations accurately predict the number of observed events with significant evidence for precession and higher-order multipoles. In particular, we find that this population model predicts that a binary with significant evidence for precession will occur once in every ∼50 detections, and a binary with significant evidence for higher-order multipoles will occur once in every ∼70 observations. However, we emphasize that since substantial evidence for precession and higher-order multipoles have only been observed in three events, any population model that includes a subpopulation of binaries yielding ∼2% of events with detectable precession and higher-order multipole moments will likely be consistent with the data.