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 non-zero 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 (LVK). 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 LVK 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 $\sim 50$ detections, and a binary with significant evidence for higher-order multipoles will occur once in every $\sim 70$ observations. However, we emphasise 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 $\sim 2\%$ of events with detectable precession and higher-order multipole moments will likely be consistent with the data.