A census of transient orbital resonances encountered during binary inspiral

Transient orbital resonances have recently been identified as potentially important to the inspiral of small bodies into large black holes. These resonances occur as the inspiral evolves through moments in which two fundamental orbital frequencies, $\Omega_\theta$ and $\Omega_r$, are in a small integer ratio to one another. Previous work has demonstrated that a binary's parameters are "kicked" each time the inspiral passes through a resonance, changing the orbit's characteristics relative to a model that neglects resonant effects. In this paper, we use exact Kerr geodesics coupled to an accurate but approximate model of inspiral to survey orbital parameter space and estimate how commonly one encounters long-lived orbital resonances. We find that the most important resonances last for a few hundred orbital cycles at mass ratio $10^{-6}$, and that resonances are almost certain to occur during the time that a large mass ratio binary would be a target of gravitational-wave observations. Resonances appear to be ubiquitous in large mass ratio inspiral, and to last long enough that they are likely to affect binary evolution in observationally important ways.