Resonant Capture of Stars by Black Hole Binaries: Extreme Eccentricity Excitation

Massive black hole (MBH) binaries in galactic nuclei are one of the leading sources of $\sim$ mHz gravitational waves (GWs) for future missions such as $\rm{\textit{LISA}}$. However, the poor sky localization of GW interferometers will make it challenging to identify the host galaxy of MBH mergers absent an electromagnetic counterpart. One such counterpart is the tidal disruption of a star that has been captured into mean motion resonance with the inspiraling binary. Here we investigate the production of tidal disruption events (TDEs) through capture into, and subsequent evolution in, orbital resonance. We examine the full nonlinear evolution of planar autoresonance for stars that lock in to autoresonance with a shrinking MBH binary. Capture into the 2:1 resonance is guaranteed for any realistic astrophysical parameters (given a relatively small MBH binary mass ratio), and the captured star eventually attains an eccentricity $e\approx 1$, leading to a TDE. Stellar disks can be produced around MBHs following an active galactic nucleus episode, and we estimate the TDE rates from resonant capture produced when a secondary MBH begins inspiralling through such a disk. In some cases, the last resonant TDE can occur within a decade of the eventual $\rm{\textit{LISA}}$ signal, helping to localize the GW event.