Lasting mEMRIs: Signatures of Multiple Black Hole Extreme Mass Ratio Inspirals from AGN discs

Encounters of stellar-mass black holes (sBH) in active galactic nuclei discs naturally form mean-motion resonances of sBH pairs. These mean-motion resonances can be broken close to the central supermassive black hole when gravitational-wave emission dominates over gas torques. We derive a simple condition that depends only on the sBH mass ratio and the resonance index for which a pair of sBH in a mean-motion resonance will remain intact and can be detectable as a multiple Extreme-Mass-Ratio-Inspirals (mEMRIs) in the LISA band. We present for the first time the gravitational-wave strain signatures of a pair of co-migrating sBH in mean-motion resonance, including additional gravitational-wave harmonics associated with orbital conjunctions of the individual EMRIs. The frequency evolution and the associated chirp mass is degenerate with isolated EMRIs of different masses. However, the mEMRI mass ratio is quantised by the resonance order and is larger than the true mass ratio. The degeneracy can be broken if the true sBH mass ratio can be inferred from individual strain amplitudes. We argue that mEMRIs should be common if disc driven EMRIs are to be detected by LISA, with about 10 mEMRIs per year in the local universe (z 0.2), highlighting the need to model mEMRI systems in future LISA data analysis.