Not All Resonances Are Created Equal: Prioritizing Tidal Resonances in EMRIs

Abstract: Tidal perturbations from nearby compact objects can drive resonant "kicks" in extreme-mass-ratio inspirals (EMRIs), imprinting potentially detectable phase shifts in LISA-band gravitational waveforms. We provide a systematic survey of these tidal resonances across EMRI parameter space in the weak-tide, three-body hierarchy, treating the perturber as stationary on the resonance timescale. For generic Kerr orbits we compute (i) resonance contours in $(p,e,x)$ that locate where each $(n,k,m)$ resonance is encountered, (ii) the associated resonance duration, and (iii) the jump amplitudes in the angular momentum $L_z$ and the Carter constant $Q$ (with $ΔE$ vanishing by time-translation symmetry in the stationary model). Combining jump amplitudes with resonance durations, we construct a practical ranking of the resonances most relevant for waveform modeling, while emphasizing that even modest resonances may still be important through their influence on the phase at which subsequent resonances are entered. All contour and jump data are publicly available.