Resonant DM scattering in the Galactic Center under the influence of extreme mass ratio inspirals

Dark matter (DM) search is one of the greatest challenges in physics. If DM consists of particles, it may form a spike around supermassive black holes prevalent in galaxy centers. This spike could be potentially observed by altering the orbits of extreme mass ratio inspirals (EMRIs), one of LISA's main targets. Meanwhile, the effects of EMRI on the DM spike have also been explored. In this study, we focus on the tidal resonances between DM particles and EMRI secondary. As the EMRI orbit evolves via gravitational wave backreaction, each DM particle experiences a significant number of resonances. Although the effect of each individual resonance is small, their cumulative impact might significantly alter the DM particle's orbit. To test this possibility, we derived an explicit form of the interaction Hamiltonian and carried out numerical simulations on generic Kerr orbits with nonzero eccentricity and inclination---cases not previously explored extensively. Extending our analysis to unprecedentedly high resonance orders, we quantified the exponential decay of higher-order resonance amplitudes. These results demonstrate that tidal resonances exert an extremely limited influence on the DM spike.