Resonant DM scattering in the galactic center under the influence of EMRI

Abstract

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 (BH) 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 examine this possibility, we explicitly derive the interaction Hamiltonian for tidal resonances and conducted numerical calculations.