Repeated tidal resonances from an inspiralling EMRI secondary shift a dark matter particle's semi-major axis by less than one percent, leaving the DM spike nearly intact in the non-overlapping-orbit regime.
As the angle variables other than χ de- fined in (29) evolve rapidly, they are irrelevant for long- term evolution
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Resonant DM scattering in the galactic center under the influence of EMRI
Repeated tidal resonances from an inspiralling EMRI secondary shift a dark matter particle's semi-major axis by less than one percent, leaving the DM spike nearly intact in the non-overlapping-orbit regime.