Boosted Dark Matter from Sagittarius A$^\star$

It was recently demonstrated that black hole binaries can gravitationally accelerate ambient dark matter (DM), producing a continuous flux of particles with velocities far exceeding those of the galactic halo. We extend this analysis to the Milky Way's nuclear star cluster, where stellar-mass black holes are expected to orbit in close proximity to the supermassive black hole Sagittarius A$^\star$. Using numerical simulations, we compute the flux of gravitationally-boosted DM sourced by this region. Because of the high DM density and large population of black holes orbiting deep within Sagittarius A$^\star$'s gravitational potential, the resulting DM ejecta attain substantially higher rates and energies compared to galactic black hole binaries, with simulated particles reaching velocities of up to $\sim 25,\!000 \, \rm km/s$. We find that the nuclear star cluster is therefore the dominant source of gravitationally-boosted DM in the Milky Way. Even under conservative assumptions about the DM profile in the inner galaxy, the ejected DM flux from this region can render large-volume DM detectors competitive with lower-threshold experiments in the sub-GeV mass range, independently of the underlying DM particle model. The gravitational nature of the boost also opens up a sizable detection window into heavy inelastic DM scenarios that are otherwise largely inaccessible to conventional halo DM searches.