Using N-body simulations of the Large Magellanic Cloud (LMCs) passage through the Milky Way (MW), tailored to reproduce observed kinematic properties of both galaxies, we show that the high-speed tail of the Solar Neighborhood dark matter distribution is overwhelmingly of LMC origin. Two populations contribute at high speeds: 1) Particles that were once bound to the LMC, and 2) MW halo particles that have been accelerated owing to the response of the halo to the recent passage of the LMC. These particles reach speeds of 700-900 km/s with respect to the Earth, above the local escape speed of the MW. The high-speed particles follow trajectories similar to the Solar reflex motion, with peak velocities reached in June. For low-mass dark matter, these high-speed particles can dominate the signal in direct-detection experiments, extending the reach of the experiments to lower mass and elastic scattering cross sections even with existing data sets. Our study shows that even non-disrupted MW satellite galaxies can leave a significant dark-matter footprint in the Solar Neighborhood.
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