Impact of non-Maxwellian κ velocity distributions on the direct detection of light dark matter

We investigate the impact of non-Maxwellian dark matter velocity distributions on the direct detection of light dark matter particles using silicon and germanium solid-state detectors at the Modane underground laboratory. Deviations from thermal equilibrium in the galactic dark matter halo are modeled with a generalized kappa distribution, and we calculate annual modulation signals and predicted mean interaction event rates for dark matter masses. We find that the interaction event rate depends strongly on both the dark matter mass and the κ index, especially in the sub-GeV regime where detectable nuclear recoils are highly sensitive to the high-velocity tail of the velocity distribution. Finite kappa distributions yield higher interaction event rates for low-mass dark matter particles, whereas the Maxwellian limit becomes increasingly favored as the dark matter mass increases. The predicted interaction event rate in the nearly Maxwellian limit (κ=60) is approximately 5.8 times larger than that obtained for a strongly non-equilibrium halo (κ=1.6). We identify an optimal κ value, denoted by κₘₐₓ, that maximizes the interaction event rate. It follows the empirical relation κₘₐₓ=a(1-mDmₐₛ)^β, for both silicon and germanium detectors. These masses mark the transition above which the Maxwellian distribution provides the highest interaction event rate. Our results demonstrate that realistic non-equilibrium halo models can significantly modify predicted interaction rates and should be incorporated into the interpretation and design of current and future direct dark matter detection experiments.