  We use the state-of-the-art high-resolution cosmological simulations by
IllustrisTNG to derive the velocity distribution and local density of dark
matter in galaxies like our Milky Way and find a substantial spread in both
quantities. Next we use our findings to examine the sensitivity to the dark
matter velocity profile of underground searches using electron scattering in
germanium and silicon targets. We find that sub-GeV dark matter search is
strongly affected by these uncertainties, unlike nuclear recoil searches for
heavier dark matter, especially in multiple electron-hole modes, for which the
sensitivity to the scattering cross-section is also weaker. Therefore, by
improving the sensitivity to lower ionization thresholds not only projected
sensitivities will be boosted but also the dependence on the astrophysical
uncertainties will become significantly reduced.
