  The velocity distribution function of dark matter particles is expected to
show significant departures from a Maxwell-Boltzmann distribution. This can
have profound effects on the predicted dark matter - nucleon scattering rates
in direct detection experiments, especially for dark matter models in which the
scattering is sensitive to the high velocity tail of the distribution, such as
inelastic dark matter (iDM) or light (few GeV) dark matter (LDM), and for
experiments that require high energy recoil events, such as many directionally
sensitive experiments. Here we determine the velocity distribution functions
from two of the highest resolution numerical simulations of Galactic dark
matter structure (Via Lactea II and GHALO), and study the effects for these
scenarios. For directional detection, we find that the observed departures from
Maxwell-Boltzmann increase the contrast of the signal and change the typical
direction of incoming DM particles. For iDM, the expected signals at direct
detection experiments are changed dramatically: the annual modulation can be
enhanced by more than a factor two, and the relative rates of DAMA compared to
CDMS can change by an order of magnitude, while those compared to CRESST can
change by a factor of two. The spectrum of the signal can also change
dramatically, with many features arising due to substructure. For LDM the
spectral effects are smaller, but changes do arise that improve the
compatibility with existing experiments. We find that the phase of the
modulation can depend upon energy, which would help discriminate against
background should it be found.
