  Tidal stripping of dark matter from subhalos falling into the Milky Way
produces narrow, cold tidal streams as well as more spatially extended "debris
flows" in the form of shells, sheets, and plumes. Here we focus on the debris
flow in the Via Lactea II simulation, and show that this incompletely
phase-mixed material exhibits distinctive high velocity behavior. Unlike tidal
streams, which may not necessarily intersect the Earth's location, debris flow
is spatially uniform at 8 kpc and thus guaranteed to be present in the dark
matter flux incident on direct detection experiments. At Earth-frame speeds
greater than 450 km/s, debris flow comprises more than half of the dark matter
at the Sun's location, and up to 80% at even higher speeds. Therefore, debris
flow is most important for experiments that are particularly sensitive to the
high speed tail of the dark matter distribution, such as searches for light or
inelastic dark matter or experiments with directional sensitivity. We show that
debris flow yields a distinctive recoil energy spectrum and a broadening of the
distribution of incidence direction.
