  In LambdaCDM, massive satellites are dragged into the disk-plane by dynamical
friction where they dissolve into a stellar thick disk and a more massive dark
matter disk. The distinctive kinematics of the dark disk matches the stars that
also entered in the satellites. The lower velocities of the dark disk with
respect to the Earth enhances detection rates at low recoil energy. For WIMP
masses > 50 GeV/c^2, the detection rate increases by up to a factor of 3 in the
5 - 20 keV recoil energy range. Comparing this with rates at higher energy will
improve constraints on the WIMP mass, particularly for masses > 100 GeV/c^2.
The annual modulation signal of the dark disk is significantly boosted and its
modulation phase is shifted by ~3 weeks relative to the dark halo. The
variation of the observed phase with recoil energy can also be used to
determine the WIMP mass once the dark disk properties are fixed by future
astronomical surveys. The constraints on the WIMP interaction cross section
from current experiments improve by factors of 1.4 to 3.5 when a typical
contribution from the dark disk is included.
