Directional recoil rates for WIMP direct detection

New techniques for the laboratory direct detection of dark matter weakly interacting massive particles (WIMPs) are sensitive to the recoil direction of the struck nuclei.We compute and compare the directional recoil rates dR/d cosθ, (where θ is the angle measured from a reference direction in the sky) for several WIMP velocity distributions including the standard dark halo and anisotropic models such as Sikivie's late-infall halo model and logarithmic-ellipsoidal models. Since some detectors may be unable to distinguish the beginning of the recoil track from its end (lack of head-tail discrimination), we introduce a folded directional recoil rate dR=dj cosθ|, where |cosθ| does not distinguish the head from the tail of the track. We compute the CS2 and CF4 exposures required to distinguish a signal from an isotropic background noise, and find that dR=d| cosθ| is effective for the standard dark halo and some but not all anisotropic models.