  We discuss a novel dark matter signature relevant for directional detection
of Weakly Interacting Massive Particles (WIMPs). For heavy enough WIMPs and low
enough recoil energies, the maximum of the recoil rate is not in the direction
of the average WIMP arrival direction but in a ring around it at an angular
radius that increases with the WIMP mass and can approach 90 degrees at very
low energies. The ring is easier to detect for smaller WIMP velocity dispersion
and larger average WIMP velocities relative to the detector. In principle the
ring could be used as an additional indication of the WIMP mass range.
