Inverted dipole feature in directional detection of exothermic dark matter

Directional dark matter detection attempts to measure the direction of motion of nuclei recoiling after having interacted with dark matter particles in the halo of our Galaxy. Due to Earth’s motion with respect to the Galaxy, the dark matter flux is concentrated around a preferential direction. An anisotropy in the recoil direction rate is expected as an unmistakable signature of dark matter. The average nuclear recoil direction is expected to coincide with the average direction of dark matter particles arriving to Earth. Here we point out that for a particular type of dark matter, inelastic exothermic dark matter, the mean recoil direction as well as a secondary feature, a ring of maximum recoil rate around the mean recoil direction, could instead be opposite to the average dark matter arrival direction. Thus, the detection of an average nuclear recoil direction opposite to the usually expected direction would constitute a spectacular experimental confirmation of this type of dark matter.