Discrimination of anisotropy in dark matter velocity distribution with directional detectors

Directional detection of dark matter has sensitivity for both recoil energy and direction of nuclear recoil. It opens the way to measure local velocity distribution of dark matter. In this paper, we study possibility to discriminate isotropic distribution and anisotropic one suggested by a N-body simulation with directional detector. Numerical simulation is performed for two cases according to the detectors, one corresponds to angular histogram and the other is energy-angular distribution of the signals. We reveal that the anisotropy of velocity distribution can be discriminated at 90% C.L. with chi-squared test if O($10^4$) signals are obtained.