Simulations of the 3-Dimensional Velocity Distribution of Halo Weakly Interacting Massive Particles for Directional Dark Matter Detection Experiments

In this paper, as a preparation of developing data analysis procedures for using 3-dimensional information offered by directional Dark Matter (DM) detection experiments, we study the patterns of the angular distribution of the Monte Carlo-generated 3-D velocity of halo Weakly Interacting Massive Particles (WIMPs) as well as apply the Bayesian fitting technique to reconstruct the radial distribution of the 3-D WIMP velocity. Besides the diurnal modulation of the angular WIMP velocity distribution, the so-called directionality of DM signals proposed in literature, we will also demonstrate possible annual modulations of both of the angular and the radial distributions of the 3-D WIMP velocity. Our Bayesian reconstruction results of (the annual modulation of) the radial WIMP velocity distribution will also be discussed in detail. For readers reference, the angular distribution patterns of the 3-D WIMP velocity in the laboratory (location)-dependent reference frames of several underground laboratories are given in the Appendix.