Reconstructing the Velocity Distribution of WIMPs from Direct Dark Matter Detection Data

Weakly interacting massive particles (WIMPs) are one of the leading candidates for dark matter. Currently, the most promising method to detect many different WIMP candidates is the direct detection of the recoil energy deposited in a low-background laboratory detector due to elastic WIMP-nucleus scattering. So far the usual procedure has been to predict the event rate of direct detection of WIMPs based on some model(s) of the galactic halo. The aim of our work is to invert this process. That is, we study what future direct detection experiment can teach us about the WIMP halo. As the first step we consider a time-averaged recoil spectrum, assuming that no directional information exists. We develop a method to construct the (time-averaged) one-dimensional velocity distribution function from this spectrum. Moments of this function, such as the mean velocity and velocity dispersion of WIMPs, can also be obtained directly from the recoil spectrum. The only input needed in addition to a measured recoil spectrum is the mass of the WIMP; no information about the scattering cross section or WIMP density is required.