Median recoil direction as a WIMP directional detection signal

Direct detection experiments have reached the sensitivity to detect dark matter weakly interacting massive particles (WIMPs). Demonstrating that a putative signal is due to WIMPs, and not backgrounds, is a major challenge, however. The direction dependence of the WIMP scattering rate provides a potential WIMP 'smoking gun'. If the WIMP distribution is predominantly smooth, the Galactic recoil distribution is peaked in the direction opposite to the direction of Solar motion. Previous studies have found that, for an ideal detector, of order 10 WIMP events would be sufficient to reject isotropy, and rule out an isotropic background. We examine how the median recoil direction could be used to confirm the WIMP origin of an anisotropic recoil signal. Specifically, we determine the number of events required to confirm the direction of solar motion as the median inverse recoil direction at 95% confidence. We find that for zero background 31 events are required, a factor of {approx}2 more than are required to simply reject isotropy. We also investigate the effect of a nonzero isotropic background. As the background rate is increased the number of events required increases, initially fairly gradually and then more rapidly, once the signal becomes subdominant. We also discuss the effect of features in the speed distribution at large speeds, as found in recent high resolution simulations, on the median recoil direction.