The median recoil direction as a WIMP directional detection signal
  Direct detection experiments have reached the sensitivity required to detect
dark matter 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 reject the null hypothesis that the median direction is
random (corresponding to an isotropic Galactic recoil distribution) at 95%
confidence. We find that for zero background 31 events are required, a factor
of roughly 2 more than are required to simply reject isotropy. We also
investigate the effect of a non-zero 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.
