Directional Statistics for WIMP direct detection II: 2-d read-out

The direction dependence of the WIMP direct detection rate provides a powerful tool for distinguishing a WIMP signal from possible backgrounds. We study the the number of events required to discriminate a WIMP signal from an isotropic background for a detector with 2-d read-out using non-parametric circular statistics. We also examine the number of events needed to i) detect a deviation from rotational symmetry, due to flattening of the Milky Way halo and ii) detect a deviation in the mean direction due to a tidal stream. If the senses of the recoils are measured then of order 20-70 events (depending on the plane of the 2-d read out) will be sufficient to reject isotropy of the raw recoil angles at 90% confidence. If the senses can not be measured these number increase by roughly two orders of magnitude (compared with an increase of one order of magnitude for the case of full 3-d read-out). The distributions of the reduced angles, with the (time dependent) direction of solar motion subtracted, are far more anisotropic, however, and if the isotropy tests are applied to these angles then the numbers of events required are similar to the case of 3-d read-out. A deviation from rotational symmetry will only be detectable if the Milky Way halo is significantly flattened. The deviation in the mean direction due to a tidal stream is potentially detectable, however, depending on the density and direction of the stream.