Directional dark matter by polar angle direct detection and application of columnar recombination

We report a systematic study on the directional sensitivity of a direct dark matter detector that detects the polar angle of a recoiling nucleus. A weakly interacting massive particle (WIMP)-mass independent method is used to obtain the sensitivity of a general detector in an isothermal galactic dark matter halo. By using two-dimensional distributions of energy and polar angle, a detector without head-tail information with 6.3 times the statistics is found to achieve the same performance level as a full three-dimensional tracking dark matter detector. Optimum operation orientations are obtained for various experimental configurations, with detectors that are space- or Earth-fixed, have head-tail capability or not, and use energy information or not. Earth-fixed detectors are found to have best sensitivity when the polar axis is oriented at a 45 degree angle from the Earth's pole. With background contamination that mimics the WIMP signal's energy distribution, the performance is found to decrease at a rate less than the decrease of signal purity. The WIMP-mass dependence of the performance of a detector with various energy thresholds that uses gaseous xenon as target material is reported. We find that with a $5\times 10^{-46} \mathrm{cm}^2$ spin-independent WIMP-nucleon cross-section and a 30 GeV WIMP, a $770$ kg$\cdot$year's exposure with a polar detector of 10 keV threshold can make a three sigma discovery of directional WIMPs in the isothermal galactic dark matter halo. For a columnar recombination detector, experimental considerations are discussed.