Triaxial haloes and particle dark matter detection

This paper presents the properties of a family of scale-free triaxial haloe s. We adduce arguments to suggest that the velocity ellipsoids of such mode ls are aligned in conical coordinates. We provide an algorithm to find the set of conically aligned velocity second moments that support a given densi ty against the gravity field of the halo. The case of the logarithmic ellip soidal model - the simplest triaxial generalization of the familiar isother mal sphere - is examined in detail. The velocity dispersions required to ho ld up the self-consistent model are analytic. The velocity distribution of the dark matter can be approximated as a triaxial Gaussian with semiaxes eq ual to the velocity dispersions. There are roughly 20 experiments worldwide that are searching for evidence of scarce interactions between weakly interacting massive-particle dark mat ter (WIMP) and detector nuclei. The annual modulation signal, caused by the Earth's rotation around the Sun, is a crucial discriminant between WIMP ev ents and the background. The greatest rate is in June, the least in Decembe r. We compute the differential detection rate for energy deposited by the r are WIMP-nucleus interactions in our logarithmic ellipsoidal halo models. T riaxiality and velocity anisotropy change the total rate by up to similar t o 40 per cent, and have a substantial effect on the amplitude of the annual modulation signal. The overall rate is greatest, but the amplitude of the modulation is weakest, in our radially anisotropic halo models. Even the si gn of the signal can be changed. Restricting attention to low energy events , the models predict that the maximum rate occurs in December, and not in J une.