This paper presents the properties of a family of scale-free triaxial haloes. We adduce arguments to suggest that the velocity ellipsoids of such models are aligned in conical coordinates. We provide an algorithm to find the set of conically aligned velocity second moments that support a given density against the gravity field of the halo. The case of the logarithmic ellipsoidal model –the simplest triaxial generalization of the familiar isothermal sphere– is examined in detail. The velocity dispersions required to hold up the self-consistent model are analytic. The velocity distribution of the dark matter can be approximated as a triaxial Gaussian with semiaxes equal to the velocity dispersions.
There are roughly 20 experiments worldwide that are searching for evidence of scarce interactions between weakly interacting massive-particle dark matter (WIMP) and detector nuclei. The annual modulation signal, caused by the Earth's rotation around the Sun, is a crucial discriminant between WIMP events and the background. The greatest rate is in June, the least in December. We compute the differential detection rate for energy deposited by the rare WIMP–nucleus interactions in our logarithmic ellipsoidal halo models. Triaxiality and velocity anisotropy change the total rate by up to ∼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 sign 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 June.