Derivation of the anisotropy profile, constraints on the local velocity dispersion, and implications for direct detection

We study the implications of a pseudo-phase-space density power-law for the anisotropy profile of a Milky Way-like dark matter halo. Requiring that the anisotropy parameter does not take non-physical values within the virial radius places a maximum value on the local radial velocity dispersion. For a plausible range of halo parameters, it is possible to take a local total velocity dispersion of up to about $300\,\mathrm{km/s}$. Making this choice uniquely specifies the anisotropy and dispersion profiles. We introduce a way to model the local velocity distribution that incorporates this anisotropy and study the impact on direct detection.