Anisotropic q-Gaussian velocity distributions in LambdaCDM halos

The velocity distribution function (VDF) of dark matter (DM) halos in $\Lambda$CDM dissipationless cosmological simulations, which must be non-separable in its radial and tangential components, is still poorly known. We present the first single-parameter, non-separable, anisotropic model for the VDF in $\Lambda$CDM halos, built from an isotropic $q$-Gaussian (Tsallis) VDF of the isotropic set of dimensionless spherical velocity components (after subtraction of streaming motions), normalized by the respective velocity dispersions. We test our VDF on 90 cluster-mass halos of a dissipationless cosmological simulation. Beyond the virial radius, $r_{\rm vir}$, our model VDF adequately reproduces that measured in the simulated halos, but no $q$-Gaussian model can adequately represent the VDF within $r_{\rm vir}$, as the speed distribution function is then flatter-topped than any $q$-Gaussian can allow. Nevertheless, our VDF fits significantly better the simulations than the commonly used Maxwellian (Gaussian) distribution, at virtually all radii within $5\,r_{\rm vir}$. Within 0.4 (1) $r_{\rm vir}$, the non-Gaussianity index $q$ is (roughly) linearly related to the slope of the density profile and also to the velocity anisotropy profile. We provide a parametrization of the modulation of $q$ with radius for both the median fits and the fit of the stacked halo. At radii of a few percent of $r_{\rm vir}$, corresponding to the Solar position in the Milky Way, our best-fit VDF, although fitting better the simulations than the Gaussian one, overproduces significantly the fraction of high velocity objects, indicating that one should not blindly use these $q$-Gaussian fits to make predictions on the direct detection rate of DM particles.