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Orbital anisotropy in cosmological haloes revisited

The velocity anisotropy of particles inside dark matter (DM) haloes is an important physical quantity, which is required for the accurate modelling of mass profiles of galaxies and clusters of galaxies. It is typically measured using the ratio of the radial-to-tangential velocity dispersions at a given distance from the halo centre. However, this measure is insufficient to describe the dynamics of realistic haloes, which are typically quite elongated. Studying the velocity distribution in massive DM haloes in cosmological simulations, we find that in the inner parts of the haloes the local velocity ellipsoids are strongly aligned with the major axis of the halo, the alignment being stronger for more relaxed haloes. In the outer regions of the haloes, the alignment becomes gradually weaker and the orientation is more random. These two distinct regions of different degree of the alignment coincide with two characteristic regimes of the DM density profile: shallower and steeper than ρr^{-2}. This alignment of the local velocity ellipsoids requires reinterpretation of features found in measurements based on the spherically averaged ratio of the radial-to-tangential velocity dispersions. In particular, we show that the velocity distribution in the central halo regions is highly anisotropic. For cluster-size haloes with mass 10^{14}-10^{15} h^-1 Msun, the velocity anisotropy along the major axis is nearly independent of radius and is equal to β=1-σ^2_{perp}/σ^2_{radial}=0.4, which is significantly larger than the previously estimated spherically averaged velocity anisotropy. The alignment of density and velocity anisotropies, and the radial trends may also have some implications for the mass modelling based on kinematical data of such objects as galaxy clusters or dwarf spheroidals, where the orbital anisotropy is a key element in an unbiased mass inference.