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 not spherical and 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 : a shallow inner cusp and a steep outer profile that are separated by a characteristic radius at which the density declines as \rho \propto r ^ { -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 } { { M _ { \odot } } } } } , the velocity anisotropy along the major axis is nearly independent of radius and is equal to \beta = 1 - \sigma ^ { 2 } _ { perp } / \sigma ^ { 2 } _ { radial } \approx 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 .