Dark matter ( DM ) halos formed in CDM cosmologies seem to be characterized by a power law phase- space density profile .
The density of the DM halos is often fitted by the NFW profile but a better fit is provided by the Sersic fitting formula .
These relations are empirically derived from cosmological simulations of structure formation but have not yet been explained on a first principle basis .
Here we solve the Jeans equation under the assumption of a spherical DM halo in dynamical equilibrium , that obeys a power law phase space density and either the NFW-like or the Sersic density profile .
We then calculate the velocity anisotropy , \beta ( r ) , analytically .
Our main result is that for the NFW-like profile the \beta~ { } - ~ { } \gamma relation is not a linear one ( where \gamma is the logarithmic derivative of the density \rho [ r ] ) .
The shape of \beta ( r ) depends mostly on the ratio of the gravitational to kinetic energy within the NFW scale radius R _ { s } .
For the Sersic profile a linear \beta~ { } - ~ { } \gamma relation is recovered , and in particular for the Sersic index of n \approx 6.0 case the linear fit of Hansen & Moore is reproduced .
Our main result is that the phase-space density power law , the Sersic density form and the linear \beta~ { } - ~ { } \gamma dependence constitute a consistent set of relations which obey the spherical Jeans equation and as such provide the framework for the dynamical modeling of DM halos .