  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 = 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.
