  Numerous numerical studies indicate that dark matter halos show an almost
universal radial density profile. The origin of the profile is still under
debate. We investigate this topic and pay particular attention to the velocity
dispersion profile. To this end we have performed high-resolution simulations
with two independent codes, ART and {\sc Gadget}. The radial velocity
dispersion can be approximated as function of the potential by $\sigma_r^2 = a
(\Phi / \Phi_{\rm{out}})^\kappa (\Phi_{\rm{out}} - \Phi)$, where
$\Phi_{\rm{out}}$ is the outer potential of the halo. For the parameters $a$
and $\kappa$ we find $a=0.29\pm0.04$ and $\kappa=0.41\pm0.03$. We find that the
power-law asymptote $\sigma^2 \propto \Phi^\kappa$ is valid out to much larger
distances from the halo center than any power asymptote for the density profile
$\rho \propto r^{-n}$. The asymptotic slope $n(r \to 0)$ of the density profile
is related to the exponent $\kappa$ via $n=2\kappa/(1+\kappa)$. Thus the value
obtained for $\kappa$ from the available simulation data can be used to obtain
an estimate of the density profile below presently resolved scales. We predict
a continuously decreasing $n$ towards the halo center with the asymptotic value
$n \lesssim 0.58$ at $r=0$.
