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 Gadget .
The radial velocity dispersion can be approximated as function of the potential by \sigma _ { r } ^ { 2 } = a ( \Phi / \Phi _ { out } ) ^ { \kappa } ( \Phi _ { out } - \Phi ) , where \Phi _ { out } is the outer potential of the halo .
For the parameters a and \kappa we find a = 0.29 \pm 0.04 and \kappa = 0.41 \pm 0.03 .
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 .