We investigate the structure and history of Dark Matter (DM) halos in galaxies and galaxy systems. Our theoretical framework is provided by the two-stage cosmogonical development of DM halos, and by the related “α-profiles”. The latter solve the Jeans equation for the self-gravitating DM equilibria, and yield the radial runs of the density ρ(r) and the velocity dispersion σr2(r) in terms of the DM “entropy” K≡σr2/ρ2/3∝rα highlighted by recent N-body simulations to have a uniform slope α within the halo “body”. The former constrains the entropy slope α to a value within the narrow range 1.25–1.3; such a value applies in the halo body since the transition time that, both in our semianalytic description and in state-of-the-art numerical simulations, is found to separate two stages in the development of a DM halo: an early fast collapse including a few violent major mergers building up the halo body by dynamical relaxation; and a later, quasi-equilibrium stage during which the body is almost unaffected while the outskirts develop from the inside-out by minor mergers and smooth accretion. These physically based α-profiles meet the overall requirements from gravitational lensing observations, being intrinsically flatter at the center and steeper in the outskirts relative to the empirical NFW formula. In quantitative detail, we test them with the recent extensive dataset from weak and strong lensing observations in and around the cluster A1689. We find an optimal fit at both small and large scales in terms of a halo constituted by an early body with α≈1.25 and by recent extended outskirts making up a concentration parameter c≈10; we consistently interpret the latter value in terms of the variance expected in the two-stage halo development under the standard ΛCDM cosmology.
