Dark Matter Equilibria in Galaxies and Galaxy Systems

In the dark matter (DM) halos embedding galaxies and galaxy systems the "entropy" K ≡ σ2/ρ2/3 (a quantity that combines the radial velocity dispersion σ with the density ρ) is found from intensive N-body simulations to follow a power-law run K vprop r α throughout the halos' bulk, with α around 1.25. Taking up from phenomenology just that α≈ const. applies, we cut through the rich analytic contents of the Jeans equation describing the self-gravitating equilibria of the DM; we specifically focus on computing and discussing a set of novel physical solutions that we name α-profiles, marked by the entropy slope α itself, and by the maximal gravitational pull κcrit(α) required for a viable equilibrium to hold. We then use an advanced semianalytic description for the cosmological buildup of halos to constrain the values of α to within the narrow range 1.25-1.29 from galaxies to galaxy systems; these correspond to halos' current masses in the range 1011-1015 M sun. Our range of α applies since the transition time that—both in our semianalytic description and in state-of-the-art numerical simulations—separates two development stages: an early violent collapse that comprises a few major mergers and enforces dynamical mixing, followed by smoother mass addition through slow accretion. In our range of α we provide a close fit for the relation κcrit(α), and discuss a related physical interpretation in terms of incomplete randomization of the infall kinetic energy through dynamical mixing. We also give an accurate analytic representation of the α-profiles with parameters derived from the Jeans equation; this provides straightforward precision fits to recent detailed data from gravitational lensing in and around massive galaxy clusters, and thus replaces the empirical Navarro-Frenk-White formula relieving the related problems of high concentration and old age. We finally stress how our findings and predictions as to α and κcrit contribute to understanding hitherto unsolved issues concerning the fundamental structure of DM halos.