DARK MATTER EQUILIBRIA IN GALAXIES AND GALAXY SYSTEMS

Abstract

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 ∝ rα 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☉. 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.