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The origin of cores and density profiles of baryonic structures

We study the origin of cores and density profiles of baryonic structures in cosmology. By treating the baryons as a viscous gas, we find that both spheres and disks are possible solutions. We find analytically that the density profiles have inner and outer solutions, which in general are different. For disks we identify a central core, with density profile ρd = constant, and the outer profile ρd ∼ r . For spherical structures we find the profile ρs ∼ r . In the presence of a dominating central black hole we find the inner profile ρ ∼ r. When a black hole dominates the mass then the preferred baryonic configuration is spherical and not disk-like. When the mass is dominated by a dark matter component then the baryonic density profile will depend on the dark matter profile, and we point out that one can use this connection to infer the DM profile directly by observing the baryonic density profile. For a spherical DM structure this relation is βbaryon = 3/2 (2 + βDM).