Baryonic Collapse within Dark Matter Halos and the Formation of Gaseous Galactic Disks

This paper constructs an analytic framework for calculating the assembly of galactic disks from the collapse of gas within dark matter halos, with the goal of determining the surface density profiles. Gas parcels (baryons) fall through the potentials of dark matter halos on nearly ballistic, zero energy orbits and collect in a rotating disk. The dark matter halos have a nearly universal form, as determined previously through numerical simulations. The calculation is first carried out for a variety of pre-collapse mass distributions and rotation profiles, including polytropic spheres in hydrostatic equilibrium with the halo potential. The resulting disk surface density profiles have nearly power-law forms, with well-defined edges. This idealized scenario is generalized to include non-spherical starting states and multiple accretion events (due to gas being added to the halo via merger events). This latter complication is explored in detail and considers a log-normal distribution for the angular momenta of the pre-collapse states. If this distribution is wide, then the composite surface density approaches a universal power-law form, independent of the shape of the constituent profiles. When the angular momentum distribution has an intermediate width, the composite surface density attains a nearly exponential form, roughly consistent with profiles of observed galaxies.