On the Origin of the Rotation Curves of Dark-Matter-Dominated Galaxies

N-body simulations of the Cold Dark Matter (CDM) model yield singular halo density profiles in apparent conflict with halo profiles of dark-matter-dominated galaxies derived from observed rotation curves. An analytical model we have derived elsewhere for the postcollapse equilibrium of cosmological halos reproduces many of the average properties of halos in CDM simulations to good accuracy, including the density profiles outside the central region, while avoiding the problem of the steeply singular cores. The halo model is a unique, truncated, isothermal sphere (TIS), with a core density proportional to the critical density at the epoch of collapse. The TIS rotation curve is in excellent agreement with the observed ones and yields the mass and collapse epoch of an observed halo from the parameters of its rotation curve. This allows us to predict correlations amongst rotation curve parameters, such as the maximum velocity and the radius at which it occurs, for different mass halos collapsing at different epochs. We thereby derive the observed vmax-rmax relation analytically, with preference for the flat ΛCDM model. This model may also be of interest as a description of halos in nonstandard CDM models like self-interacting dark matter, proposed to eliminate the discrepancy between the cuspy halos of standard CDM simulations and observed halos with uniform-density cores. Subject headings: cosmology: theory – dark matter – galaxies: general – galaxies: formation – galaxies: halos – galaxies: kinematics and dynamics