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

Rotation curves of dark matter-dominated galaxies measure the mass profiles of galactic halos and thereby test theories of their cosmological origin. While attention has focused lately on the possible discrepancy at small galactocentric radii between observed rotation curves and the singular density profiles predicted by N-body simulations of the cold dark matter (CDM) model, the observed rotation curves nevertheless contain valuable additional information with which to test the theory and constrain the fundamental cosmological parameters, despite this uncertainty at small radii. An analytical model we derived elsewhere for the postcollapse equilibrium of cosmological halos as truncated, nonsingular, isothermal spheres (TISs) reproduces many of the average properties of halos in CDM simulations to good accuracy, including the density profiles outside the central region. The circular velocity profile of this TIS model, moreover, is in excellent agreement with the observed ones and yields the mass and formation epoch of an observed halo from the parameters of its rotation curve. This allows us to predict correlations among rotation curve parameters, such as the maximum velocity and the radius at which it occurs, for different mass halos forming at different epochs in the CDM model. As an example, we derive the observed vmax-rmax relation analytically, with preference for the flat ΛCDM model.