  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 (TIS)
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 is, moreover, 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 amongst 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
v_max-r_max relation analytically, with preference for the flat Lambda-CDM
model.
