The kinematic connection between galaxies and dark matter haloes

Using estimates of dark halo masses from satellite kinematics, weak gravitational lensing and halo abundance matching, combined with the Tully-Fisher (TF) and Faber-Jackson relations, we derive the mean relation between the optical, V-opt, and virial, V-200, circular velocities of early- and late-type galaxies at redshift z similar or equal to 0. For late-type galaxies, V-opt similar or equal to V-200 over the velocity range V-opt = 90-260 km s-1, and is consistent with V-opt = V-max,V-h [the maximum circular velocity of NFW dark matter haloes in the concordance Lambda cold dark matter (Lambda CDM) cosmology]. However, for early-type galaxies V-opt not equal V-200, with the exception of early-type galaxies with V-opt similar or equal to 350 km s-1. This is inconsistent with early-type galaxies being, in general, globally isothermal. For low-mass (V-opt less than or similar to 250 km s-1) early-types V-opt > V-max,V-h, indicating that baryons have modified the potential well, while high-mass (V-opt > rsim 400 km s-1) early-types have V-opt < V-max,V-h. Folding in measurements of the black hole mass-velocity dispersion relation, our results imply that the supermassive black hole-halo mass relation has a logarithmic slope which varies from similar or equal to 1.4 at halo masses of similar or equal to 1012 h-1 M-circle dot to similar or equal to 0.65 at halo masses of 1013.5 h-1 M-circle dot. The values of V-opt/V-200 we infer for the Milky Way (MW) and M31 are lower than the values currently favoured by direct observations and dynamical models. This offset is due to the fact that the MW and M31 have higher V-opt and lower V-200 compared to typical late-type galaxies of the same stellar masses. We show that current high-resolution cosmological hydrodynamical simulations are unable to form galaxies which simultaneously reproduce both the V-opt/V-200 ratio and the V-opt-M-star (Tully-Fisher/Faber-Jackson) relation.