2010MNRAS.407....2D

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, V₂₀₀, circular velocities of early- and late-type galaxies at redshift z ≃ 0. For late-type galaxies, V_opt≃ V₂₀₀ over the velocity range V_opt= 90-260 km/s, and is consistent with V_opt= V_max,h[the maximum circular velocity of NFW dark matter haloes in the concordance Λ cold dark matter (Λ CDM) cosmology]. However, for early-type galaxies V_opt≠ V₂₀₀, with the exception of early-type galaxies with V_opt ≃ 350 km/s. This is inconsistent with early-type galaxies being, in general, globally isothermal. For low-mass (V_opt≲ 250 km/s) early-types V_opt> V_max,h, indicating that baryons have modified the potential well, while high-mass (V_opt> rsim 400 km/s) early-types have V_opt< V_max,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 ≃1.4 at halo masses of ≃ 10¹²h^–1 M_☉to ≃0.65 at halo masses of 10^13.5h^–1 M_☉. The values of V_opt/V₂₀₀ 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 V₂₀₀ 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/V₂₀₀ ratio and the V_opt-M_star(Tully-Fisher/Faber-Jackson) relation.