The weak dependence of velocity dispersion on disc fractions, mass-to-light ratio, and redshift: implications for galaxy and black hole evolution

Velocity dispersion (sigma) is a key driver for galaxy structure and evolution. We here present a comprehensive semi-empirical approach to compute sigma via detailed Jeans modelling assuming both a constant and scale-dependent mass-to-light ratio M*/L. We compare with a large sample of local galaxies from MaNGA and find that both models can reproduce the Faber-Jackson (FJ) relation and the weak dependence of sigma on bulge-to-total (B/T) ratio (for B/T greater than or similar to 0.25). The dynamical-to-stellar mass ratio within R less than or similar to R-e can be fully accounted for by a gradient in M*/L. We then build velocity dispersion evolutionary tracks sigma(ap)[M*, z] (within an aperture) along the main progenitor dark matter haloes assigning stellar masses, effective radii, and Sersic indices via a variety of abundance matching and empirically motivated relations. We find: (1) clear evidence for downsizing in sigma(ap)[M*, z] along the progenitor tracks; (2) at fixed stellar mass sigma proportional to (1 + z)(0.2-0.3) depending on the presence or not of a gradient in M*/L. We extract sigma(ap)[M*, z] from the TNG50 hydrodynamic simulation and find very similar results to our models with constant M*/L. The increasing dark matter fraction within R-e tends to flatten the sigma(ap)[M*, z] along the progenitors at z greater than or similar to 1 in constant M*/L models, while sigma(ap)[M*, z] have a steeper evolution in the presence of a stellar gradient. We then show that a combination of mergers and gas accretion is likely responsible for the constant or increasing sigma(ap)[M*, z] with time. Finally, our sigma(ap)[M*, z] are consistent with a nearly constant and steep M-bh - sigma relation at z less than or similar to 2, with black hole masses derived from the L-X - M* relation.