The weak dependence of velocity dispersion on disc fractions, mass-to-light ratio, and redshift: implications for galaxy and black hole evolution. Issue 4 (22nd December 2021) - Marsden, Christopher; Shankar, Francesco; Bernardi, Mariangela; Sheth, Ravi K; Fu, Hao; Lapi, Andrea
ABSTRACT: Velocity dispersion (σ) is a key driver for galaxy structure and evolution. We here present a comprehensive semi-empirical approach to compute σ 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 σ on bulge-to-total (B/T) ratio (for B/T ≳ 0.25). The dynamical-to-stellar mass ratio within R ≲ R e can be fully accounted for by a gradient in M */ L . We then build velocity dispersion evolutionary tracks σap [ M *, z ] (within an aperture) along the main progenitor dark matter haloes assigning stellar masses, effective radii, and Sérsic  indices via a variety of abundance matching and empirically motivated relations. We find: (1) clear evidence for downsizing in σap [ M *, z ] along the progenitor tracks; (2) at fixed stellar mass σ ∝ (1 + z ) 0.2−0.3 depending on the presence or not of a gradient in M */ L . We extract σap [ 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 σap [ M *, z ] along the progenitors at z ≳ 1 in constant M */ L models, while σap [ 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 σap [ M *, z ] with time. Finally, our σap [ M *, z ] are consistent with a nearly constant and steep M bh − σ relation at z ≲ 2, with black hole masses derived from the LX − M * relation.