Curvature in the scaling relations of early-type galaxies
  We select a sample of about 50,000 early-type galaxies from the Sloan Digital Sky Survey (SDSS), calibrate fitting formulae which correct for known problems with photometric reductions of extended objects, apply these corrections, and then measure a number of pairwise scaling relations in the corrected sample. We show that, because they are not seeing corrected, the use of Petrosian-based quantities in magnitude limited surveys leads to biases, and suggest that this is one reason why Petrosian-based analyses of BCGs have failed to find significant differences from the bulk of the early-type population. These biases are not present when seeing-corrected parameters derived from deVaucouleur fits are used. Most of the scaling relations we study show evidence for curvature: the most luminous galaxies have smaller velocity dispersions, larger sizes, and fainter surface brightnesses than expected if there were no curva-ture. These statements remain true if we replace luminosities with stellar masses; they suggest that dissipation is less important at the massive end. There is curvature in the dynamical to stellar mass relation as well: the ratio of dynamical to stellar mass increases as stellar mass increases, but it curves upwards from this scaling both at small and large stellar masses. In all cases, the curvature at low masses becomes apparent when the sample becomes dominated by objects with stellar masses smaller than 3 x 10^10 M_Sun. We quantify all these trends using second order polynomials; these generally provide significantly better description of the data than linear fits, except at the least luminous end. 
J. B. Hyde and M. Bernardi