Luminosity L_B/L_⊙ vs. velocity dispersion σ (in km s⁻¹) relation of our model galaxies. For each mass (labeled M_B(t_G), as indicated) three relations are shown: (1) original models with no revision of the radii (lines made of filled black squares); (2) models whose luminosity is derived from the relation with the original β and (curves made of red squares) together with the linear fit limited to the descending branch of each curve (black solid lines); (3) models in which the radii have been revised and new values of β and are calculated (green curves). In each case the luminosity–sigma relation bends past the stage that roughly corresponds to the maximum stellar activity. From this stage the luminosity and velocity dispersion decrease (see text for details). The inset shows the case of M_B(t_G) = 10¹⁰ M_⊙ for the sake of clarity. The models are compared with the data by Burstein et al. (1997) from GCs to GCGs; the same color-coding as in the previous figures is used.