Systematic effects on the size–luminosity relations of early- and late-type galaxies: dependence on model fitting and morphology

We quantify the systematics in the size–luminosity relation of galaxies in the Sloan Digital Sky Survey main sample (i.e. at z ∼ 0.1) which arise from fitting different one- and two-component model profiles to the r-band images. For objects brighter than L *, fitting a single Sérsic profile to what is really a two-component SerExp system leads to biases: the half-light radius is increasingly overestimated as n of the fitted single component increases; it is also overestimated at B/T ∼ 0.6. For such objects, the assumption of a single Sérsic component is particularly misleading. However, the net effect on the R-L relation is small, except for the most luminous tail. We then study how this relation depends on morphology. Our analysis is one of the first to use Bayesian-classifier-derived weights, rather than hard cuts, to define morphology. For the R-L relation Es, S0s and Sas are early types, whereas Sbs and Scds are late, although S0s tend to be 15 per cent smaller than Es of the same luminosity, and faint Sbs are more than 25 per cent smaller than faint Scds. Neither the early- nor the late-type relations are pure power laws: both show significant curvature, which we quantify. This curvature confirms that two mass scales are special for both early- and late-type galaxies: M * ∼ 3 × 1010 and 2 × 1011 M⊙. Also, although the R disc-L disc and R disc-M *disc relations of discs of disc-dominated galaxies run parallel to the corresponding relations for the total light in late types (i.e. they are significantly curved), R bulge-L bulge and R bulge-M *bulge for bulge-dominated systems show almost no curvature (i.e. unlike for the total light of early-type galaxies). Finally, the intrinsic scatter in the R-L relation decreases at large L and/or M * and should provide additional constraints on models of how the most massive galaxies formed.