Size is another fundamental property of a galaxy. As shown in Figs. 1 and 2., galaxies of a given luminosity may have very different sizes (and therefore surface brightnesses). Based on a large sample of galaxies in the SDSS, Shen et al. (2003) found that the size distribution for galaxies of a given luminosity L can roughly be described by a log-normal function,
where 
is the median and 
the dispersion. Fig. 3 shows that R̅ increases with galaxy luminosity roughly as a power law for both early-type and late-type galaxies, and that the dependence is stronger for early types. The dispersion , on the other hand, is similar for both early-type and late-type galaxies, decreasing from 
for galaxies with 
to 
for brighter galaxies.
Fig.1. The effective radius (left panel) and the average surface brightness within the effective radius (right panel) of elliptical galaxies plotted against their absolute magnitude in the B-band. The vertical dotted lines correspond to 
= -20.5. [Data compiled and kindly made available by A. Graham (see Graham & Guzmán, 2003), combined with data taken from Bender et al. (1992)]
Fig. 2. The effective radius (left panel) and the surface brightness at the effective radius (right panel) of disk dominated galaxies plotted against their absolute magnitude in the B-band. [Based on data published in Impey et al. (1996b)]
Fig. 3. The median (upper panel) and dispersion (lower panel) of the size distribution of galaxies in the SDSS as function of their r-band magnitude. Results are shown separately for early-type (solid dots) and late-type (open triangles) galaxies defined according to the Sérsic index 
. [Kindly provided to us by 
. Shen, based on data published in Shen et al. (2003)]
