Galaxy luminosities, stellar masses, sizes, velocity dispersions as a function of morphological type

We provide fits to the distribution of galaxy luminosity, size, velocity dispersion and stellar mass as a function of concentration index C(r) and morphological type in the Sloan Digital Sky Survey (SDSS). (Our size estimate, a simple analogue of the SDSS cmodel magnitude, is new: it is computed using a combination of seeing-corrected quantities in the SDSS data base, and is in substantially better agreement with results from more detailed bulge/disc decompositions.) We also quantify how estimates of the fraction of 'early'- or 'late'-type galaxies depend on whether the samples were cut in colour, concentration or light profile shape, and compare with similar estimates based on morphology. Our fits show that ellipticals account for about 20 per cent of the r-band luminosity density, rho(Lr), and 25 per cent of the stellar mass density, rho(*); including S0s and Sas increases these numbers to 33 per cent and 40 per cent, and 50 per cent and 60 per cent, respectively. The values of rho(Lr) and rho(*), and the mean sizes, of E, E+S0 and E+S0+Sa samples are within 10 per cent of those in the Hyde & Bernardi, C(r) >= 2.86 and C(r) >= 2.6 samples, respectively. Summed over all galaxy types, we find rho(*) similar to 3 x 10(8) M(circle dot) Mpc(-3) at z similar to 0. This is in good agreement with expectations based on integrating the star formation history. However, compared to most previous work, we find an excess of objects at large masses, up to a factor of similar to 10 at M(*) similar to 5 x 10(11) M(circle dot). The stellar mass density further increases at large masses if we assume different initial mass functions for elliptical and spiral galaxies, as suggested by some recent chemical evolution models, and results in a better agreement with the dynamical mass function. We also show that the trend for ellipticity to decrease with luminosity is primarily because the E/S0 ratio increases at large L. However, the most massive galaxies, M(*) >= 5 x 10(11) M(circle dot), are less concentrated and not as round as expected if one extrapolates from lower L, and they are not well fit by pure deVaucouleur laws. This suggests formation histories with recent radial mergers. Finally, we show that the age-size relation is flat for ellipticals of fixed dynamical mass, but, at fixed M(dyn), S0s and Sas with large sizes tend to be younger. Hence, samples selected on the basis of colour or C(r) will yield different scalings. Explaining this difference between E and S0 formation is a new challenge for models of early-type galaxy formation.