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 SDSS. We also quantify how estimates of the fraction
of `early' or `late' type galaxies depend on whether the samples were cut in
color, concentration or light profile shape, and compare with similar estimates
based on morphology. Our fits show that Es account for about 20% of the r-band
luminosity density, rho_Lr, and 25% of the stellar mass density, rho_*;
including S0s and Sas increases these numbers to 33% and 40%, and 50% and 60%,
respectively. Summed over all galaxy types, we find rho_* ~ 3 * 10^8 M_Sun
Mpc^{-3} at z ~ 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 ~ 10 at
M_* ~ 5*10^{11} M_Sun. The stellar mass density further increases at large
masses if we assume different IMFs for Es 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 * 10^{11} M_Sun, 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 Es of fixed dynamical mass, but, at fixed M_dyn, S0s and
Sas with large sizes tend to be younger. Explaining this difference between E
and S0 formation is a new challenge for models of early-type galaxy formation.
