Luminosity Function of Morphologically Classified Galaxies in the Sloan Digital Sky Survey

The morphological dependence of the luminosity function is studied using a sample containing approximately 1500 bright galaxies classified into Hubble types by visual inspections for a homogeneous sample obtained from the Sloan Digital Sky Survey (SDSS) northern equatorial stripes. Early-type galaxies are shown to have a characteristic magnitude by 0.45 mag brighter than spiral galaxies in the $r^{\ast}$ band, consistent with the `universal characteristic luminosity' in the $B$ band. The shape of the luminosity function differs rather little among different morphological types: we do not see any symptoms of the sharp decline in the faint end for the luminosity function for early-type galaxies at least 2 mag fainter than the characteristic magnitude, although the faint end behaviour shows a slight decline ($\alpha\lsim -1$) compared with the total sample. We also show that a rather flat faint end slope for early-type galaxies is not due to an increasing mixture of the dwarf galaxies which have softer cores. This means that there are numerous faint early-type galaxies with highly concentrated cores.