The Galaxy Luminosity Function and Luminosity Density at Redshiftz= 0.1

Using a catalog of 147,986 galaxy redshifts and fluxes from the Sloan DigitalSky Survey (SDSS) we measure the galaxy luminosity density at z=0.1 in fiveoptical bandpasses corresponding to the SDSS bandpasses shifted to match theirrestframe shape at z=0.1. We denote the bands {0.1}{u}, {0.1}{g}, {0.1}{r},{0.1}{i}, {0.1}{z}, with \lambda_{eff} = [3216, 4240, 5595, 6792, 8111]Angstroms respectively. We use a maximum likelihood method which allows for ageneral form for the shape of the luminosity function, simple luminosity andnumber evolution, incorporates flux uncertainties, and accounts for the fluxlimits of the survey. We find luminosity densities at z=0.1 in absolute ABmagnitudes in a Mpc^3 of [-14.10 \pm 0.15, -15.18 \pm 0.03, -15.90 \pm 0.03,-16.24 \pm 0.03, -16.56 \pm 0.02] in [{0.1}{u}, {0.1}{g}, {0.1}{r}, {0.1}{i},{0.1}{z}], respectively, using \Omega_0 =0.3, \Omega_\Lambda=0.7, and h=1, andusing Petrosian magnitudes. Similar results are obtained using Sersic modelmagnitudes, suggesting that flux from outside the Petrosian apertures is not amajor correction. In the {0.1}{r} band, the best fit Schechter function to ourresults has \phi_\ast = (1.49 \pm 0.04) \times 10^{-2} h^3 Mpc^{-3}, M_\ast -5\log_{10} h = -20.44 \pm 0.01, and \alpha = -1.05\pm 0.01. In solarluminosities, the luminosity density in {0.1}{r} is (1.84 \pm 0.04) h 10^8L_{{0.1}{r},\odot} Mpc^{-3}. Our results are consistent with other estimates ofthe luminosity density, from the Two-degree Field Galaxy Redshift Survey andthe Millenium Galaxy Catalog. They represent a substantial change (\sim 0.5mag) from earlier SDSS luminosity density results based on commissioning data,almost entirely because of the inclusion of evolution in the luminosityfunction model.Comment: submitted to Ap