The Galaxy Luminosity Function and Luminosity Density at Redshift<i>z</i>= 0.1

Using a catalog of 147,986 galaxy redshifts and fluxes from the Sloan Digital Sky Survey (SDSS), we measure the galaxy luminosity density at z = 0.1 in five optical bandpasses corresponding to the SDSS bandpasses shifted to match their rest-frame 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 Angstrom), respectively. To estimate the luminosity function, we use a maximum likelihood method that allows for a general form for the shape of the luminosity function,fits for simple luminosity and number evolution, incorporates the flux uncertainties, and accounts for the flux limits of the survey. We find luminosity densities at z = 0.1 expressed in absolute AB magnitudes in a Mpc(3) to be (-14.10 +/- 0.15, -15.18 +/- 0.03, - 15.90 +/- 0.03, -16.24 +/- 0.03, -16.56 +/- 0.02) in ((0.1)u, (0.1)g, (0.1)r, (0.1)i, (0.1)z), respectively, for a cosmological model with Omega(0) = 0.3, Omega(Lambda) = 0.7, and h = 1 and using SDSS Petrosian magnitudes. Similar results are obtained using Sersic model magnitudes, suggesting that flux from outside the Petrosian apertures is not a major correction. In the (0.1)r band, the best-fit Schechter function to our results has phi* = (1.49 +/- 0.04) x 10(-2) h(3) Mpc(-3), M-* - 5 log(10) h = - 20.44 +/- 0.01, and alpha = - 1.05 +/- 0.01. In solar luminosities, the luminosity density in (0.1)r is (1.84 +/- 0.04) x 10(8) h L-0.1r,L-. Mpc(-3). Our results in the (0.1)g band are consistent with other estimates of the luminosity density, from the Two-Degree Field Galaxy Redshift Survey and the Millennium Galaxy Catalog. They represent a substantial change ( similar to 0.5 mag) from earlier SDSS luminosity density results based on commissioning data, almost entirely because of the inclusion of evolution in the luminosity function model.