The Luminosity Function of Galaxies in SDSS Commissioning Data

During commissioning observations, the Sloan Digital Sky Survey (SDSS) has produced one of the largest existing galaxy redshift samples selected from CCD images. Using 11,275 galaxies complete to r^* = 17.6 over 140 square degrees, we compute the luminosity function of galaxies in the r^* band over a range -23 < M < -16 (for h=1). The result is well-described by a Schechter function with parameters phi_* = 0.0146 +/- 0.0012 h^3 Mpc^{-3}, M_* = -20.83 +/- 0.03, and alpha = -1.20 +/- 0.03. The implied luminosity density in r^* is j = (2.6 +/- 0.3) x 10^8 h L_sun Mpc^{-3}. The surface brightness selection threshold has a negligible impact for M < -18. We measure the luminosity function in the u^*, g^*, i^*, and z^* bands as well; the slope at low luminosities ranges from alpha=-1.35 to alpha=-1.2. We measure the bivariate distribution of r^* luminosity with half-light surface brightness, intrinsic color, and morphology. High surface brightness, red, highly concentrated galaxies are on average more luminous than low surface brightness, blue, less concentrated galaxies. If we synthesize results for R-band or b_j-band using the Petrosian magnitudes with which the SDSS measures galaxy fluxes, we obtain luminosity densities 2.5 times that found by the Las Campanas Redshift Survey in R and 1.4 times that found by the Two-degree Field Galaxy Redshift Survey in b_j. We are able to reproduce the luminosity functions obtained by these surveys if we also mimic their isophotal limits for defining galaxy magnitudes, which are shallower and more redshift dependent than the Petrosian magnitudes used by the SDSS. (Abridged)