The Luminosity Function of Galaxies in SDSS Commissioning Data

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Abstract
In the course of its commissioning observations, the Sloan Digital Sky Survey (SDSS) has produced one of the largest redshift samples of galaxies selected from CCD images. Using 11,275 galaxies complete to r* = 17.6 over 140 deg2, 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 * = (1.46 ± 0.12) × 10-2 h3 Mpc-3, M* = -20.83 ± 0.03, and α = -1.20 ± 0.03. The implied luminosity density in r* is j ≈ (2.6 ± 0.3) × 108h L⊙ Mpc-3. We find that the surface brightness selection threshold has a negligible impact for M < -18. Using subsets of the data, we measure the luminosity function in the u*, g*, i*, and z* bands as well; the slope at low luminosities ranges from α = -1.35 to α = -1.2. We measure the bivariate distribution of r* luminosity with half-light surface brightness, intrinsic g*-r* color, and morphology. In agreement with previous studies, we find that high surface brightness, red, highly concentrated galaxies are on average more luminous than low surface brightness, blue, less concentrated galaxies. An important feature of the SDSS luminosity function is the use of Petrosian magnitudes, which measure a constant fraction of a galaxy's total light regardless of the amplitude of its surface brightness profile. If we synthesize results for RGKC band or bj band using these Petrosian magnitudes, we obtain luminosity densities 2 times that found by the Las Campanas Redshift Survey in RGKC and 1.4 times that found by the Two Degree Field Galaxy Redshift Survey in bj. However, 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.