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 ^ { \ast } = 17.6 over 140 square degrees , we compute the luminosity function of galaxies in the r ^ { \ast } band over a range -23 < M _ { r ^ { \ast } } < -16 ( for h = 1 ) .
The result is well-described by a Schechter function with parameters \phi _ { \ast } = ( 1.46 \pm 0.12 ) \times 10 ^ { -2 } h ^ { 3 } Mpc ^ { -3 } , M _ { \ast } = -20.83 \pm 0.03 , and \alpha = -1.20 \pm 0.03 .
The implied luminosity density in r ^ { \ast } is j \approx ( 2.6 \pm 0.3 ) \times 10 ^ { 8 } hL _ { \odot } Mpc ^ { -3 } .
We find that the surface brightness selection threshold has a negligible impact for M _ { r ^ { \ast } } < -18 .
Using subsets of the data , we measure the luminosity function in the u ^ { \ast } , g ^ { \ast } , i ^ { \ast } , and z ^ { \ast } bands as well ; the slope at low luminosities ranges from \alpha = -1.35 to \alpha = -1.2 .
We measure the bivariate distribution of r ^ { \ast } luminosity with half-light surface brightness , intrinsic g ^ { \ast } - r ^ { \ast } 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 R _ { \mathrm { GKC } } -band or b _ { j } -band using these Petrosian magnitudes , we obtain luminosity densities 2 times that found by the Las Campanas Redshift Survey in R _ { \mathrm { GKC } } and 1.4 times that found by the Two-degree Field Galaxy Redshift Survey in b _ { j } .
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 .