Galaxy Number Counts from the Sloan Digital Sky Survey Commissioning Data

We present bright galaxy number counts in five broad bands ($u', g', r', i',z'$) from imaging data taken during the commissioning phase of the SloanDigital Sky Survey (SDSS). The counts are derived from two independent stripesof imaging scans along the Celestial Equator, one each toward the North and theSouth Galactic cap, covering about 230 and 210 square degrees, respectively. Acareful study is made to verify the reliability of the photometric catalog. Forgalaxies brighter than $r^* = 16$, the catalog produced by automated softwareis examined against eye inspection of all objects. Statistically meaningfulresults on the galaxy counts are obtained in the magnitude range $12 \le r^*\le 21$, using a sample of 900,000 galaxies. The counts from the two stripesdiffer by about 30% at magnitudes brighter than $r^*= 15.5$, consistent with alocal $2\sigma$ fluctuation due to large scale structure in the galaxydistribution. The shape of the number counts-magnitude relation brighter than$r^* = 16$ is well characterized by $N \propto 10^{0.6m}$, the relationexpected for a homogeneous galaxy distribution in a ``Euclidean'' universe. Inthe magnitude range $ 16 < r^* < 21$, the galaxy counts from both stripes agreevery well, and follow the prediction of the no-evolution model, although thedata do not exclude a small amount of evolution. We use empirically determinedcolor transformations to derive the galaxy number counts in the $B$ and$I_{814}$ bands. We compute the luminosity density of the universe at zeroredshift in the five SDSS bands and in the $B$ band. We find ${\cal L}_{B} =2.4 \pm 0.4 \times 10^8L_\odot h $Mpc$^{-3}$, for a reasonably wide range ofparameters of the Schechter luminosity function in the $B$ band.Comment: 48 pages, 15 figure