We present the first measurements of clustering in the Sloan Digital Sky Survey ( SDSS ) galaxy redshift survey .
Our sample consists of 29 , 300 galaxies with redshifts 5 , 700 { km s ^ { -1 } } \leq cz \leq 39 , 000 { km s ^ { -1 } } , distributed in several long but narrow ( 2.5 - 5 ^ { \circ } ) segments , covering 690 square degrees .
For the full , flux-limited sample , the redshift-space correlation length is approximately 8 h ^ { -1 } { Mpc } .
The two-dimensional correlation function \xi ( r _ { p } , \pi ) shows clear signatures of both the small-scale , “ fingers-of-God ” distortion caused by velocity dispersions in collapsed objects and the large-scale compression caused by coherent flows , though the latter can not be measured with high precision in the present sample .
The inferred real-space correlation function is well described by a power law , \xi ( r ) = ( r / 6.1 \pm 0.2 h ^ { -1 } { Mpc } ) ^ { -1.75 \pm 0.03 } , for 0.1 h ^ { -1 } { Mpc } \leq r \leq 16 h ^ { -1 } { Mpc } .
The galaxy pairwise velocity dispersion is \sigma _ { 12 } \approx 600 \pm 100 { km s ^ { -1 } } for projected separations 0.15 h ^ { -1 } { Mpc } \leq r _ { p } \leq 5 h ^ { -1 } { Mpc } .
When we divide the sample by color , the red galaxies exhibit a stronger and steeper real-space correlation function and a higher pairwise velocity dispersion than do the blue galaxies .
The relative behavior of subsamples defined by high/low profile concentration or high/low surface brightness is qualitatively similar to that of the red/blue subsamples .
Our most striking result is a clear measurement of scale-independent luminosity bias at r \lesssim 10 h ^ { -1 } { Mpc } : subsamples with absolute magnitude ranges centered on M _ { * } -1.5 , M _ { * } , and M _ { * } +1.5 have real-space correlation functions that are parallel power laws of slope \approx - 1.8 with correlation lengths of approximately 7.4 h ^ { -1 } { Mpc } , 6.3 h ^ { -1 } { Mpc } , and 4.7 h ^ { -1 } { Mpc } , respectively .