Two‐dimensional Topology of the Sloan Digital Sky Survey

We present the topology of a volume-limited sample of 11,884 galaxies,selected from an apparent-magnitude limited sample of over 100,000 galaxiesobserved as part of the Sloan Digital Sky Survey (SDSS). The data currentlycover three main regions on the sky: one in the Galactic north and one in thesouth, both at zero degrees declination, and one area in the north at higherdeclination. Each of these areas covers a wide range of survey longitude but anarrow range of survey latitude, allowing the two dimensional genus to bemeasured. The genus curves of the SDSS sub-samples are similar, after appropriatelynormalizing these measurements for the different areas. We sum the genus curvesfrom the three areas to obtain the total genus curve of the SDSS. The totalcurve has a shape similar to the genus curve derived from mock catalogs drawnfrom the Hubble Volume Lambda CDM simulation and is similar to that of aGaussian random field. Likewise, comparison with the genus of the 2dFGRS, afternormalization for the difference in area, reveals remarkable similarity in thetopology of these samples. We test for the effects of galaxy type segregation by splitting the SDSS datainto thirds, based on the u^*- r^* colors of the galaxies, and measure thegenus of the reddest and bluest sub-samples. This red/blue split in u^*- r^* isessentially a split by morphology (Strateva et al. 2001). We find that thegenus curve for the reddest galaxies exhibits a ``meatball'' shift of thetopology -- reflecting the concentration of red galaxies in high densityregions -- compared to the bluest galaxies and the full sample, in agreementwith predictions from simulations.Comment: ApJ Accepted with very minor revision