Topology Analysis of the Sloan Digital Sky Survey. I. Scale and Luminosity Dependence

• Published in: The Astrophysical journal 2005-11, Vol.633 (1), p.11-22
• Main Authors: Park, Changbom, Choi, Yun-Young, Vogeley, Michael S, Gott III, J. Richard, Kim, Juhan, Hikage, Chiaki, Matsubara, Takahiko, Park, Myeong-Gu, Suto, Yasushi, Weinberg, David H
• Format: Article
• Language: English
• Subjects: Astronomy; Earth, ocean, space; Exact sciences and technology
• ISSN: 0004-637X; 1538-4357
• DOI: 10.1086/452625

We measure the topology of volume-limited galaxy samples selected from a parent sample of 314,050 galaxies in the Sloan Digital Sky Survey (SDSS), which is now complete enough to describe the fully three-dimensional topology and its dependence on galaxy properties. We compare the observed genus statistic G( sub(f)) to predictions for a Gaussian random field and to the genus measured for mock surveys constructed from new large-volume simulations of the CDM cosmology. In this analysis we carefully examine the dependence of the observed genus statistic on the Gaussian smoothing scale R sub(G) from 3.5 to 11 h super(-1) Mpc and on the luminosity of galaxies over the range -22.50 < M sub(r) < -18.5. The void multiplicity A sub(V) is less than unity at all smoothing scales. Because A sub(V) cannot become less than 1 through gravitational evolution, this result provides strong evidence for biased galaxy formation in low-density environments. We also find clear evidence of luminosity bias of topology within the volume-limited subsamples. The shift parameter nu indicates that the genus of brighter galaxies shows a negative shift toward a "meatball" (i.e., cluster dominated) topology, while faint galaxies show a positive shift toward a "bubble" (i.e., void dominated) topology. The transition from negative to positive shift occurs approximately at the characteristic absolute magnitude M sub(r)* = -20.4. Even in this analysis of the largest galaxy sample to date, we detect the influence of individual large-scale structures, as the shift parameter nu and cluster multiplicity A sub(C) reflect (at 63 s) the presence of the Sloan Great Wall and an X-shaped structure that runs for several hundred megaparsecs across the survey volume.