Changbom Park  (Korea Institute for Advanced Study)

Topology of Large Scale Structure

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     The Sloan Digital Sky Survey (SDSS) is an imaging and spectroscopic CCD survey of the high Galactic latitude regions of the sky using a wide-field 2.5m telescope at Apache Point Observatory. The survey began in April 2000, and will end in June 2005 followed by an extension survey. Even though the SDSS focuses on galaxies and quasars, its data are being applied to all areas of astronomy from asteroids to quasars. In this talk I review the scientific achievements in the fields of cosmology and the large scale structure of galaxies which have been made possible through the SDSS data.
     The SDSS has been designed for the study of galaxies, quasars and the large scale structure, in particular. The survey is characterized by a wide angle coverage (about a quarter of the all sky), deep and dense sampling of objects. The Third Data Release (DR3) of the SDSS became public in September 2004. The DR3 contains data taken up until July 2003, and includes 141 million objects in the imaging data, and about 0.53 million objects in the spectroscopic data.
     Because of unprecedented large number of surveyed galaxies and quasars the relations among various physical properties of these objects and their environmental dependences are able to be studied in great details. Due to large volume of the survey the primordial density and velocity fields in the linear regime can be restored for understanding of the generation mechanism for the initial density fluctuation. Dense sampling of the survey made it possible to study cosmological voids and rare galaxies in voids. Topology of the large scale structure at a few mega parsec scales is sensitive to galaxy formation mechanism, and can be also studied because of the high number density of galaxies in the SDSS sample. Some of the recent progresses in these works are reviewed.
    In this talk I will introduce the genus statistic as a measure of intrinsic topology of shape of the large scale structure. I briefly review the history of topology study of large scale structure since 1986. Then the recent numerical and analytic studies on the effects of gravitational evolution, redshift space distortion, and biasing on the genus statistic are explained. I present the results of genus analysis of the SDSS Sample 14 data. The scale and luminosity dependences of genus are studied. It has been found that the bright galaxies show the 'meat-ball' shift while the faint galaxies show 'sponge' and 'bubble' shifts. The transition occurs near the characteristic absolute magnitude Mr= -20.4. The degree of shifts is much stronger than that predicted by gravitational evolution and must be mainly due to biasing. We also confirm that the number of voids are smaller than what is predicted for a Gaussian field.