Topology from the Simulated Sloan Digital Sky Survey

Abstract

We measure the topology (genus curve) of the galaxy distribution in a mock\nredshift catalog designed to resemble the upcoming Sloan Digital Sky Survey\n(SDSS). The catalog, drawn from a large N-body simulation of a Lambda-CDM cos-\nmological model, mimics the anticipated spectroscopic selection procedures of\nthe SDSS in some detail. Sky maps, redshift slices, and 3-D contour maps of the\nmock survey reveal a rich and complex structure, including networks of voids\nand superclusters that resemble the patterns seen in the CfA redshift survey\nand the Las Campanas Redshift Survey (LCRS). The 3-D genus curve can be\nmeasured from the simulated catalog with superb precision; this curve has the\ngeneral shape predicted for Gaussian, random phase initial conditions, but the\nerror bars are small enough to demonstrate with high significance the subtle\ndepartures from this shape caused by non-linear gravitational evolution. These\ndistortions have the form predicted by Matsubara's (1994) perturbative anal-\nysis, but they are much smaller in amplitude. We also measure the 3-D genus\ncurve of the radial peculiar velocity field measured by applying distance-\nindicator relations (with realistic errors) to the mock catalog. This genus\ncurve is consistent with the Gaussian random phase prediction, though it is of\nrelatively low precision because of the large smoothing length required to\novercome noise in the measured velocity field. Finally, we measure the 2-D\ntopology in redshift slices, similar to early slices from the SDSS and to\nslices already observed in the LCRS. The genus curves of these slices are\nconsistent with the observed genus curves of the LCRS, providing further\nevidence in favor of the inflationary CDM model with Omega_M~0.4. The catalog\nis publicly available at http://www.astronomy.ohio-state.edu/~dhw/sdss.html.\n

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Affiliated Institutions

• The Ohio State University US
• Harvard University US
• Seoul National University KR
• Princeton University US

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