Topology from the simulated Sloan Digital Sky Survey

We measure the topology (genus curve) of the galaxy distribution in a very large cosmological simulation designed to resemble closely results from the upcoming Sloan Digital Sky Survey (SDSS). The mock survey is based on a large N-body simulation that uses 54,872,000 particles in a periodic cube 600 h(-1) Mpc on a side. The adopted inflationary cold dark matter (CDM) model has parameters Omega(CDM) = 0.4, Omega(Lambda) = 0.6, h = 0.6, b = 1.3. We "observe" this simulation to produce a simulated redshift catalog of similar to 10(6) galaxies over pi steradians, mimicking the anticipated spectroscopic selection procedures of the SDSS in some detail. Sky maps, redshift slices, and three-dimensional contour maps of the mock survey reveal a rich and complex structure, including networks of voids and superclusters that resemble the patterns seen in the CfA redshift survey and the Las Campanas Redshift Survey (LCRS). The three-dimensional genus curve can be measured from the simulated catalog with superb precision; this curve not only has the general shape predicted for Gaussian, random phase initial conditions, but the error bars are small enough to demonstrate with high significance the subtle departures from this shape caused by nonlinear gravitational evolution on a 10 h(-1) Mpc smoothing scale (where sigma(gal) = 0.4). These distortions have the form predicted by Matsubara's perturbative analysis, but they are smaller in amplitude. We also measure the three-dimensional genus curve of the radial peculiar velocity field measured by applying distance-indicator relations (with realistic errors) to the mock catalog. The genus curve is consistent with the Gaussian random phase prediction, though it is of relatively low precision because of the large smoothing length required to overcome noise in the measured velocity held. Finally, we measure the two-dimensional topology in redshift slices, similar to those which will become available early in the course of the SDSS and to those already observed in the LCRS. The genus curves of these slices are consistent with the observed genus curves of the LCRS, suggesting that our inflationary CDM model with Omega(CDM) similar to 0.4 is a good choice. Our mock redshift catalog is publicly available for the use of other researchers.