Genus Topology of Structure in the Sloan Digital Sky Survey: Model Testing

Abstract

We measure the three-dimensional topology of large-scale structure in the Sloan Digital Sky Survey (SDSS). This allows the genus statistic to be measured with unprecedented statistical accuracy. The sample size is now sufficiently large to allow the topology to be an important tool for testing galaxy formation models. For comparison, we make mock SDSS samples using several state-of-the-art N -body simulations: the Millennium run of Springel et al. (10 billion particles), the Kim & Park CDM models (1.1 billion particles), and the Cen & Ostriker hydrodynamic code models (8.6 billion cell hydro mesh). Each of these simulations uses a different method for modeling galaxy formation. The SDSS data show a genus curve that is broadly characteristic of that produced by Gaussian random-phase initial conditions. Thus, the data strongly support the standard model of inflation where Gaussian random-phase initial conditions are produced by random quantum fluctuations in the early universe. But on top of this general shape there are measurable differences produced by nonlinear gravitational effects and biasing connected with galaxy formation. The N -body simulations have been tuned to reproduce the power spectrum and multiplicity function but not topology, so topology is an acid test for these models. The data show a "meatball" shift (only partly due to the Sloan Great Wall of galaxies) that differs at the 2.5 σ level from the results of the Millenium run and the Kim & Park dark halo models, even including the effects of cosmic variance.