The Topology of LargeScale Structure. II. Nonlinear Evolution of Gaussian Models
Abstract
A widely used hypothesis is that the observed structure in the universe arose from nonlinear gravitational evolution of a random phase (Gaussian) spectrum of perturbations. In such a Gaussian distribution, quantitative measures of the topology are calculable, and the initial conditions of numerical models follow the expected behavior. Since nonGaussian test distributions show very different behavior, we study in this paper the evolution of nonGuassian behavior from Gaussian initial conditions. We apply topology measures developed in previous papers to the smoothed initial, final, and biased matter distributions of cold dark matter, white noise, and massive neutrino simulations. When the smoothing length is approximately twice the mass correlation length or larger, our evolved models look like the initial conditions, suggesting we can test the random phase hypothesis in cosmology with adequate data sets. When a smaller smoothing length is used, we recover nonlinear effects, so nonlinear effects on topology can be detected in redshift surveys after smoothing at the mean intergalaxy separation. Models with substantial power on small scale continue to show topology that is Guassian in form even in the final conditions, but they have a reduced number of "holes." This effect can be interpreted in terms of a merging of structures and/or changes in the slope of the power spectrum. Hot dark matter (neutrinopancake) models develop manifestly nonGuassian behavior attributable to phase correlations, with a topology reminiscent of "bubble" or "sheet" distributions. Cold dark matter models remain Gaussian, and biasing does not disguise this. Thus, models with similar final power spectra can have very different topologies. We show that observing models in redshift space has a negligible effect on topology. Data sets adequate to test these models will exist soon, if they do not exist already.
 Publication:

The Astrophysical Journal
 Pub Date:
 May 1988
 DOI:
 10.1086/166267
 Bibcode:
 1988ApJ...328...50M
 Keywords:

 Cosmology;
 Dark Matter;
 Galactic Clusters;
 Normal Density Functions;
 Random Processes;
 Red Shift;
 Computational Astrophysics;
 Correlation;
 Perturbation Theory;
 Power Spectra;
 Astrophysics;
 COSMOLOGY;
 DARK MATTER;
 GALAXIES: CLUSTERING