The Topology of LargeScale Structure. Topology and the Random Phase Hypothesis
Abstract
Many models for the formation of galaxies and largescale structure assume a spectrum of random phase (Gaussian), smallamplitude density fluctuations as initial conditions. In such scenarios, the topology of the galaxy distribution on large scales relates directly to the topology of the initial density fluctuations. Here a quantitative measure of topology  the genus of contours in a smoothed density distribution  is described and applied to numerical simulations of galaxy clustering, to a variety of threedimensional toy models, and to a volumelimited sample of the CfA redshift survey. For random phase distributions the genus of density contours exhibits a universal dependence on threshold density. The clustering simulations show that a smoothing length of 23 times the mass correlation length is sufficient to recover the topology of the initial fluctuations from the evolved galaxy distribution. Cold dark matter and white noise models retain a random phase topology at shorter smoothing lengths, but massive neutrino models develop a cellular topology.
 Publication:

The Astrophysical Journal
 Pub Date:
 October 1987
 DOI:
 10.1086/165612
 Bibcode:
 1987ApJ...321....2W
 Keywords:

 Astronomical Models;
 Galactic Clusters;
 Galactic Evolution;
 Galactic Structure;
 Topology;
 Cosmology;
 Dark Matter;
 Density Distribution;
 Gravitational Fields;
 Neutrinos;
 Three Dimensional Models;
 White Noise;
 Astrophysics;
 COSMOLOGY;
 GALAXIES: CLUSTERING;
 GALAXIES: FORMATION