Topology in two dimensions. I. The Lick Galaxy Catalogue.
Abstract
We apply a quantitative topologymeasuring algorithm to investigate the pattern of galaxy clustering revealed by the ShaneWirtanen galaxy counts. We examine the EulerPoincare characteristic of high and low density regions and compare the results with those expected for a two dimensional Gaussian random field. The large data set allows us to demonstrate clear departures from Gaussian topology when we look at the data at high resolution (i.e. when smoothed on a small angular scale), but the behaviour rapidly approaches that of the Gaussian as we lower the resolution (i.e. smooth on a larger angular scale). In the popular jargon, the nonGaussian behaviour we find on small scales could be described as characteristic of a `meatball' topology. At intermediate resolution we find that a nonGaussian model such as the lognormal, based on a local transformation of a Gaussian model, adequately describes the topology. On large scales, we find no evidence for departures from Gaussian statistics. We deduce that our results are consistent with models where largescale structures grow via gravitational instability from Gaussian quantum fluctuations generated in an inflationary epoch, but only further detailed Monte Carlo simulations (in an accompanying paper) will allow us to put rigorous constraints on specific nonGaussian models.
 Publication:

Monthly Notices of the Royal Astronomical Society
 Pub Date:
 May 1991
 DOI:
 10.1093/mnras/250.1.75
 Bibcode:
 1991MNRAS.250...75C
 Keywords:

 Astronomical Catalogs;
 Galactic Clusters;
 Galaxies;
 Spatial Distribution;
 Topology;
 Universe;
 Cosmology;
 Galactic Evolution;
 Gravitational Effects;
 Monte Carlo Method;
 Red Shift;
 Astrophysics