TOPOLOGY IN 2 DIMENSIONS .1. THE LICK GALAXY CATALOG

We apply a quantitative topology-measuring algorithm to investigate the pattern of galaxy clustering revealed by the Shane-Wirtanen galaxy counts. We examine the Euler-Poincare 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 non-Gaussian behaviour we find on small scales could be described as characteristic of a 'meatball' topology. At intermediate resolution we find that a non-Gaussian 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 large-scale 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 non-Gaussian models.