TOPOLOGY IN 2 DIMENSIONS .3. MODELING PROJECTED GALAXY CATALOGS

We investigate the properties of the Euler-Poincare characteristic (EPC) as a statistical descriptor of galaxy clustering, using static Monte Carlo simulations to determine the ability of the EPC to reveal real three-dimensional information in the presence of projection effects. We model the deep Lick galaxy catalogue on intermediate scales, where weak non-linear gravitational evolution is expected, with a 2D lognormal density field and with a 3D lognormal density field projected on to the sky. We find that a significant non-Gaussian signal is retained despite projection effects and that the projection of a lognormal field is approximately lognormal. The effect of nearby small-scale structure upon the 2D topology is also investigated. We find that, despite the presence of nearby non-linear structures, the EPC still reveals a non-Gaussian signal due to the large-scale density field. The fact that a 3D lognormal field is a good fit to the Lick map on these scales implies that the Lick map is consistent with the result of gravitational instability acting on Gaussian initial perturbations. The usefulness of shallower depth angular galaxy catalogues for topological studies is assessed. Weinberg's algorithm for measuring the 2D genus of isodensity contours is applied to both cold dark matter (CDM) and Voronoi models of galaxy clustering. These models both display very similar topologies in 2D despite the fact that they are expected to display very different topologies with a 3D analysis, showing the limitations of 2D studies of this type of catalogue.