Large-Scale Clustering in Bubble Models

We analyze the statistical properties of bubble models for the large-scale distribution of galaxies. To this aim, we realize static simulations, in which galaxies are mostly randomly arranged in the regions surrounding bubbles. As a first test, we realize simulations of the Lick map, by suitably projecting the three-dimensional simulations. In this way, we are able to safely compare the angular correlation function implied by a bubbly geometry to that of the APM sample. Quite remarkably, we find that several bubble models provide an adequate amount of large-scale correlation, which nicely fits that of APM galaxies. Further, we apply the statistics of the count-in-cell moments to the three-dimensional distribution and compare them with available observational data on variance, skewness and kurtosis. Based on our purely geometrical constructions, we find that a well defined hierarchical scaling of higher order moments up to scales ∼ 70hMpc. We show that this must be expected for any non-Gaussian distribution in the weak-coherence regime. The overall emerging picture is that the bubbly geometry is well suited to reproduce several aspects of large-scale clustering. Furthermore, the statistical test we apply are able to discriminate between different models. We find that models with fixed bubble radius have troubles to account for the angular correlation of APM galaxies, while a shallow spectrum fails to reproduce the observed three-dimensional skewness. A model with a rather steep spectrum of bubble of radii is rather adequate to account for the observational tests that we considered.