Superclustering in the explosion scenario

In the explosion scenario, the deep potential wells at "knots" where three shells intersect are the natural sites for the formation of rich galaxy clusters. We use a simple toy model to study the spatial distribution of rich clusters in a generic type of explosion scenario. The model, parametrized by the distribution of shell radii and the filling factor, places spherical shells at random and identifies each "knot" as a cluster. Even though the distribution of shell centers is random, the resulting cluster correlation function is close to a power law extending to the diameter of the largest spheres (beyond which it vanishes), ξcc_ (r) = (r/r₀_) ^-γ^, with γ typically ~1. 5-2. Richer clusters form at the intersections of bigger shells and so have stronger correlations. The correlation length in our basic models, when scaled to the mean neighbor separation dᵇar^, exceeds the observed value by a factor ~3. Plausible modifications to account for the effects of shell interactions and mergers of nearby clusters reduce this discrepancy. Typical shell radii R ~ 20-40h^-1^ Mpc and filling factors f ~ 0. 3-0. 6 are required to produce the observed number density of clusters. Models with a power-law radius distribution, P (R) is proportional to Rbeta^ for R < Rₘax_, β ~ -4, also reproduce the richness distribution of clusters in the Abell catalog. Analytic estimates show that a physical model in which 20-40h^-1^ Mpc shells overlap at z ~ 5-10 can produce clusters of mass ~10¹5^ Mₛun_. We compute other measures of large-scale structure, which depend on higher order correlations. Supercluster multiplicity functions, void probabilities, number counts, topology statistics, and velocity correlations confirm the presence of strong superclustering and quantify the non-Gaussian nature of the model. Superclustering in the explosion scenario substantially exceeds that in more conventional models where clusters form by the gravitational collapse of Gaussian density fluctuations-this may be the only current theory that can produce the observed cluster-cluster correlations in an OMEGA = 1 universe. Our most successful model has a power-law radius distribution with β = -4. 5, Rₘax_ = 30h^-1^ Mpc, and modifications to account for shell interactions and cluster mergers. It appears consistent with the available observational data, except that its correlation length, r₀_ = 41h^-1^ Mpc, exceeds the observed value by ~50%~ (~2 σ). Primordial explosions amplified by several generations of galaxy formation, cosmological detonation waves with efficiencies ~ 10^-4^, and plasma sweeping by superconducting cosmic strings can generate shells of the required size.