We present the first application of a spherical collapse model to a supercluster of galaxies. Positions and redshifts of ~3000 galaxies in the Shapley supercluster (SSC) are used to define velocity caustics that limit the gravitationally collapsing structure in its central part. This is found to extend at least to 8 h-1 Mpc of the central cluster, A3558, enclosing 11 ACO clusters. Infall velocities reach ~2000 km s-1. Dynamical models of the collapsing region are used to estimate its mass profile. An upper bound on the mass, based on a pure spherical infall model, gives M(8 h-1 Mpc) 1.3 × 1016 h-1 M ⊙ for an Einstein–de Sitter (critical) universe and M(8 h-1 Mpc) 8.5 × 1015 h-1 M ⊙ for an empty universe. The Diaferio & Geller model, based on estimating the escape velocity, gives a significantly lower value, M(8 h-1 Mpc) ≈ 2.1 × 1015 h-1 M⊙, very similar to the mass Geller et al. found around the Coma cluster by the same method and comparable to or slightly lower than the dynamical mass in the virialized regions of clusters enclosed in the same region of the SSC. In both models, the overdensity in this region is substantial, but it is far from the value required to account for the peculiar motion of the Local Group with respect to the cosmic microwave background.
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