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We present the first application of a spherical collapse model to asupercluster of galaxies. Positions and redshifts of $\sim 3000$ galaxies inthe Shapley Supercluster (SSC) are used to define velocity caustics that limitthe gravitationally collapsing structure in its central part. This is found toextend at least to $8 h^{-1}$ Mpc of the central cluster, A 3558, enclosing 11ACO clusters. Infall velocities reach $\sim 2000$ km s$^{-1}$. Dynamical modelsof the collapsing region are used to estimate its mass profile. An upper boundon the mass, based on a pure spherical infall model, gives $M(<8 h^{-1}{\rmMpc}) ^{<}_{\sim} 1.3\times 10^{16}h^{-1}M_\odot$ for an Einstein-de Sitter(critical) Universe and $M(<8 h^{-1}{\rm Mpc}) ^{<}_{\sim} 8.5\times10^{15}h^{-1}M_\odot$ for an empty Universe. The model of Diaferio & Geller(1997), based on estimating the escape velocity, gives a significantly lowervalue, $M(<8 h^{-1}{\rm Mpc})\approx 2.1\times 10^{15}h^{-1}M_\odot$, verysimilar to the mass found around the Coma cluster by the same method (Geller etal. 1999), and comparable to or slightly lower than the dynamical mass in thevirialized regions of clusters enclosed in the same region of the SSC. In bothmodels, the overdensity in this region is substantial, but far from the valuerequired to account for the peculiar motion of the Local Group with respect tothe cosmic microwave background.Comment: 28 pages, 10 figures, aastex v5.0. To appear in The Astronomical  Journal August 200

The Shapley Supercluster. III. Collapse Dynamics and Mass of the Central Concentration