Growth of aspherical structure in the universe: is the local supercluster an unusual system

The growth and subsequent collapse of homogeneous ellipsoidal perturbations in a uniform expanding background is considered as a simple model for the formation of large-scale aspherical structures in the observed universe. Numerical calculations of the evolution of such perturbations turn out to be well described by an approximate analytic solution of the equations of motion, and simple relationships are found between the initial shape of a perturbation and its shape and kinematic properties at the time of collapse. Perturbations do not change their shape significantly until they reach a density contrast of order unity. As a result, structures with the kinematic properties of the Local Supercluster should form much more commonly in a low-density universe than in a flat universe. The homogeneity of the local Hubble flow, the motion of the Milky Way with respect to the microwave background, and the flattening of the Local Supercluster can be successfully accounted for by these models provided that the initial perturbation is sufficiently flattened. Viable models are obtanied only if the ratio of the lengths of the two smaller axes of the initial perturbation is at least 3:1 in an Einstein--de Sitter universe or at least 1.8:1 in a universe for which Ω is of order 0.1 when the protocluster pancakes