THE STABILITY OF A COLLISIONLESS COSMOLOGICAL SHELL

We have used the P3M technique to simulate the evolution of collisionless shells in an Ω = 1 universe. We start from the well known spherical similarity solution, and we use a bootstrap technique to follow the evolution over very large expansion factors. We find that the overall structure follows the similarity solution for a long period during which bound clumps grow within the shell. In the early stages these clumps tend to be more massive (by a factor of 2-3) than clumps in the external medium, and they have somewhat different structure. The larger condensations on the shell are rounder and rotate less rapidly than objects formed by hierarchical clustering. In addition, their positions on the shell tend to be anticorrelated. We find that at late times the growth of structure depends on induced velocity perturbations in material outside the shell. If such perturbations are suppressed, structure on the shell becomes self-similar; nonlinear clumps have a well-defined characteristic mass m* ≈ mshell/150, in rough agreement with estimates from earlier work. When induced motions in the background medium are correctly included, the evolution at late times is dominated by large-scale modes as predicted by linear stability analysis. The characteristic mass of clumps then slowly approaches the mass of the shell. The stable final state appears to consist of one or two massive clumps on the edge of a spherical void. This, rather than a spherical shell, seems to be the generic end-state of a localized positive energy perturbation in an otherwise uniform Einstein-de Sitter universe. The growth of nonlinear clumps on a shell is slow, and in most situations their characteristic mass, will be overtaken by that of the clumps growing by hierarchical clustering in the external material. We discuss the possible application of these results to the origin of galaxies and large-scale structure.