Collisionless formation of filaments in an expanding universe

This paper reports on a series of numerical simulations of the nonlinear gravitational collapse of collisionless matter in an Omega=1 expanding universe. We focused on the collapse of an isolated and smooth maximum of the density field and restricted ourselves to the case of one- and two-dimensional perturbations which makes possible very high resolution particle-in-cell simulations (we use a 512 x 512 mesh). We investigate the influence of the dimensionality on the collapse process by comparing the collapse of one caustics and the collapse of two caustics at right angle. We find that the filament collapse occurs for an expansion factor which is 75% smaller than in the plane collapse case. With an expansion factor of 1.6 after the collapse, the filament density profile becomes smooth and isotropic (cylindrical), and the characteristic spikes of the plane collapse are unobservable in the central region. The existence of a virialized core, as well as its size, are determined by the properties of the initial state, i.e., its temperature and homogeneity level. On the contrary, the halo is characteristic of the collapse process itself: whatever the initial conditions may be, the collapsed filament follows a self-similar evolution. The halo density profile is well-fitted by a power law of index - 1.1 +/- 0.05, the amplitude increasing with the expansion factor a approximately as a(0.55). The evolution of the velocity distribution also becomes self-similar with an expansion factor of 1.6 after the collapse, and a typical peculiar velocity then scales as similar to a(-0.3). We are confident that these results are physical and not affected by perverse numerical effects. The measured departure from the expected slope of -1 (from semianalytic arguments) for the halo power law in the two-dimensional case is attributed to the presence of compensating troughs, which should have important consequences for the three-dimensional case, in particular if clusters form at the intersection of three caustics.