Self-similar Collapse of Axisymmetric Systems

Self-similar solutions are found for the collisionless collapse of axisymmetric density perturbations in an Einstein-de Sitter universe. At large radii, the isodensity contours of the model perturbations are assumed to be oblate spheroids (with axis ratios 3/5) or prolate spheroids (with axis ratios 5/3). The spherically averaged density profiles of the oblate and prolate models are similar to those of spherically symmetric models with the same asymptotic density slope; the main difference is that the nonspherical models have a shallower density profile in the central regions. The self-similar collisionless solutions do not show "pancakes" or "needles"; that is, the axis ratios in the inner regions are not much more extreme than those in the outer regions. One of the models examined, which is oblate at large radii, is prolate at smaller radii.