SELF-SIMILAR EXPANSION OF AXISYMMETRICAL VOIDS

Self-similar solutions are found for the collisionless expansion of ax isymmetric density deficits (voids) in an Einstein-de Sitter universe. At large radii, the isodensity contours of the model voids are assume d to be either oblate spheroids, with axis ratio 3:5, or prolate spher oids, with axis ratio 5:3. The asymptotic density profile has the form delta is-proportional-to - r(-nu); I investigate voids with nu = 1 to nu = 2.5. Both oblate and prolate voids with nu > 2 form nearly spher ical dense shells surrounding the central void. Models with nu = 2 for m partial shells, taking the form of polar caps for an oblate void and an equatorial belt for a prolate void. Models with nu < 2 which are o blate at large radii have isodensity contours which are approximately spherical at intermediate radii and even become prolate in the central regions, where delta less than or similar to -0.9. Similarly, models with nu > 2 which are prolate at large radii become oblate in the cent ral regions. In all the models examined, the peculiar velocity of each particle is smaller than its Hubble velocity relative to the void cen ter.