Self-similar secondary infall and accretion in an Einstein-de Sitter universe

Similarity solutions are given for secondary infall onto an accreting center in an Einstein-de Sitter universe. The case of a central black hole quietly accreting all the infalling gas is considered first. If there is no central black hole and the gas is collisional, a shock forms and propagates outward; similarity solutions are given for the adiabatic postshock flow. Solutions for collisionless fluid shells and for a collisional fluid with omega much less than one moving in the potential of the omega = 1 collisionless solution are presented. A comparison is made with similarity solutions found recently for expanding voids by Bertschinger (1985), and it is shown how the collisionless similarity solutions can be used to infer the ages of objects formed by secondary infall.

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