Cosmological self-similar shock waves and galaxy formation

Similarity solutions are found which are valid for times long compared to the Hubble time for adiabatic shock waves in open and Einstein-de Sitter Friedmann universes. The fluid equations and boundary conditions are given and integrals of the motion are derived from similarity arguments. Initially the shock wave formed satisfied the Sedov solution for adiabatic evolution in a constant medium, but it is modified by the cosmological expansion to form a self-similar thin dense shell which cools by adiabatic expansion and is unstable to gravitational fragmentation and collapse. The shock solution is applied to the explosive amplification model of galaxy formation of Ostriker and Cowie (1981). One generation of explosive amplification from an initial seed galaxy produces a shell of about 300 billion solar masses in galaxies, with radius and velocity dispersion typical of small groups.