A GENERAL-CLASS OF SELF-SIMILAR SELF-GRAVITATING FLUIDS

I present a general classification of self-similar solutions to the eq uations of gravitational hydrodynamics that contain many previous resu lts as special cases. For cold flows with spherical symmetry, the solu tion space can be classified into several regions of behavior similar to the Bondi (1952) solutions for steady flow. A full description of t hese solutions is possible, which serves as the asymptotic limit for t he general problem. By applying a shock jump condition, exact general solutions can be constructed. The isothermal case allows an extra exac t integral and can be asymptotically analyzed in the presence of finit e pressure. These solutions serve as analytic models for problems such as spherical accretion for star formation, infall or outflow of gas i nto galaxies, Lyman-alpha cloud dynamics, etc. Most previous self-simi lar results are obtained as special cases. The critical values for a c osmological flow with OMEGA = 1 and gamma = 4/3 turn out to play a spe cial role.