The spherical collapse of a gas cloud initially in hydrostatic equilibrium is examined using self-similar solutions. We assume an initial density distribution of the form pαr-s and that some central energy loss or cooling initiates the collapse. The continued collapse can occur on a hydrodynamic time scale (hydro-regulated) or be regulated by the cooling process (cooling-regulated). The hydrodynamic time scale is roughly equal to the free-fall time. Provided the adiabatic index γ ≤ 5/3, collapse under self-gravity is hydro-regulated, although if s ≲ 2, the flow remains subsonic to the origin for γ = 5/3. In an external gravitational acceleration of the form r-n, hydro-regulated flows are possible for a wide range of γ only for n = 2, i.e., the gravitational field of a central point mass. For n < 2 and γ= 5/3, the flow is cooling-regulated. The collapse of gas clouds to form galaxies could occur on a hydrodynamic time scale only if the gas dominated the gravitational field and the inflow formed a central dominant mass. The likelihood of a collisionless component and the observation of extended mass distributions in galaxies implies that the collapse of a hot protogalactic cloud is cooling-regulated. We examine how the Galaxy might form from an initially smooth, hot cloud and show that some nonlinear substructure must initially be present.
