The collapse of the cores of slowly rotating isothermal clouds

Abstract

The authors present here a semianalytic perturbational solution for the collapse of a slowly rotating cloud core. The initial equilibrium state is exact and corresponds to the uniformly rotating analogue of the singular isothermal sphere. Star (and disk) formation proceeds because the equilibrium is unstable to core collapse. The evolution in time can be followed by performing a perturbational analysis on the known similarity solution for the nonrotating case. The hydrodynamic equations, including self-gravity, can be reduced to a set of linear ordinary differential equations, which is solved by the method of matched asymptotic expansions. These calculations provide a self-consistent description of the dynamical collapse of rotating molecular cloud cores and a framework for the study of the formation of stars and nebular disks.