Collapse of the cores of slowly rotating isothermal clouds

Rotation plays an important role in the formation of stars and planetary systems, but detailed calculations of its effects have been limited by the difficulty of following the collapse from interstellar dimensions to those characteristic of the solar system or binary stars. We 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. This equilibrium state has a density profile which is proportional to 1/r2 in its inner regions and attaches smoothly to a uniform background, a plausible approximation for the core of a molecular cloud plus its envelope. We note that for reasonable values of interstellar parameters, the inner solar mass of the cloud has a total angular momentum on the order of that possessed by the augmented solar system, where the planetary masses are scaled to reflect solar abundances (Hoyle 1960; Safranov 1969). 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. The solutions have inner limiting forms that attach smoothly to existing solutions for the buildup of protostars (Stahler, Shu, and Taam 1980a, b; Mercer-Smith, Cameron, and Epstein 1983) and protostellar disks (Cassen and Moosman 1981). Taken together, 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