Do we understand rotating isothermal collapses yet?

The scalar virial equation can be used to elucidate many interesting properties of equilibrium gas clouds when the effects of surface pressure, rotation, self-gravity, and internal isothermal gas pressure are considered simultaneously. Details regarding the internal structure of rotating isothermal gas clouds are ignored in order to obtain an analytical expression describing global cloud properties. Excellent agreement is obtained between the simple analytical model and other previously published, more detailed models in physical regimes where other models have been constructed. For the first time, a physical connection is drawn between the surface-pressure-dominated equilibrium models of S. W. Stahler (1983, Astrophys. J. 268, 155–184) and the rotation-dominated models of C. Hayashi, S. Narita, and S. M. Miyama (1982, Prog. Theor. Phys. 68, 1949–1966). Stable axisymmetric models of any mass and angular momentum can be constructed. Using the analytic expression for virial equilibrium as a foundation, all rotating, isothermal collapse calculations can now be well understood. Limiting properties of isothermal clouds are outlined, and realistic “starting” models for cloud collapse are proposed.