The equilibria of rotating, isothermal clouds. I - Method of solution. II - Structure and dynamical stability

Abstract

In an effort to resolve the current controversy in dynamical models of rotating protostellar collapse, a detailed study has been made of the axisymmetric equilibrium configurations for differentially rotating, isothermal clouds. In this paper, the physical assumptions underlying the calculation are stated and the numerical technique outlined. The clouds are assumed to have the angular momentum distribution of rigidly rotating, uniform-density spheres of the same mass. Magnetic and viscous effects are neglected. The computational method is designed to handle highly flattened structures, should they arise, and to yield numerical values of the density with a maximum local error of order 1/N/sup 2//sub X/, where N/sub X/ is the number of zones covering the cloud's equatorial radius. A preliminary calculation, with N/sub X/ = 10, of nonrotating spherical equilibria reproduces the Lane--Emden result to within the desired accuracy. Errors in global properties, as measured by a test of the virial theorem, are about a factor of 10 lower than the maximum local error.