Abstract
We use an approximate, analytic solution to the full radial extent of the non-singular, isothermal, self-gravitating sphere to derive analytically the general properties of the resulting spheres, and their stability to radial perturbations. We rederive the stability criterion of Bonnor and Ebert, and confirm analytically their (numerical) results. Finally, we compute spherically symmetric simulations of the time-dependent, Lagrangean, gas-dynamic equations, showing that the transition between stable and unstable solutions does occur for a value of the outer radius of the sphere close to the one obtained from Bonnor's stability criterion.
