Self-similar condensation of spherically symmetric self-gravitating isothermal gas clouds

Abstract

The authors show that similarity solutions for the condensation of spherically symmetric self-gravitating isothermal gas clouds are much more abundant than was hitherto believed; they have discovered that each of the discrete solutions found by previous authors must be replaced by a bounded two-parameter continuum of such solutions. Moreover, the two parameters (z0, w0) admit a clear and useful physical interpretation. z0 characterizes the asymptotic form of a solution as t-->-∞ (i.e. at very early times), and reflects how intrinsically unstable against contraction the cloud interior is from the outset. w0 characterizes the asymptotic form of a solution as t-->+∞ (i.e. at very late times) and reflects how important external pressure is in driving compression. The evolution of the flow is presented and discussed.