Abstract

We present a general method for solving the non-linear differential equation of monotonically increasing steady-state radiation driven winds. We graphically identify all the singular points before transforming the momentum equation to a system of differential equations with all the gradients explicitly given. This permits a topological classification of all singular points and to calculate the maximum and minimum mass-loss of the wind. We use our method to analyse for the first time the topology of the non-rotating frozen-in ionisation m-CAK wind, with the inclusion of the finite disk correction factor, and find up to 4 singular points, three of the x-type and one attractor-type. The only singular point (and solution passing through) that satisfies the boundary condition at the stellar surface is the standard m-CAK singular point. © 2007 WILEY-VCH Verlag GmbH & Co. KGaA.