The influence of rotation in radiation driven winds from hot stars. II. CAK topological analysis

The topological analysis from Bjorkman (\cite{Bjorkman95}) for the standard model that describes the winds from hot stars by Castor et al. (\cite{Castor75}) has been extended to include the effect of stellar rotation and changes in the ionization of the wind. The differential equation for the momentum of the wind is non-linear and transcendental for the velocity gradient. Due to this non-linearity the number of solutions that this equation possess is not known. After a change of variables and the introduction of a new physically meaningless independent variable, we manage to replace the non-linear momentum differential equation by a system of differential equations where all the derivatives are explicitely given. We then use this system of equations to study the topology of the rotating-CAK model. For the particular case when the wind is frozen in ionization (δ=0) only one physical solution is found, the standard CAK solution, with a X-type singular point. For the more general case (δ ≠q 0), besides the standard CAK singular point, we find a second singular point which is focal-type (or attractor). We find also, that the wind does not adopt the maximal mass-loss rate but almost the minimal.