Co-existence and switching between fast and $\Omega$-slow wind solutions in rapidly rotating massive stars

Most radiatively-driven massive star winds can be modelled with m-CAK theory resulting in so called fast solution. However, those most rapidly rotating among them, especially when the stellar rotational speed is higher than $\sim 75\%$ of the critical rotational speed, can adopt a different solution called $\Omega$-slow solution characterized by a dense and slow wind. Here, in this work we study the transition region of the solutions where the fast solution changes to the $\Omega$-slow. Using both time-steady and time-dependent numerical codes, we study this transition region for different equatorial models of B-type stars. In all the cases, at certain range of rotational speeds, we found a region where the fast and $\Omega$-slow solution can co-exist. We find that the type of solution obtained in this co-existence region depends heavily on the initial conditions of our models. We also test the stability of the solutions within the co-existence region by performing base density perturbations in the wind. We find that under certain conditions, the fast solution can switch to a $\Omega$-slow solution, or vice versa. Such solution switching may be a possible contributor of material injected into the circumstellar environment of Be stars, without requiring rotational speeds near critical values.