On the origin of 'dividing lines' for late-type giants and supergiants

We show how a change in the nature of the stellar dyanmo can lead to a transition in the topological character of stellar magnetic fields of evolved stars, from being mainly closed on the blueward side of the giant tracks in the Hertzsprung-Russell (H-R) diagram to being mainly open on their redward side. If such a topological transition occurs, then these stars naturally segregate into two classes: those having hot coronae on the blueward side, and those having massive cool winds on the redward side, thus leading naturally to the so-called dividing lines.