On the magnetic structure and wind parameter profiles of Alfvén wave driven winds in late-type supergiant stars

Cool stars at giant and supergiant evolutionary phases present low velocity and high density winds, responsible for the observed high mass-loss rates. Although presenting high luminosities, radiation pressure on dust particles is not sufficient to explain the wind acceleration process. Among the possible solutions to this still unsolved problem, Alfvén waves are, probably, the most interesting for their high efficiency in transfering energy and momentum to the wind. Typically, models of Alfvén wave driven winds result in high velocity winds if they are not highly damped. In this work we determine self-consistently the magnetic field geometry and solve the momentum, energy and mass conservation equations, to demonstrate that even a low damped Alfvén wave flux is able to reproduce the low velocity wind. We show that the magnetic fluxtubes expand with a super-radial factor S > 30 near the stellar surface, larger than that used in previous semi-empirical models. The rapid expansion results in a strong spatial dilution of the wave flux. We obtained the wind parameter profiles for a typical supergiant star of 16 M⊙. The wind is accelerated in a narrow region, coincident with the region of high divergence of the magnetic field lines, up to 100 km s. For the temperature, we obtained a slight decrease near the surface for low damped waves, because the wave heating mechanism is less effective than the radiative losses. The peak temperature occurs at r ≃ 1.5 r0 reaching 6000 K. Propagating outwards, the wind cools down mainly due to adiabatic expansion.