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We present the first magnetohydrodynamic model of the stellar chromosphericheating and acceleration of the outer atmospheres of cool evolved stars, usingalpha Tau as a case study. We used a 1.5D MHD code with a generalized Ohm's lawthat accounts for the effects of partial ionization in the stellar atmosphereto study Alfven wave dissipation and wave reflection. We have demonstrated thatdue to inclusion of the effects of ion-neutral collisions in magnetized weaklyionized chromospheric plasma on resistivity and the appropriate gridresolution, the numerical resistivity becomes 1-2 orders of magnitude smallerthan the physical resistivity. The motions introduced by non-linear transverseAlfven waves can explain non-thermally broadened and non-Gaussian profiles ofoptically thin UV lines forming in the stellar chromosphere of alpha Tau andother late-type giant and supergiant stars. The calculated heating rates in thestellar chromosphere due to resistive (Joule) dissipation of electric currents,induced by upward propagating non-linear Alfven waves, are consistent withobservational constraints on the net radiative losses in UV lines and thecontinuum from alpha Tau. At the top of the chromosphere, Alfven wavesexperience significant reflection, producing downward propagating transversewaves that interact with upward propagating waves and produce velocity shear inthe chromosphere. Our simulations also suggest that momentum deposition bynon-linear Alfven waves becomes significant in the outer chromosphere at 1stellar radius from the photosphere. The calculated terminal velocity and themass loss rate are consistent with the observationally derived wind propertiesin alpha Tau.

Toward A Self Consistent MHD Model of Chromospheres and Winds From Late Type Evolved Stars