STELLAR WINDS WITH NON-WKB ALFVEN WAVES .2. WIND MODELS FOR COOL, EVOLVED STARS

We construct Alfveb wave-driven mind models for physical conditions ap propriate to the expanding envelopes of cool, evolved stars. To derive wind properties, we assume steady, isothermal, spherically symmetric flow, but do not use the WKB (i.e., short-wavelength) approximation to calculate the wave amplitudes. Instead, we make use of the formalism developed in the first paper of this series (MacGregor & Charbonneau 1 994), which describes wave reflection and associated modifications to the wave force, and consistently incorporates these effects into the t reatment of wind dynamics. For flows containing undamped Alfven waves of arbitrarily long wavelength we find that the occurrence of wave ref lection has profound consequences for wind acceleration and mass loss. Specifically, in all of our computed models, the outward-directed wav e force near the base of the flow is significantly reduced relative to that in comparable WKB models. As a result, the initial expansion spe eds and mass flux densities of model winds that include non-WKB effect s are smaller than those of corresponding WKB winds. Moreover, at larg e distances from the star, wave reflection leads to an enhancement of the wave force relative to models in which all waves are presumed to b e outwardly propagating. This tendency, when combined with the previou sly noted reduction in mass flux, produces winds with higher asymptoti c flow speeds than those driven by high-frequency, short-wavelength Al fven waves. Given that the challenge of modeling winds from cool evolv ed stars is to produce winds with high mass fluxes and low asymptotic flow speeds, we argue that Alfven waves provide an acceptable driving mechanism only if their wavelengths are sufficiently short that minima l reflection occurs near the base of the flow. For stellar parameters characteristic of a supergiant star with spectral type similar to K5, this translates into an upper bound on Alfven wave periods of similar to 1 day.