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Astron. Astrophys. 325, 709-713 (1997)

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1. Introduction

The M-type supergiant [FORMULA]  Ori (M2 Iab) is a well studied object and a broad range of dynamical atmospheric features has been identified. Alpha Ori is a noncoronal star with an extended atmosphere and a cool, massive wind. Alpha Ori has an extended chromosphere with temperatures in excess of 6000 K (Newell & Hjellming 1982). The size of the chromosphere is uncertain as it is probably strongly dependent on the spectral diagnostics used. Basri et al. (1981) have calculated a semiempirical chromosphere model for [FORMULA]  Ori by fitting the Mg II and Ca II line fluxes given by IUE assuming smooth functions for the atmospheric density and pressure. They found a steady increase of the atmospheric temperature starting from 2820 K in the temperature minimum layer up to 7000 K at a mass column density of [FORMULA] g cm-2. These observational data have been re-interpreted by Hartmann & Avrett (1984) assuming a combined chromosphere-wind model. The model was calculated considering momentum deposition by Alfvén waves described by means of a time-independent dissipation law. Theoretical calculations based on stochastic acoustic shocks have been given by Cuntz (1992a, b). These models are self-consistent, time-dependent and fully nonlinear. They give information about the propagation and dissipation of nonmagnetic energy in the chromosphere and allow predictions about the expected range of chromospheric temperatures and velocity fields.

In the meantime, high resolution spectra obtained by HST-GHRS have become available. Results are given by Carpenter et al. (1994a, b), Robinson & Carpenter (1995), Brandt et al. (1995), and Carpenter & Robinson (1997). These data contain a large amount of novel spectral information, largely because of the increase in spectral resolution. They also indicate the presence of complex chromospheric velocity fields (both sub- and supersonic, both inwardly and outwardly directed flows), which in principle cannot be explained by either the semiempirical model of Basri et al. (1981) or the time-independent Alfvén wave driven wind model given by Hartmann & Avrett (1984). The various components of the Fe II emission features, for instance, point to the existence of different dynamic atmospheric components with radial velocities ranging from -14 km s-1 (inwardly directed) to +15 km s-1 (outwardly directed) relative to the stellar photosphere (Carpenter & Robinson 1997). A further interesting velocity feature was described by Robinson & Carpenter (1995). They found that the Mg II lines, which have profiles similar to the strong Fe II lines, have wings with drastically different inferred radial velocities, with values of -11 km s-1 and +10 km s-1 for the h and k lines, respectively. These results are still not understood and are difficult to interpret because of scattering effects and opacity broadening.

The new observational results for [FORMULA]  Ori are a strong motivation to further explore acoustic shock wave models. It is therefore the goal of this paper to evaluate the formation of sub- and supersonic velocity patterns at different atmospheric heights. In particular, I will discuss monochromatic wave calculations having a fixed wave period and stochastic wave calculations with periods determined by a random number generator assuming modified Gaussian distributions. Understandably, the monochromatic wave models are not realistic and are only given as comparison. The paper is structured as follows: In Sect. 2, I discuss the method and model assumptions considered. Sect. 3 gives the results. Conclusions are presented in Sect. 4.

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© European Southern Observatory (ESO) 1997

Online publication: April 28, 1998