A Spatially Resolved, Semiempirical Model for the Extended Atmosphere of α Orionis (M2 Iab)

We have constructed a detailed mean density and temperature model for the extended outer atmosphere of the O-rich supergiant Betelgeuse (??Ori [M2 Iab]), which extends from 1.0 to 10.0 stellar radii. A one-dimensional model is based on fitting NRAO VLA centimeter visibility data, and two-dimensional models are constructed using the intensity contours of the 0.7 cm observations of Lim et al. As one moves in toward the star from about 10 R* the mean electron temperature increases to a value of 3800 K, then declines down below Teff, and then rises to photospheric values. The peak mean model temperature is less than the typical chromospheric temperatures found in previous models. Observations of H? and chromospheric ultraviolet (UV) emission show that higher temperature components must also exist, but they do not dominate the weighted mean temperature structure. We tentatively identify the radius where the temperature distribution peaks (R 1.45 R*) with the dominant chromospheric UV emission region and find an areal filling factor of ?. In the extended semiempirical model the dominant source of electrons is from photoionized metals and is dominated by carbon. The low ionization of hydrogen leads to a dominance by H- (free-free) opacity at centimeter wavelengths. We derive simple estimates of the radio spectral indices for other similar M supergiants. We have constructed two-dimensional models to examine whether the intensity asymmetry observed at 0.7 cm is most likely to result from density or temperature variations. Adopting an elliptical two-dimensional model, a density asymmetry along the axes of symmetry would need to be 20?:?1. If we assume the radial wind velocity is independent of angle the integrated mass-loss rate is only a factor of ~2 greater than that derived from the one-dimensional model. However, previous H? speckle observations that sample the same spatial regions suggest the asymmetry observed at 0.7 cm is not due to such a large-scale density asymmetry. A modest change in temperature can more easily provide the asymmetry, increasing both the opacity and the thermal source term. If the radial density structure is assumed to be the same as in 1992 September, when HST/GHRS spectra were obtained, then the Fe II wind absorption features provide an estimate of the mass-loss rate of 3.1(?1.3) ? 10-6 M? yr-1. This further implies that the cool material dominates the mass of the extended atmosphere and that the radio-emitting region is within the base of the outflow observed in the circumstellar layers. A simple silicate dust model is constructed and the semiempirical model suggests an onset of dust formation at R 33 R* where Tdust ~ 360 K. This region lies outside the semiempirical model but simple extrapolations suggest that at this radius Te ~ 220 K, and the mean hydrogen density nH ~ 3 ? 106 cm-3. We address the difficult question of whether the mean thermal model based on the radio data can be consistent with the observed off-limb H? scattering emission if inhomogeneities are present.