CHROMOSPHERIC EXTENTS PREDICTED BY TIME-DEPENDENT ACOUSTIC-WAVE MODELS

In the present work I compute time-dependent acoustic wave models for the outer atmospheres of Arcturus (K2 IIIp), Aldebaran (K5 III), and Betelgeuse (M2 lab). I discuss the propagation of short-period monochromatic shock waves as well as acoustic frequency spectra. My wave models show that the dissipation of the mechanical wave energy leads to an increase of the atmospheric temperatures up to chromospheric values. The combined effect of the higher temperatures and the momentum transfer of the waves increases the pressure scale heights of the atmospheres considerably. However, the chromospheric extents for the adopted stars, denned by the monotonic decrease with height of the time-averaged electron densities in the wave models, remain small compared with the stellar radii. For Arcturus and Aldebaran, I find a chromospheric extent of 1.12 and 1.13 R*, respectively, corresponding to a time-averaged electron density of 107 cm-3. For Betelgeuse, the chromospheric extent is 1.22 R*. The small chromospheric extents in my wave models are in agreement with the observational result of Judge that the "extended chromospheres" of late-type giant and supergiant stars are due only to the low gravity of these stars. This result is further strong evidence that dissipating acoustic waves are an appropriate heating mechanism for the chromospheres of inactive late-type stars.