Chromospheric heating by acoustic shocks: A confrontation of GHRS observations of α tauri (K5 III) with ab initio calculations

We compare ab initio calculations of C II] line profiles near 2325 A with recently published observations of the inactive red giant α Tau (K5 III) obtained using the GHRS on board the Hubble Space Telescope. Our one-dimensional, time-dependent calculations assume that the chromosphere is heated by stochastic acoustic shocks generated by photospheric convection. We calculate various models using results from traditional (mixing length) convection zone calculations as input to hydrodynamical models. The C II] line profiles and ratios provide sensitive diagnostics of chromospheric velocity fields, electron densities, and temperatures. We identify major differences between observed and computed line profiles which are related to basic gas dynamics and which are probably not due to technical modeling restrictions. If the GHRS observations are representative of chromospheric conditions at all epochs, then one (or more) of our model assumptions must be incorrect. We suggest the following possibilities: (i) the convection zone has acoustical properties substantially different from those of traditional models, (ii) the atmospheric structure is determined by three-dimensional turbulence and/or horizontal flows not included in our models, (iii) acoustic shocks are not responsible for heating chromospheres of inactive "basal flux" giant stars. We predict time variability of C II] lines for comparison with observations. Based upon data from the IUE archives, we argue that photospheric motions associated with supergranulation or global pulsation modes are unimportant in heating the chromosphere of α Tau. Granule-scale motions would produce variations of a ± few percent on time scales ∼2 × 10⁵ s (2-3 days). Such variations are consistent with existing IUE data, but further data are needed.