The outer atmospheres of cool M dwarfs

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M dwarfs are known to exhibit vastly different levels of magnetic activity, manifesting itself in star spots, X-ray emission and - at optical wavebands - chromospheric emission lines. In order to better understand the physics of these heated outer atmospheric layers for different spectral sub-types and activity levels among M dwarfs, we propose to perform 1D and 3D chromospheric modeling for these stars in the framework of this funding application. We specifically propose to compute both 3D chromospheric models and 1D chromospheric models and check, if the atmospheric inhomogeneities can be accounted for by single or linear combinations of 1D models, and juxtapose this modeling with state-of-the-art observations obtained by CARMENES. We therefore propose to use the atmosphere code PHOENIX for constructing a model grid of classical 1D chromospheres for M dwarfs and confront our modeling with high-resolution spectral observations taken with the CARMENES spectrograph. For selected objects we propose to perform a detailed comparison between observed and modeled spectra to better characterize the physics of the chromospheres of the selected individual stars.