The CARMENES search for exoplanets around M dwarfs. Chromospheric modeling of M2-3 V stars with PHOENIX

Chromospheric modeling of observed differences in stellar activity lines is imperative to fully understand the upper atmospheres of late-type stars. We present one-dimensional parametrized chromosphere models computed with the atmosphere code PHOENIX using an underlying photosphere of 3500 K. The aim of this work is to model chromospheric lines of a sample of 50 M2-3 dwarfs observed in the framework of the CARMENES, the Calar Alto high-Resolution search for M dwarfs with Exo-earths with Near-infrared and optical Echelle Spectrographs, exoplanet survey. The spectral comparison between observed data and models is performed in the chromospheric lines of Na I D2, H$\alpha$, and the bluest Ca II infrared triplet line to obtain best-fit models for each star in the sample. We find that for inactive stars a single model with a VAL C-like temperature structure is sufficient to describe simultaneously all three lines adequately. Active stars are rather modeled by a combination of an inactive and an active model, also giving the filling factors of inactive and active regions. Moreover, the fitting of linear combinations on variable stars yields relationships between filling factors and activity states, indicating that more active phases are coupled to a larger portion of active regions on the surface of the star.