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On the Limb Darkening, Spectral Energy Distribution, and Temperature Structure of Procyon

We have fit synthetic visibilities from three-dimensional (CO5BOLD+PHOENIX) and one-dimensional (PHOENIX, ATLAS 12) model stellar atmospheres of Procyon (F5 IV) to high-precision interferometric data from the VLT Interferometer (K band) and from the Mark III interferometer (500 and 800 nm). These data sets provide a test of theoretical wavelength-dependent limb-darkening predictions. The work of Allende Prieto et al. has shown that the temperature structure from a spatially and temporally averaged three-dimensional hydrodynamic model produces significantly less limb darkening at 500 nm relative to the temperature structure of a one-dimensional MARCS model atmosphere with a standard mixing-length approximation for convection. Our direct fits to the interferometric data confirm this prediction. A one-dimensional ATLAS 12 model with "approximate overshooting" provides the required temperature gradient. We show, however, that one-dimensional models cannot reproduce the ultraviolet spectrophotometry below 160 nm with effective temperatures in the range constrained by the measured bolometric flux and angular diameter. We find that a good match to the full spectral energy distribution can be obtained with a composite model consisting of a weighted average of 12 one-dimensional model atmospheres based on the surface intensity distribution of a three-dimensional granulation simulation. We emphasize that one-dimensional models with overshooting may realistically represent the mean temperature structure of F-type stars such as Procyon, but the same models will predict redder colors than observed because they lack the multicomponent temperature distribution expected for the surfaces of these stars.