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

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Abstract
We have fit synthetic visibilities from 3-D (CO5BOLD + PHOENIX) and 1-D (PHOENIX, ATLAS 12) model stellar atmospheres of Procyon (F5 IV) to high-precision interferometric data from the VLTI Interferometer (K-band) and from the Mark III interferometer (500 nm 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 3-D hydrodynamical model produces significantly less limb darkening at 500 nm relative to the temperature structure of a 1-D MARCS model atmosphere with a standard mixing-length approximation for convection. Our direct fits to the interferometric data confirm this prediction. A 1-D ATLAS 12 model with ``approximate overshooting'' provides the required temperature gradient. We show, however, that 1-D 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 twelve 1-D model atmospheres based on the surface intensity distribution of a 3-D granulation simulation. We emphasize that 1-D models with overshooting may realistically represent the mean temperature structure of F-type stars like 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.

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