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Hydrodynamic simulations for shallow regions of the stellar convection zone have been performed. Three dimensional numerical models for photospheric convection in a compressible, radiation-coupled, non-magnetic, gravitationally stratified medium have been calculated to find the general properties of stellar convection zones, using a realistic equation of state and opacities. To test the credibility of a given simulation, a synthetic spectral line is derived. The properties of simulated convection produce the characteristic line bisector shape, which we can observe from solar spectral lines.
From the detailed analysis of the simulation, the characteristics of solar granulation in shallow regions have been parameterized and compared with that of Chan and Sofia's deep, efficient convection simulations (Chan and Sofia 1989). Furthermore, the validity of the mixing length approximation for these shallow regions has been studied, which this talk will focus on. \\
This research was supported in part by NASA grant NAGW-2531 to Yale University.
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