We show that under certain circumstances the differences between the absorption mean and Planck mean opacities can lead to multiple solutions for an LTE atmospheric structure. Since the absorption and Planck mean opacities are not expected to differ significantly in the usual case of radiative equilibrium, non-irradiated atmospheres, the most interesting situations where the effect may play a role are strongly irradiated stars and planets, and also possibly structures where there is a significant deposition of mechanical energy, such as stellar chromospheres and accretion disks. We have presented an illustrative example of a strongly irradiated giant planet where the bifurcation effect is predicted to occur for a certain range of distances from the star.
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