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.Comment: 22 pages, 6 figures, submitted to Ap