Effects of the non-gray absorption in a simple radiative equilibrium model

Analytical solutions of the atmospheric vertical temperature profile are the first step in the analysis of planetary atmospheres. These types of studies usually make use of the gray assumption (i.e., absorption of radiation independent of wavelength). Since atmospheric gases absorb radiation at selective wavelengths, here we examine the implications of the non-gray absorption in a simple and analytically solvable planetary atmosphere. d that in some cases the non-gray absorption by itself limits the maximum optical thickness that can be reached by the planetary atmosphere. The existence of a liquid phase at the surface in equilibrium with its vapor phase in the atmosphere also restricts the value of the optical thickness. For a constant value of absorbed sunlight, the non-gray atmosphere may produce two stable states, in comparison with the single one obtained in gray atmospheres. This result supports the existence of a warm ocean in an optically thick atmosphere with a low value of absorbed sunlight.