The standard problem of nonlocal thermodynamic equilibrium radiative transfer in the rovibrational band of the planetary atmosphere

The standard problem of radiative transfer in a rovibrational band is formu lated for an optically semi-infinite plane-parallel planetary atmosphere us ing a model of a linear molecule with two vibrational states. The solution of the problem describes the variation with height of the population of the excited vibrational state due to the existence of the upper boundary of th e atmosphere. We seek this solution as a function of the specially introduc ed dimensionless parameters-the atmosphere depth and four similarity parame ters-and study it for the parameter values that can be realized in the plan etary atmospheres, including the atmospheres of extrasolar planets. It is s hown that an increase in the optical density of the atmosphere can reduce t he population of an excited vibrational state in the band at the upper boun dary of the atmosphere by as much as several orders of magnitude as compare d to the population corresponding to the "optically thin band" limit. The a nomalous decrease in the opacity of the atmosphere, when only several lines of the band are involved in radiative transfer, is predicted. We also dete rmined the accuracy of calculating the population in the approximation of t he Doppler line profile. An approximate formula is obtained for the dimensi onless height of the boundary of the layer in which the local thermodynamic equilibrium exists for vibrational states. We propose a model and the form ula following from this model to roughly evaluate the decrease in this heig ht due to the impact on the population of additional radiative transitions between the state being considered and the underlying state belonging to an other vibrational mode of the molecule.