A study of the energy balance in the atmospheres of the major planets

Abstract

The monochromatic absorption of infrared and microwave radiation due to pressure-induced rotational and translational transitions in H2 gas and gaseous mixtures of H2 and He is investigated quantitatively. Existing laboratory data are used to obtain semi-empirical absorption coefficients of the rotational transitions as a function of frequency. A quantum mechanical calculation is carried out to obtain the translational absorption coefficient as a function of frequency for a diatomic gas, mixtures of diatomic and monatomic gases and mixtures of monatomic gases. The resulting expressions are used to compute the translational absorption coefficient for H2 and the enhancement in H2-He mixtures using a 6 - 12 Lennard-Jones potential for the molecular interaction and the EXP-4 model for the expectation value of the induced dipole moment over the ground electronic and vibrational states. A numerical method is devised for the efficient computation of the translational absorption and the results of the computations are given. The infrared opacity of NH3 is also considered. With certain assumptions, existing laboratory data are used to obtain approximate, semi-empirical mean transmissions over the rotation structure of NH3 as a function of frequency. Several non-gray model atmospheres are constructed for Jupiter, Saturn, Uranus and Neptune for various effective temperatures and He-H2 ratios taking the opacity due to H2 and He into account. The effect of adding the opacity due to NH3 is considered. The models are examined for self consistency and characteristic phenomena. They are then compared with the observations. The observations are used to restrict the range of the free parameters of the models. It is found that models of Jupiter and Neptune for which only the thermal opacity of H2 and NH3 is taken into account are incompatible with the observations. The presence of He is strongly indicated in the atmospheres of Jupiter, Uranus and Neptune. In the case of Jupiter, a rather large N(He)/N(H2) value is implied if there is no internal heat source. However, the observations indicate a preference for N(He)/N(H2) less than 2 and thus imply the existence of a small internal heat source greater than one-tenth of the incident solar flux. The effect of NH3 on the thermal equilibrium of the major planets is negligible except possibly in the case of Jupiter. However, its presence in the Jovian atmosphere does not alter the above conclusions.