Theory of the Curve of Growth and Phase Effects in a Cloudy Atmosphere. Applications to Venus

Abstract

The analysis of a planetary spectrum is most rapidly accomplished with the help of the curve of growth. When the atmosphere of a planet contains haze or clouds which cause the process of line formation to be dominated by multiple scattering, the usual curve-of-growth technique leads to serious errors in pressure and chemical abundance. Here we develop the theory of the curve of growth for pressure-broadened lines formed in a scattering atmosphere, and apply it to Venus. The atmosphere is modeled on a homogeneous, semi-infinite cloud as has previously been done by Chamberlain. The model is, however, extended to the non-conservative case and to strong lines. In its asymptotic regimes, the curve of growth for the scattering atmosphere is found to be qualitatively similar to that for lines formed in a clear atmosphere. However, a major difference between the two is the existence of an extended transition region in the scattering case for which the equivalent widths of unsaturated lines follow an approximately square-root dependence on the amount of absorber and pressure. The dependence of the equivalent widths on phase is considered in the case of both strong and weak lines. While the model considered here gives the correct sense for the phase variation, it is not in good quantitative agreement with observation. This discrepancy suggests that the model requires serious modification. Simple asymptotic expressions for the equivalent widths of very weak and strong lines are developed which will allow a rapid preliminary analysis of new data. These expressions also apply to homogeneous models with anisotropic scattering and finite thickness. The theory is applied to published spectroscopic data on CO2, H2O, HCl, HF and CO yields the following description of the atmosphere in the vicinity of clouds: pressure, 0.2 atm; temperature, 240-270K; and specific amounts of: CO2, 2?104 cm atm; H2O, 2 cm atm; CO, 2?6 cm atm; HCl, 2?10?2 cm atm; HF, 2-6?10?4 cm atm; O2, <7?10?1 cm atm.