Isotropic Phase Function Research Articles

The infrared limb darkening of Venus

The observed infrared limb darkening of Venus in the 8- to 13-micron interval and over the observed range in μ, the cosine of the Venus zenith angle, can be expressed as μa, where α ≈ 0.5, according to two independent sets of measurements. Three general categories of models of the atmosphere and clouds of Venus are here proposed to explain the observed limb darkening. For each model, convective and then radiative equilibrium is assumed. In models A, limb darkening is attributed to the temperature gradient in an unknown, approximately gray absorber above the visible cloud deck. Other properties of the absorber, required so that α ≈ 0.5, render these models rather unlikely. In models B, limb darkening is attributed to a combination of the temperature gradient and the angular dependence of the emissivity in approximately gray multiply scattering clouds, initially with isotropic phase functions. In convective model B1, agreement with observation is secured for moderate values of , the albedo for infrared single scattering, if the clouds are diffuse by terrestrial standards; high implies more compact clouds. The temperature range with depth, particle number density, and composition of the clouds are discussed. Moderate variation of the extinction coefficient with depth in the clouds has little effect on the predicted limb darkening over the range in μ reliably observed; but closer to the limb, and for low values of , such variation may significantly influence the limb darkening. In radiative model B2, high values of lead to predictions of the planetary bolometric albedo in conflict with observations. Moderate values of lead to the observed limb-darkening law if the 8- to 13-μ opacity is about 2.5 times the mean opacity, which is a property of silicate clouds. The preceding models are extended to anisotropic phase functions and to other values of α. An anisotropic phase function of the form (1 + cos θ) increases the contribution of the emissivity to a by about 20%. In models C, the clouds coherently redistribute radiation emitted by the underlying atmosphere. The absence of marked spectral features in 8- to 13-μ Venus spectroscopy leads to the rejection of model C. Methods are described for removing the remaining ambiguity among the models.