The microwave phase effect of Venus

The disk-integrated brightness temperature of Venus between 8 mm and 10 cm has been observed to vary with phase angle, the lowest temperature occuring just after inferior conjuction. We apply the equations of heat conduction and radiative transfer to thermal emission from a nonsynchronously but slowly rotating planet of arbitrary obliquity which is heated by combination of direct insolation and radiative and convective transport from the atmosphere. Even with this variety of heat sources, symmetry considerations permit the surface temperature distribution to be specified approximately by a one-parameter family of isotherms, characterized by a, an index of the equator-to-pole temperature gradient. The theory predicts that the 3-cm and 10-cm time-averaged brightness temperatures should be identical, but the 3-cm temperature amplitude (the maximum variation with phase angle) be greater than the 10-cm amplitude. Both predictions are in accord with observations. If the obliquity of the Cytherean rotation axis were large, different Cytherean temperature regimes would be presented for terrestrial view at successive apparitions and the brightness temperature should vary from synodic period to synodic period. The observed constancy of the temperature for consecutive inferior conjuctions argues for an obliquity less than about 8° for reasonable choices of the parameter a and the analytic form in which it appears. An intercomparison of phase data at several frequencies, coupled with the radar reflectivities, can potentially provide information on the chemistry and structure of the Cytherean subsurface material. From considerations of cosmic abundances, terrestrial analogy, and chemical equilibrium, a variety of silicates, carbonates, and oxides, an one variety of organic molecule—poly-cyclic aromatic hydrocarbons—can be postulated as primary constituents of the Cytherean surface. Their thermal, magnetic, and electrical properties are analyzed, as a function of frequency, temperature, porosity, granularity, and impurity content. A naive application of results obtained for inappropriate values of these parameters may lead to significant errors. The comparison of Venus and laboratory data shows that fused quartz and a wide range of powdered oxides, carbonates, and silicates may, to within observational uncertainty, be primary Cytherean surface materials. Magnetic materials, granite, and the hydrocarbons are excluded. An analysis of the phase retardation data for the surviving materials points uniquely to retrograde rotation. The surface phase lag is very small. The bulk electrical properties of the lunar and Cytherean surface materials are shown to be closely similar. The theory of the present paper predicts a 21-cm brightness temperature at inferior conjuction close to one recent measured value. The 8-mm brightness temperature amplitude is in disagreement with values expected from the theory if atmospheric water vapor or carbon dioxide were the source of the millimeter wave opacity, and is in agreement with theory if the opacity is due to dust distributed through the lower atmosphere, and preferentially abundant in the illuminated hemisphere. But attenuation by the clouds secures excellent agreement with observation. They are probably the primary microwave absorbers, but this conclusion does not imply any particular cloud composition. Determination of plausible surface materials properties permits the following estimates to be made of surface temperatures: mean disk, 700°K; mean darkside, 600°K; mean brightside, 800°K; subsolar point, 1000°K; antisolar point, 610°K; pole 470°K. Corresponding surface pressures are ∼50 atm. The low radar reflectivity at 3.6 cm cannot be due to a general 3.6-cm absorption by the atmosphere and clouds. The result can be attributed to anomalously high absorption above a surface cold spot in the first radar Fresnel zone, or to the variation of porosity, and therefore of dielectric constant, with depth.