Infrared brightness temperature of Saturn's rings based on the inhomogeneous multilayer assumption

Models of Saturn's rings based on the classical multilayer assumption have been studied in the infrared. Thermal energy balance of Saturn's rings is treated rigorously by solving the infrared radiative transfer equations. It was found that a homogeneous multilayer model is incompatible with the observed infrared brightness variation of the A and B rings, although it can fit that of the C ring. The alternative inhomogeneous multilayer model with dark particles within a bright haze of small icy particles is presented in order to satisfy the available infrared data of the A, B, and C rings. The results based on the inhomogeneous multilayer model may be summarized as follows: The observed infrared brightness data of the three rings are explained in terms of the different optical thickness without having significant differences in the ring-particle properties, such as albedo, spin rate, and sizes. But each ring contains a different amount of bright haze particles and their concentration within the rings depends on whether or not dark particles emit radiation mostly from one hemisphere (slow rotator and/or low thermal inertia). If a dark particle is an isothermal radiator, the possible ranges of A₁ and A₂ for all three rings are given by 0.9 ? A₁ ? 0.95 and 0.0 ? A₂ ? 0.15, where A₁ and A₂ are the bolometric bond albedos of a bright haze and a dark particle, respectively. The possible ranges of the optical thickness ratio X of the dark particle layer to the total ring layer for the rings A, B, and C are given by 0.65 ? X ? 0.75, 0.8 ? X ? 0.9, and 0.8 ? X ? 1.0, respectively. If a dark particle is a slow rotator, we obtain 0.9 ? A₁ ? 0.95 and 0.0 ? A₂ ? 0.4 for all three rings. The ranges of X for the rings A, B, and C are given by 0.35 ? X ? 0.7, 0.65 ? X ? 0.9, and 0.35 ? X ? 1.0, respectively. In this paper, for the first time, a consistent model is presented which is applicable to all three rings from the multilayer point of view.