A multilayer model for thermal infrared emission of Saturnʹs rings: Basic formulation and implications for Earth-based observations

We present our new model for the thermal infrared emission of Saturnʹs rings based on a multilayer approximation. In our model, (1) the equation of classical radiative transfer is solved directly for both visible and infrared light, (2) the vertical heterogeneity of spin frequencies of ring particles is taken into account, and (3) the heat transport due to particles motion in the vertical and azimuthal directions is taken into account. We adopt a bimodal size distribution, in which rapidly spinning small particles (whose spin periods are shorter than the thermal relaxation time) with large orbital inclinations have spherically symmetric temperatures, whereas non-spinning large particles (conventionally called slow rotators) with small orbital inclinations are heated up only on their illuminated sides. The most important physical parameters, which control ring temperatures, are the albedo in visible light, the fraction of fast rotators ( f fast ) in the optical depth, and the thermal inertia. In the present paper, we apply the model to Earth-based observations. Our model can well reproduce the observed temperature for all the main rings (A, B, and C rings), although we cannot determine exact values of the physical parameters due to degeneracy among them. Nevertheless, the range of the estimated albedo is limited to 0 – 0.52 ± 0.05 , 0.55 ± 0.07 – 0.74 ± 0.03 , and 0.51 ± 0.07 – 0.74 ± 0.06 for the C, B, and A rings, respectively. These lower and upper limits are obtained assuming all ring particles to be either fast and slow rotators, respectively. For the C ring, at least some fraction of slow rotators is necessary ( f fast ⩽ 0.9 ) in order for the fitted albedo to be positive. For the A and B rings, non-zero fraction of fast rotators ( f fast ⩾ 0.1 – 0.2 ) is favorable, since the increase of the brightness temperature with increasing solar elevation angle is enhanced with some fraction of fast rotators.