Dynamics of planetary rings under thermal forces
Planetary rings provide natural laboratories for studying the fundamental processes that govern the evolution of planetary systems. However, several key features, such as the sharp inner edges of Saturn's rings remain unresolved. In this work, we introduce and quantify the Eclipse-Yarkovsky (EY) effect, a thermal torque arising from asymmetric thermal emission of particles during planetary eclipses, which is effective for particles larger than millimeters in size. We formulate this effect within a continuum framework appropriate for collisionally coupled planetary rings and derive the continuum evolution equation that includes the EY torque and viscous diffusion (Eq.26), constraining its magnitude using ring particle spin distributions obtained from N-body simulations. We find that the EY effect systematically produces a positive angular momentum flux that could overcome the viscous torque, driving ring material outward and leading to long-term decretion. The total EY torque principally depends on the optical depth, in which we identify three dynamical regimes: dense, transitional, and tenuous regimes, each exhibiting distinct evolutionary pathways. In the dense or transition regimes, the EY torque can produce a sharp inner edge such as that of Saturn's A ring. In the tenuous regime, it can drive an entire ring outward while preserving shape. This outward transport may also facilitate satellite formation beyond the Roche limit. We also quantitatively show that planetary thermal radiation on rings exerts an opposing torque, namely planetary-Yarkovsky effect, whose importance depends on planetary emissivity and ring-particle albedo, and may lead to inward transport in Saturn's close-in rings.