Thermal forces on planetary ring particles: application to the main system of Saturn

Abstract

Context. The motion of small particles in planetary rings is affected in the long-term by radiation forces. While the Poynting-Robertson effect has been extensively discussed and applied to the dynamics of micron-sized ring particles, studies of thermal self-acceleration of particles are only in their infancy. Aims. We extend the pioneering work of Rubincam (2006, Icarus 184, 532) by a more thorough analytical formulation of both planetary and solar thermal forces on ring particles. Methods. Within a sparse disk model we analytically compute both seasonal and diurnal variants of the thermal forces and we demonstrate that the diurnal effect components vanish for a sample of rapidly rotating particles with randomly oriented spin axes. For sufficiently slowly rotating ring particles, though, these diurnal components might significantly modify the expected planetocentric secular drift rates of their orbits. We also take into account the orbital effects of Poynting-Robertson drag that begin to dominate the thermal forces for particles with sizes <5 mm. Our formulation of the Poynting-Robertson drag is the first to account properly for the influence of the planetary shadow. Results. We critically review the previous suggestion that Saturn's A and B ring boundaries might correlate with radiative null-torque orbits of small particles. Using the best estimates of optical and thermal parameters of Saturn's ring particles, we show that the millimetre to several centimetre size particles mostly drift inward to the planet with a characteristic radial speed ν r ∼ 3 × 10 -6 cm/s, corresponding to drift across the whole main ring system in ∼(1-5) x 10 8 years if the effects of inter-particle collisions are neglected. The radial speed is comparable to, or even larger than, the effective radial drift rate of small particles due to redistribution of collisional ejecta from micrometeoroid impacts. Therefore, radiation forces may be important for estimating the evolution timescales of Saturn's rings as derived from the ballistic transport theory. We propose that, in addition to collisional coagulation, radiation forces may efficiently remove centimetre-sized particles and thus help explain the observed paucity of these particles in Saturn's rings. A population of particles with spin axes aligned with normal to the disk plane, if it exists, would experience a net outward drift provided their rotation rate is larger than their orbital frequency.