Gravitational accretion of particles in Saturnʹs rings

Gravitational accretion in the rings of Saturn is studied with local N-body simulations, taking into account the dissipative impacts and gravitational forces between particles. Common estimates of accretion assume that gravitational sticking takes place beyond a certain distance (Roche distance) where the self-gravity between a pair of ring particles exceeds the disrupting tidal force of the central object, the exact value of this distance depending on the ring particlesʹ internal density. However, the actual physical situation in the rings is more complicated, the growth and stability of the particle groups being affected also by the elasticity and friction in particle impacts, both directly via sticking probabilities and indirectly via velocity dispersion, as well as by the shape, rotational state and the internal packing density of the forming particle groups. These factors are most conveniently taken into account via N-body simulations. In our standard simulation case of identical 1 m particles with internal density of solid ice, ρ = 900   kg m −3 , following the Bridges et al., 1984 elasticity law, we find accretion beyond a = 137 , 000 – 146 , 000   km , the smaller value referring to a distance where transient aggregates are first obtained, and the larger value to the distance where stable aggregates eventually form in every experiment lasting 50 orbital periods. Practically the same result is obtained for a constant coefficient of restitution ε n = 0.5 . In terms of r p parameter, the sum of particle radii normalized by their mutual Hill radius, the above limit for perfect accretion corresponds to r p < 0.84 . Increased dissipation ( ε n = 0.1 ), or inclusion of friction (tangential force 10% of normal force) shifts the accretion region inward by about 5000 km. Accretion is also more efficient in the case of size distribution: with a q = 3 power law extending over a mass range of 1000, accretion shifts inward by almost 10 , 000   km . The aggregates forming in simulations via gradual accumulation of particles are synchronously rotating.