FORMATION OF MOONLETS IN SATURN'S RINGS: THE ROLE OF THE CONSTRUCTIVE INTERFERENCE OF LIN-SHU-TYPE CIRCULAR AND SPIRAL DENSITY WAVES

Localized kilometer-sized propeller features, recently detected in Cassini images of Saturn's A ring, may be interpreted as signatures of small hundred-meter-sized moonlets embedded within the broad ring. We propose that these moonlets are formed due to the constructive interference of the gravitationally unstable axisymmetric and nonaxisymmetric perturbations of the self-gravitating Saturnian ring disk. The hydrodynamical slab model of the disk is studied to determine its instability against low-frequency compression-type, or Lin-Shu-type, oscillations whose propagation vector is perpendicular to the axis of the disk's rotation. The linear instability analysis is performed in the following way. First, we derive the general dispersion relation for the gravity perturbations inside the slab within the standard local short-wavelength approach. Next, we match the solutions to the solutions of the Poisson equation outside the slab to arrive at the particular dispersion relation. The particular dispersion relation describes the development of symmetric Jeans' perturbations which cause density enhancements. From this dispersion relation, the growth rate of Jeans-unstable oscillations developing in the spatially homogeneous slab model is obtained. The dispersion relation shows that perturbations of both types, axisymmetric and nonaxisymmetric, are excited simultaneously due to the Jeans' gravitational instability. As a result, circular and spiral patterns develop. We suggest that clumping occurs due to the enhanced density increase at the intersections of the patterns. We also speculate that these clumps further develop into propeller moonlets.