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Vertical structures induced by embedded moonlets in Saturn's rings: the gap region

We study the vertical extent of propeller structures in Saturn's rings. Our focus lies on the gap region of the propeller and on non-inclined propeller moonlets. In order to describe the vertical structure of propellers we extend the model of Spahn and Sremcevic (2000) to include the vertical direction. We find that the gravitational interaction of ring particles with the non-inclined moonlet does not induce considerable vertical excursions of ring particles, but causes a considerable thermal motion in the ring plane. We expect ring particle collisions to partly convert the lateral induced thermal motion into vertical excursions of ring particles. For the gap region of the propeller, we calculate gap averaged propeller heights on the order of 0.7 Hill radii, which is of the order of the moonlet radius. In our model the propeller height decreases exponentially until viscous heating and collisional cooling balance. We estimate Hill radii of 370m and 615m for the propellers Earhart and Bleriot. Our model predicts about 120km for the azimuthal extent of the Earhart propeller at Saturn's 2009 equinox, being consistent with values determined from Cassini images.