Hydrodynamic Simulations of Asymmetric Propeller Structures in Saturn's Rings

The observation of the non-Keplerian behavior of propeller structures in Saturn's outer A ring (Tiscareno et al. 2010, Seiler et al. 2017, Spahn et al. 2018) raises the question, how the propeller responds to the wandering of the central embedded moonlet. Here, we study numerically how the induced propeller is changing for a librating moonlet. It turns out, that the libration of the moonlet induces an asymmetry in the structural imprint of the propeller, where the asymmetry is depending on the moonlet's libration period and amplitude. Further, we study the dependence of the asymmetry on the libration period and amplitude for a moonlet with 400 m Hill radius, which is located in the outer A ring. In this way, we are able to apply our findings to the largest found propeller structures -- such as Bl\'eriot -- which are expected to be of similar size. For Bl\'eriot, we can conclude that, supposed the moonlet is librating with the largest observed period of 11.1 years and an azimuthal amplitude of about 1845 km (Seiler et al. 2017, Spahn et al. 2018), a small assymmetry should be measurable but depends on the moonlet's libration phase at the observation time. The excess motions of the other giant propellers -- such as Santos Dumont and Earhart -- have similar amplitudes as Bl\'eriot and thus might allow the observation of larger asymmetries due to their smaller azimuthal extent. This would permit to scan the whole gap structure for asymmetries. Although the librational model of the moonlet is a simplification, our results are a first step towards the development of a consistent model for the description of the formation of asymmetric propellers caused by a freely moving moonlet.