A Librational Model for the Propeller Bl\'eriot in the Saturnian Ring System

Abstract

The reconstruction of the orbital evolution of the propeller structure Bl\'eriot orbiting in Saturn's A ring from recurrent observations in Cassini ISS images yielded a considerable offset motion from the expected Keplerian orbit (Tiscareno et al., 2010). This offset motion can be composed by three sinusoidal harmonics with amplitudes and periods of 1845, 152, 58 km and 11.1, 3.7 and 2.2 years, respectively (Srem\v{c}evi\'c et al., 2014). In this paper we present results from N-Body simulations, where we integrated the orbital evolution of a moonlet, which is placed at the radial position of Bl\'eriot under the gravitational action of the Saturnian satellites. Our simulations yield, that especially the gravitational interactions with Prometheus, Pandora and Mimas is forcing the moonlet to librate with the right frequencies, but the libration-amplitudes are far too small to explain the observations. Thus, further mechanisms are needed to explain the amplitudes of the forced librations - e.g. moonlet-ring interactions. Here, we develop a model, where the moonlet is allowed to be slightly displaced with respect to its created gaps, resulting in a breaking point-symmetry and in a repulsive force. As a result, the evolution of the moonlet's longitude can be described by a harmonic oscillator. In the presence of external forcings by the outer moons, the libration amplitude gets the more amplified, the more the forcing frequency gets close to the eigenfrequency of the disturbed propeller oscillator. Applying our model to Bl\'eriot, it is possible to reproduce a libration period of 13 years with an amplitude of about 2000 km.