The seven-lobed shape of the outer edge of Saturn’s A ring

Abstract

Using the complete set of stellar and radio occultation data from the Cassini mission, we fit a multimode model to the outer edge of Saturn’s A ring, similar to that previously applied to the B ring edge by Spitale and Porco (2010) and Nicholson et al. (2014a). Our model takes into account the coorbital libration of the satellite Janus, whose 7:6 Lindblad resonance is believed to be responsible for maintaining the edge at its observed location. Consistent with previous analyses (Spitale and Porco, 2009; El Moutamid et al., 2016), we find that the shape of the ring’s edge is dominated by a 7-lobed radial distortion that rotates with the same angular velocity as Janus during the periods when the satellite is on the inner leg of its 8-yr libration. The amplitude of this distortion is ∼12 km, and one of the seven minima is aligned within a few degrees of the satellite’s mean longitude. At times when Janus is on the outer leg of its libration, however, the 7-lobed pattern disappears completely. In addition to this resonantly-forced distortion, our data reveal the presence of a rich spectrum of normal modes sculpting the ring edge. When the 7-lobed pattern is present, the principal secondary mode has m=5, while when the 7-lobed pattern is absent, the shape of the edge is dominated by modes with m=9 and m=12, all with radial amplitudes of 4–6 km. The data strongly suggest that the m=5 mode actually persists, but at an undetectable level, throughout the latter period. Lower-amplitude modes are also seen with m=3, 4, 6, 8, 10 and 18, though not at all times. The normal mode frequencies are consistent with a simple analytic model whereby each mode exists within a resonant cavity near the edge of the ring (Borderies et al., 1985; Longaretti, 2018), from which we estimate an average surface mass density in this region of ∼20g cm−2, consistent with that derived from weak density waves (Tiscareno and Harris, 2018). Despite the relative complexity of the best-fitting model, the RMS deviations between it and the observed edge radii range from 1.7 to 5.5 km, substantially exceeding the measurement errors of ∼0.3 km and strongly suggesting the existence of additional, as-yet-uncharacterized perturbations. Contrary to previous analyses, we find no evidence for beating between the strong m=7 signature due to Janus and a weaker signature due to its coorbital companion Epimetheus (Spitale and Porco, 2009) and only weak evidence for an m=−3 mode driven by a gravity anomaly within Saturn (El Moutamid et al., 2016).