Driving Planetary Period Oscillations From the Hall Conducting Layer of Saturn's Upper Atmosphere

We develop a simple physical model of the planetary period oscillations (PPOs) observed in Saturn's magnetosphere. The model couples together flows and currents in five two-dimensional systems: an upper and lower atmospheric layer in each hemisphere, and the equatorial magnetosphere. We neglect the curved geometry of the planet and the magnetosphere but use a simple scaling argument to account for the very different sizes of the two systems. We show that it is possible to drive a PPO current system with many of the observed properties by invoking a twin vortex system in the Hall conducting layer of either hemisphere. The twin vortex system is able to generate divergent currents because our model includes a representation of the latitudinal variation of conductance. The large inertia and low Pedersen conductance of this layer of the atmosphere means that the twin vortex system and the PPO currents have a very stable rotation velocity and a very long dissipation timescale, explaining the long term persistence and stability of the PPO current systems. For a range of realistic parameters, part of the PPO current system closes through the equatorial magnetosphere, and part through the opposite hemisphere, as observed. We make predictions about the phase relationships between these closure currents that allow our model to be tested. Although the wind speeds required to produce the observed currents are implausibly large, interaction with enhanced electron density in the auroral regions reduces the necessary wind speeds to plausible values.