Sometimes You Just Can't Put a Ring on It: Setting Constraints on Rings around Moons from Magnetic Fields

Abstract

All four giant planets and several minor bodies in the Solar System host rings. However, rings around moons have yet to be observed. A host planet can produce magnetic fields that affect its moons, adding a wealth of dynamical phenomena that could shape the properties of such ring systems. In this study, we investigate constraints on the stability of circumsatellitial rings (CSRs) under the effect of magnetic fields originating from the host planet, using both analytical and numerical methods. We find that the electric field induced by the rotation of the ambient planetary magnetosphere constitutes a significant perturbation on charged grains in CSRs. We demonstrate that this effect can de-orbit sufficiently charged grains on short timescales, providing a novel approach to constrain the properties of CSRs.

Figures (6)

• Figure 1: Schematic diagram (not to scale) of a planet, a moon, and a grain in a CSR (shaded region). The inset illustrates the forces (per unit mass) acting on a grain in the moon's frame: The electric force ($\vec{F}_E$), the magnetic force ($\vec{F}_B$), the gravitational force from the moon ($\vec{F}_{\rm g,m}$), and the gravitational perturbation due to the host planet ($\vec{F}_{\rm g,p}$).
• Figure 2: Separation distance from moon ($r$), periapsis distance ($p$), semimajor axis ($a$), and eccentricity ($e$) plotted as functions of time for a grain orbiting Rhea. Our numerical results are presented for grains with charge-to-mass ratios of $-0.2$, $-0.1$, $0$, and $+0.2\,\rm{C/kg}$.
• Figure 3: The eccentricity of a grain with initial orbital radius $1.2\,R_{\rm m}$ plotted as a function of time for Rhea (top), Titan (mid), and Iapetus (bottom). For Rhea, the charge-to-mass ratio was chosen to be $-0.1\,\rm{C/kg}$, while for Titan and Iapetus, it was $-1.0\,\rm{C/kg}$. Our analytical results, given by Eq. (\ref{['sol']}), are compared with our numerical results.
• Figure 4: Same as Fig. \ref{['fig:ts']}, but with the solutions presented up to $t=5T_{\rm m}$. To extend it to $5T_{\rm m}$, we took the absolute value of the analytical solution.
• Figure 5: The critical initial orbital radius, below which a grain will crash into the moon's surface, plotted as a function of the charge-to-mass ratio for Rhea (top), Titan (mid), and Iapetus (bottom). Our analytical results, given by Eq. (\ref{['analytic']}), are compared with our numerical results, and the Roche limit is indicated by a horizontal dashed line.