Saturn's G ring: insights from the dynamical evolution of dust particles from the G-ring arc

To explore the formation and properties of Saturn's G ring, we study the dynamics of micron-sized dust particles originating from the arc of debris near the inner edge of the ring. The dynamical evolution of particles due to various perturbation forces and the plasma sputtering that erodes the particles is simulated by a well-tested numerical code. Based on the simulation results, the normal $I/F$ of the G ring observed by the Cassini spacecraft can be explained by dust particles originating from the arc. Other properties of the G ring are also estimated, including the steady-state size distribution and the number density of ring particles, the geometric optical depth, the apparent edge-on thickness, the age and the remaining lifetime of the G ring. We find that the particle size distribution of the G ring follows a power law with an exponent of 2.8, and dust particles in the size range of $[5, 10]\,{\mu}$m are dominant within the ring. The average number density of particles of the G ring in the radial direction is about $10^{-3}$-$10^{-2}\,\mathrm{m}^{-3}$. The peak value of the edge-on geometric optical depth of the G ring is about $3.9\times10^{-2}$. The maximum apparent edge-on thickness of the G ring with the geometric optical depth larger than $1\times10^{-8}$ is approximately $9,000\,\mathrm{km}$. The age of the G ring is estimated to be $10^{6}$-$10^{7}\,\mathrm{years}$, and the remaining lifetime of the ring is on the order of $10^{4}\,\mathrm{years}$.