Constraints on the initial mass, age and lifetime of Saturn’s rings from viscous evolutions that include pollution and transport due to micrometeoroid bombardment

Abstract

The Cassini spacecraft provided key measurements during its more than twelve year mission that constrain the absolute age of Saturn’s rings. These include the extrinsic micrometeoroid flux at Saturn, the volume fraction of non-icy pollutants in the rings, and a measurement of the ring mass. These observations taken together limit the ring exposure age to be ≲ a few 100 Myr if the flux was persistent over that time (Kempf et al., 2022). In addition, Cassini observations during the Grand Finale further indicate the rings are losing mass (Hsu et al., 2018; Waite et al., 2018) suggesting the rings are ephemeral as well. In a companion paper (Durisen and Estrada, 2022), we show that the effects of micrometeoroid bombardment and ballistic transport of their impact ejecta can account for these loss rates for reasonable parameter choices. In this paper, we conduct numerical simulations of an evolving ring in a systematic way in order to determine initial conditions that are consistent with these observations.We begin by revisiting the ancient massive ring scenario of Salmon et al. (2010). Here, we model not just the viscous evolution, but we subject the ring to pollution by micrometeoroid bombardment over the age of the Solar System. We find that regardless of initial mass, the ring always ends up with more pollutant than is currently observed, because the ring spends the majority of its lifetime at relatively low mass where it is most susceptible to darkening. We then show that models with initial disk masses of ∼1–3 Mimas masses reach volume fractions of pollutant consistent with the observed volume fractions of non-icy material in the A and B rings within a time scale of ∼ a few 100 Myr.Finally, we use the analysis of Durisen and Estrada (2022) to add the dynamical effects of meteoroid bombardment into the evolution equations, namely, mass loading and ballistic transport. The treatment of mass loading is exact, while ballistic transport is handled in an approximate way. Simulations show that: (1) mass loading and ballistic transport applied to an initially high optical depth annulus inevitably produce a lower density C ring analog interior to the annulus; and (2) high density rings subject to persistent micrometeoroid bombardment do not have an asymptotic mass but instead have an asymptotic lifetime much shorter than the age of the Solar System. This is because micrometeoroid bombardment and ballistic transport drive the dynamical evolution of the ring once viscosity weakens, indicating that the exposure age of the rings and their dynamical age are connected.