Effects of Meteoroid Erosion in Planetary Rings

This grant supported continuing studies of the effects of ballistic transport on the evolution of Saturn's rings. Ballistic transport, as used in this context, refers to the net transport of mass and angular momentum caused by the exchange of meteoroid impact ejecta between neighboring ring regions (Ip 1983, 1984, Morfill et al. 1983, Lissauer 1984, Durisen 1984a,b). The characteristic time scale associated with this process is the gross erosion time t(sub g) the time it would take a ring region to be completed eroded if all impact ejecta were lost. This time scale is estimated to be about 10(exp 5) to 10(exp 6) years for a ring region with normal optical depth tau approximately 1. Earlier work by myself and collaborators developed the physical theory and simulation techniques to model this process (Durisen et al. 1989, Cuzzi and Durisen 1990). Detailed simulations, supported in part by this grant, have demonstrated that ballistic transport can produce observed structures in Saturn's rings, especially at and near the inner edges of the A and B Rings (Durisen et al. 1992, 1996). The structures of interest in the real rings are illustrated in Figures 1 and 2. Most of these structures were previously unexplained. The computational results plus analytic treatments place useful constraints on fundamental ring properties, including the indication of a relatively young ring age less than or equal 10(exp 8) years (see reviews by Nicholson and Dones 1991, Esposito 1993, Cuzzi 1995, and Porco 1995). This grant also supported development of the faster computational algorithms necessary to permit longer evolutions. Resulting simplications in the ballistic transport equations permitted an analytic linear stability analysis (Durisen 1995), which has provided considerable insight into ballistic transport processes and applications to Saturn's rings. All these accomplishments are described in more detail below

Planetary ring dynamics and morphology

Evidence for a moonlet belt in the region between Saturn's close-in moonrings Pandora and Prometheus is discussed. It is argued that little-known observations of magnetospheric electron density by Pioneer 11 imply substantial, ongoing injections of mass into the 2000 km region which surrounds the F ring. A hypothesis is presented that these events result naturally from interparticle collisions between the smaller members of an optically thin belt of moonlets. Also discussed is work on Uranus ring structure and photometry, image processing and analysis of the Jonian ring strucure, photometric and structural studies of the A ring of Saturn, and improvements to an image processing system for ring studies

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

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., 2023). 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, 2023), 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.Comment: 31 pages, 19 figures, 2 tables, Published in Icaru

Planetary ring studies

The following topics are covered: (1) characterization of the fine scale structure in Saturn's A and B rings; (2) ballistic transport modeling and evolution of fine ring structure; (3) faint features in the rings of Saturn; (4) the Encke moonlet; (5) dynamics in ringmoon systems; (6) a nonclassical radiative transfer model; and (7) particle properties from stellar occultation data

Combined Structural and Compositional Evolution of Planetary Rings Due to Micrometeoroid Impacts and Ballistic Transport

We introduce improved numerical techniques for simulating the structural and compositional evolution of planetary rings due to micrometeoroid bombardment and subsequent ballistic transport of impact ejecta. Our current, robust code is capable of modeling structural changes and pollution transport simultaneously over long times on both local and global scales. In this paper, we describe the methodology based on the original structural code of Durisen et al. (1989, Icarus 80, 136-166) and on the pollution transport code of Cuzzi and Estrada (1998, Icarus 132, 1-35). We provide demonstrative simulations to compare with, and extend upon previous work, as well as examples of how ballistic transport can maintain the observed structure in Saturn's rings using available Cassini occultation optical depth data. In particular, we explicitly verify the claim that the inner B (and presumably A) ring edge can be maintained over long periods of time due to an ejecta distribution that is heavily biased in the prograde direction through a balance between the sharpening effects of ballistic transport and the broadening effects of viscosity. We also see that a "ramp"-like feature forms over time just inside that edge. However, it does not remain linear for the duration of the runs presented here unless a less steep ejecta velocity distribution is adopted. We also model the C ring plateaus and find that their outer edges can be maintained at their observed sharpness for long periods due to ballistic transport. We hypothesize that the addition of a significant component of a retrograde-biased ejecta distribution may help explain the linearity of the ramp and is probably essential for maintaining the sharpness of C ring plateau inner edges. This component would arise for the subset of micrometeoroid impacts which are destructive rather than merely cratering. Such a distribution will be introduced in future work

On The Possibility of Enrichment and Differentiation in Gas Giants During Birth by Disk Instability

We investigate the coupling between rock-size solids and gas during the formation of gas giant planets by disk fragmentation in the outer regions of massive disks. In this study, we use three-dimensional radiative hydrodynamics simulations and model solids as a spatial distribution of particles. We assume that half of the total solid fraction is in small grains and half in large solids. The former are perfectly entrained with the gas and set the opacity in the disk, while the latter are allowed to respond to gas drag forces, with the back reaction on the gas taken into account. To explore the maximum effects of gas-solid interactions, we first consider 10cm-size particles. We then compare these results to a simulation with 1 km-size particles, which explores the low-drag regime. We show that (1) disk instability planets have the potential to form large cores due to aerodynamic capturing of rock-size solids in spiral arms before fragmentation; (2) that temporary clumps can concentrate tens of $M_{\oplus}$ of solids in very localized regions before clump disruption; (3) that the formation of permanent clumps, even in the outer disk, is dependent on the grain-size distribution, i.e., the opacity; (4) that nonaxisymmetric structure in the disk can create disk regions that have a solids-to-gas ratio greater than unity; (5) that the solid distribution may affect the fragmentation process; (6) that proto-gas giants and proto-brown dwarfs can start as differentiated objects prior to the H$_2$ collapse phase; (7) that spiral arms in a gravitationally unstable disk are able to stop the inward drift of rock-size solids, even redistributing them to larger radii; and, (8) that large solids can form spiral arms that are offset from the gaseous spiral arms. We conclude that planet embryo formation can be strongly affected by the growth of solids during the earliest stages of disk accretion.Comment: Accepted by ApJ. 55 pages including 24 figures. In response to comments from the referee, we have included a new simulation with km-size objects and have revised some discussions and interpretations. Major conclusions remain unchanged, and new conclusions have been added in response to the new ru