Composition of Massive Giant Planets

The two current models for giant planet formation are core accretion and disk instability. We discuss the core masses and overall planetary enrichment in heavy elements predicted by the two formation models, and show that both models could lead to a large range of final compositions. For example, both can form giant planets with nearly stellar compositions. However, low-mass giant planets, enriched in heavy elements compared to their host stars, are more easily explained by the core accretion model. The final structure of the planets, i.e., the distribution of heavy elements, is not firmly constrained in either formation model.Comment: 6 pages, Proceedings of IAU Symposium 276 (Invited talk), The Astrophysics of Planetary Systems: Formation, Structure, and Dynamical Evolution. Turin, Italy, Oct. 201

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

Large mass inflow rates in Saturn's rings due to ballistic transport and mass loading

The Cassini mission provided key measurements needed to determine the absolute age of Saturn's rings, including the extrinsic micrometeoroid flux at Saturn, the volume fraction of non-icy pollutants in the rings, and the total ring mass. These three factors constrain the ring age to be no more than a few 100 Myr (Kempf et al., 2023). Observations during the Cassini Grand Finale also showed that the rings are losing mass to the planet at a prodigious rate. Some of the mass flux falls as "ring rain" at high latitudes. However, the influx in ring rain is considerably less than the total measured mass influx of 4800 to 45000 kg/s at lower latitudes (Waite et al., 2018). In addition to polluting the rings, micrometeoroid impacts lead to ballistic transport, the mass and angular momentum transport due to net exchanges of meteoroid impact ejecta. Because the ejecta are predominantly prograde, they carry net angular momentum outward. As a result, ring material drifts inward toward the planet. Here, for the first time, we use a simple model to quantify this radial mass inflow rate for dense rings and find that, for plausible choices of parameters, ballistic transport and mass loading by meteoroids can produce a total inward flux of material in the inner B ring and in the C ring that is on the order of a few x 10^3 to a few x 10^4 kg/s, in agreement with measurements during the Cassini Grand Finale. From these mass inflow rates, we estimate that the remaining ring lifetime is ~15 to 400 Myr. Combining this with a revised pollution age of ~120 Myr, we conclude that Saturn's rings are not only young but ephemeral and probably started their evolution on a similar timescale to their pollution age with an initial mass of one to a few Mimas masses.Comment: 25 pages, 6 figures, Published in Icaru

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

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

Convergence studies of mass transport in disks with gravitational instabilities. I. the constant cooling time case

We conduct a convergence study of a protostellar disk, subject to a constant global cooling time and susceptible to gravitational instabilities (GIs), at a time when heating and cooling are roughly balanced. Our goal is to determine the gravitational torques produced by GIs, the level to which transport can be represented by a simple α-disk formulation, and to examine fragmentation criteria. Four simulations are conducted, identical except for the number of azimuthal computational grid points used. A Fourier decomposition of non-axisymmetric density structures in cos ($m\phi$), sin ($m\phi$) is performed to evaluate the amplitudes $A_{m}$ of these structures. The $A_{m}$, gravitational torques, and the effective Shakura & Sunyaev α arising from gravitational stresses are determined for each resolution. We find nonzero $A_{m}$ for all $m$-values and that $A_{m}$ summed over all $m$ is essentially independent of resolution. Because the number of measurable $m$-values is limited to half the number of azimuthal grid points, higher-resolution simulations have a larger fraction of their total amplitude in higher-order structures. These structures act more locally than lower-order structures. Therefore, as the resolution increases the total gravitational stress decreases as well, leading higher-resolution simulations to experience weaker average gravitational torques than lower-resolution simulations. The effective $\alpha$ also depends upon the magnitude of the stresses, thus $\alpha_{\text{eff}}$ also decreases with increasing resolution. Our converged $\alpha_{\text{eff}}$ is consistent with predictions from an analytic local theory for thin disks by Gammie, but only over many dynamic times when averaged over a substantial volume of the disk

On the Evolution and Survival of Protoplanets Embedded in a Protoplanetary Disk

We model the evolution of a Jupiter-mass protoplanet formed by the disk instability mechanism at various radial distances accounting for the presence of the disk. Using three different disk models, it is found that a newly-formed Jupiter-mass protoplanet at radial distance of $\lesssim$ 5-10 AU cannot undergo a dynamical collapse and evolve further to become a gravitational bound planet. We therefore conclude that {\it giant planets, if formed by the gravitational instability mechanism, must form and remain at large radial distances during the first $\sim$ 10$^5-10^6$ years of their evolution}. The minimum radial distances in which protoplanets of 1 Saturn-mass, 3 and 5 Jupiter-mass protoplanets can evolve using a disk model with $\dot{M}=10^{-6} M_{Sun}/yr$ and $\alpha=10^{-2}$ are found to be 12, 9, and 7 AU, respectively. The effect of gas accretion on the planetary evolution of a Jupiter-mass protoplanet is also investigated. It is shown that gas accretion can shorten the pre-collapse timescale substantially. Our study suggests that the timescale of the pre-collapse stage does not only depend on the planetary mass, but is greatly affected by the presence of the disk and efficient gas accretion.Comment: 26 pages, 2 tables, 10 figures. Accepted for publication in Ap

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