Collisional Velocities and Rates in Resonant Planetesimal Belts

We consider a belt of small bodies around a star, captured in one of the external or 1:1 mean-motion resonances with a massive perturber. The objects in the belt collide with each other. Combining methods of celestial mechanics and statistical physics, we calculate mean collisional velocities and collisional rates, averaged over the belt. The results are compared to collisional velocities and rates in a similar, but non-resonant belt, as predicted by the particle-in-a-box method. It is found that the effect of the resonant lock on the velocities is rather small, while on the rates more substantial. The collisional rates between objects in an external resonance are by about a factor of two higher than those in a similar belt of objects not locked in a resonance. For Trojans under the same conditions, the collisional rates may be enhanced by up to an order of magnitude. Our results imply, in particular, shorter collisional lifetimes of resonant Kuiper belt objects in the solar system and higher efficiency of dust production by resonant planetesimals in debris disks around other stars.Comment: 31 pages, 11 figures (some of them heavily compressed to fit into arxiv-maximum filesize), accepted for publication at "Celestial Mechanics and Dynamical Astronomy

Origin and Evolution of Saturn's Ring System

The origin and long-term evolution of Saturn's rings is still an unsolved problem in modern planetary science. In this chapter we review the current state of our knowledge on this long-standing question for the main rings (A, Cassini Division, B, C), the F Ring, and the diffuse rings (E and G). During the Voyager era, models of evolutionary processes affecting the rings on long time scales (erosion, viscous spreading, accretion, ballistic transport, etc.) had suggested that Saturn's rings are not older than 100 My. In addition, Saturn's large system of diffuse rings has been thought to be the result of material loss from one or more of Saturn's satellites. In the Cassini era, high spatial and spectral resolution data have allowed progress to be made on some of these questions. Discoveries such as the ''propellers'' in the A ring, the shape of ring-embedded moonlets, the clumps in the F Ring, and Enceladus' plume provide new constraints on evolutionary processes in Saturn's rings. At the same time, advances in numerical simulations over the last 20 years have opened the way to realistic models of the rings's fine scale structure, and progress in our understanding of the formation of the Solar System provides a better-defined historical context in which to understand ring formation. All these elements have important implications for the origin and long-term evolution of Saturn's rings. They strengthen the idea that Saturn's rings are very dynamical and rapidly evolving, while new arguments suggest that the rings could be older than previously believed, provided that they are regularly renewed. Key evolutionary processes, timescales and possible scenarios for the rings's origin are reviewed in the light of tComment: Chapter 17 of the book ''Saturn After Cassini-Huygens'' Saturn from Cassini-Huygens, Dougherty, M.K.; Esposito, L.W.; Krimigis, S.M. (Ed.) (2009) 537-57

Accretional evolution of a planetesimal swarm: 1. A new simulation

This novel simulation of planetary accretion simultaneously treats many interacting heliocentric distance zones and characterizes planetesimals via Keplerian elements. The numerical code employed, in addition to following the size distribution and the orbit-element distribution of a planetesimal swarm from arbitrary size and orbit distributions, treats a small number of the largest bodies as discrete objects with individual orbits. The accretion algorithm used yields good agreement with the analytic solutions; agreement is also obtained with the results of Weatherill and Stewart (1989) for gravitational accretion of planetesimals having equivalent initial conditions

Accretional evolution of a Planetesimal Swarm. II. The terrestrial zone.

We use our multi-zone simulation code (D. Spaute, S. Weidenschilling, D. R. Davis, and F. Marzari, Icarus 92, 147-164, 1991) to model numerically the accretion of a swarm of planetesimals in the region of the terrestrial planets. The hybrid code allows interactions between a continuum distribution of small bodies in a series of orbital zones and a population of large, discrete planetary embryos in individual orbits. Orbital eccentricities and inclinations evolve independently, and collisional and gravitational interactions among the embryos are treated stochastically by a Monte Carlo approach. The spatial resolution of our code allows modeling of the intermediate stage when particle-in-a-box methods lose validity due to nonuniformity in the planetesimal swarm. The simulations presented here bridge the gap between such early-stage models and N-body calculations of the final stage of planetary accretion. The code has been tested for a variety of assumptions for stirring of eccentricities and inclinations by gravitational perturbations and the presence or absence of damping by gas drag. Viscous stirring, which acts to increase relative velocities of bodies in crossing orbits, produces so-called ``orderly'' growth, with a power-law size distribution having most of the mass in the largest bodies. Addition of dynamical friction, which tends to equalize kinetic energies and damp the velocities of the more massive bodies, produces rapid ``runaway'' growth of a small number of embryos. Their later evolution is affected by distant perturbations between bodies in non-crossing orbits. Distant perturbations increase eccentricities while allowing inclinations to remain low, promoting collisions between embryos and reducing their tendency to become dynamically isolated. Growth is aided by orbital decay of smaller bodies due to gas drag, which prevents them from being stranded between orbits of the embryos. We report results of a large-scale simulation of accretion in the region of terrestrial planets, employing 100 zones spanning the range 0.5 to 1.5 AU and spanning 10^6 years of model time. The final masses of the largest bodies are several times larger than predicted by a simple analytic model of runaway growth, but a minimal-mass planetesimal swarm still yields smaller bodies, in more closely spaced orbits, than the actual terrestrial planets. Longer time scales, additional physical phenomena, and/or a more massive swarm may be needed to produce Earth-like planets

Dynamics and Planet Formation in/Around Binaries

The extent to which planetesimal accretion is affected by the perturbing presence of a companion star is an important issue in the formation of planets in and around binary systems. In this chapter, we review this issue by concentrating on one crucial parameter: the distribution of encounter velocities within the planetesimal swarm. The evolution of this parameter is numerically explored accounting for the secular perturbations of the binary and the friction due to the very likely presence of gas in the disk. Maps of the average encounter velocity \u27e8\u394v\u27e9 between different size planetesimals are presented for a total of 120 stellar dynamical configurations obtained by different combinations of the binary semimajor axis a b and eccentricity e b . According to the different values of \u27e8\u394v\u27e9, 3 different planetesimal accumulation modes are identified: 1) in regions where \u27e8\u394v\u27e9 is comparable to that derived for planetesimal swarms around single-stars, "standard" accretion is likely, eventually via runaway growth, 2) in regions where \u27e8\u394v\u27e9 is larger than v ero , the threshold velocity above which all impacts are eroding, no accretion is possible and planet growth is stopped, 3) in between these two extremes, there is a large fraction of binary configurations where the increase in \u27e8\u394v\u27e9 is still below the erosion threshold. Planetesimal accumulation can still occur but it possibly proceeds at a slower rate than in the single-star case, following the so-called type II runaway growth mode

Formation of Terrestrial Planets

The past decade has seen major progress in our understanding of terrestrial planet formation. Yet key questions remain. In this review we first address the growth of 100 km-scale planetesimals as a consequence of dust coagulation and concentration, with current models favoring the streaming instability. Planetesimals grow into Mars-sized (or larger) planetary embryos by a combination of pebble- and planetesimal accretion. Models for the final assembly of the inner Solar System must match constraints related to the terrestrial planets and asteroids including their orbital and compositional distributions and inferred growth timescales. Two current models -- the Grand-Tack and low-mass (or empty) primordial asteroid belt scenarios -- can each match the empirical constraints but both have key uncertainties that require further study. We present formation models for close-in super-Earths -- the closest current analogs to our own terrestrial planets despite their very different formation histories -- and for terrestrial exoplanets in gas giant systems. We explain why super-Earth systems cannot form in-situ but rather may be the result of inward gas-driven migration followed by the disruption of compact resonant chains. The Solar System is unlikely to have harbored an early system of super-Earths; rather, Jupiter's early formation may have blocked the ice giants' inward migration. Finally, we present a chain of events that may explain why our Solar System looks different than more than 99\% of exoplanet systems