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

Collisional evolution of eccentric planetesimal swarms

Models for the steady state collisional evolution of low eccentricity planetesimal belts identify debris disks with hot dust at 1AU, like eta Corvi and HD69830, as anomalous since collisional processing should have removed most of the planetesimal mass over their >1 Gyr lifetimes. This paper looks at the effect of large planetesimal eccentricities (e>>0.3) on their collisional lifetime and the amount of mass that can remain at late times M_{late}. For an axisymmetric planetesimal disk with common pericentres and eccentricities e, we find that M_{late} \propto e^{-5/3}(1+e)^{4/3}(1-e)^{-3}. For a scattered disk-like population (i.e., common pericentres), in the absence of dynamical evolution, the mass evolution at late times would be as if only planetesimals with the largest eccentricity were present. Despite the increased remaining mass, higher eccentricities do not increase the hot emission from the collisional cascade until e>0.99, partly because most collisions occur near pericentre thus increasing the dust blow-out diameter. However, at high eccentricities (e>0.97) the blow-out population extending out from pericentre may be detectable above the collisional cascade; higher eccentricities also increase the probability of witnessing a recent collision. All of the imaging and spectroscopic constraints for eta Corvi can be explained with a single planetesimal population with pericentre at 0.75AU, apocentre at 150AU, and mass 5M_\oplus; however, the origin of such a high eccentricity population remains challenging. The mid-IR excess to HD69830 can be explained by the ongoing destruction of a debris belt produced in a recent collision in an eccentric planetesimal belt, but the lack of far-IR emission requires small bound grains to be absent from the parent planetesimal belt, possibly due to sublimation.Comment: MNRAS in pres

Accretion among preplanetary bodies: the many faces of runaway growth

(abridged) When preplanetary bodies reach proportions of ~1 km or larger in size, their accretion rate is enhanced due to gravitational focusing (GF). We have developed a new numerical model to calculate the collisional evolution of the gravitationally-enhanced growth stage. We validate our approach against existing N-body and statistical codes. Using the numerical model, we explore the characteristics of the runaway growth and the oligarchic growth accretion phases starting from an initial population of single planetesimal radius R_0. In models where the initial random velocity dispersion (as derived from their eccentricity) starts out below the escape speed of the planetesimal bodies, the system experiences runaway growth. We find that during the runaway growth phase the size distribution remains continuous but evolves into a power-law at the high mass end, consistent with previous studies. Furthermore, we find that the largest body accretes from all mass bins; a simple two component approximation is inapplicable during this stage. However, with growth the runaway body stirs up the random motions of the planetesimal population from which it is accreting. Ultimately, this feedback stops the fast growth and the system passes into oligarchy, where competitor bodies from neighboring zones catch up in terms of mass. Compared to previous estimates, we find that the system leaves the runaway growth phase at a somewhat larger radius. Furthermore, we assess the relevance of small, single-size fragments on the growth process. In classical models, where the initial velocity dispersion of bodies is small, these do not play a critical role during the runaway growth; however, in models that are characterized by large initial relative velocities due to external stirring of their random motions, a situation can emerge where fragments dominate the accretion.Comment: Accepted for publication in Icaru

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