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Collision Rates......................................... (2004)
BibTeX
@MISC{Goldreich04collisionrates.........................................,
author = {Peter Goldreich and Yoram Lithwick},
title = {Collision Rates.........................................},
year = {2004}
}
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Abstract
Planets form in the circumstellar disks of young stars. We review the basic physical processes by which solid bodies accrete each other and alter each others ’ random velocities, and we provide order-of-magnitude derivations for the rates of these processes. We discuss and exercise the two-groups approximation, a simple yet powerful technique for solving the evolution equations for protoplanet growth. We describe orderly, runaway, neutral, and oligarchic growth. We also delineate the conditions under which each occurs. We refute a popular misconception by showing that the outer planets formed quickly by accreting small bodies. Then we address the final stages of planet formation. Oligarchy ends when the surface density of the oligarchs becomes comparable to that of the small bodies. Dynamical friction is no longer able to balance viscous stirring and the oligarchs ’ random velocities increase. In the inner-planet system, oligarchs collide and coalesce. In the outer-planet system, some of the oligarchs are ejected. In both the inner- and outerplanet systems, this stage ends once the number of big bodies has been reduced to the point that their mutual interactions no longer produce large-scale chaos. Subsequently, dynamical friction by the residual small bodies circularizes and flattens their orbits. The final stage of planet formation involves the clean up
Keyphrases
collision rate small body dynamical friction planet formation final stage circumstellar disk order-of-magnitude derivation two-groups approximation outer-planet system mutual interaction popular misconception young star oligarchic growth evolution equation inner-planet system basic physical process viscous stirring oligarch collide protoplanet growth outerplanet system oligarch random velocity increase large-scale chaos solid body residual small body circularizes big body surface density oligarch becomes powerful technique
