Collins, Benjamin F. and Schlichting, Hilke E. and Sari, Re'em (2007) The Self-Similarity of Shear-dominated Viscous Stirring. Astronomical Journal, 133 (5). pp. 2389-2392. ISSN 0004-6256 http://resolver.caltech.edu/CaltechAUTHORS:20091027-105526150
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We examine the growth of eccentricities of a population of particles with nearly circular orbits around a central massive body. Successive encounters between pairs of particles increase the eccentricities in the disk on average. We describe the system in terms of a Boltzmann equation. As long as the epicyclic motions of the particles are small compared to the shearing motion between circular Keplerian orbits, there is no preferred scale for the eccentricities, and the evolution is self-similar. This simplification reduces the full time-dependent Boltzmann equation to two separate equations: one that describes the shape of the distribution and another that describes the evolution of the characteristic eccentricity on which the distribution is centered. We find that the shape of the eccentricity distribution function is a general feature of such systems, and is of the form (1 + x^2)^(-3/2). In particular, bodies evolving under only their own excitations have the same eccentricity distribution profile as bodies whose excitations are balanced by dynamical friction. We find exact expression for the typical eccentricity for these two cases, and allow for time-dependent damping and excitation rates. Full numerical N-body simulations of a disk with 200 planetesimals verify our analytical self-similar distribution.
|Additional Information:||© 2007 The American Astronomical Society. Received 2006 September 21; accepted 2007 February 8. We thank Yair Shokef for his enlightening comments, and the anonymous referee for several suggestions that have improved this manuscript. R. S. is a Packard Fellow and an Alfred P. Sloan Fellow.|
|Subject Keywords:||planets and satellites : formation; solar system : formation|
|Official Citation:||The Self-Similarity of Shear-dominated Viscous Stirring Benjamin F. Collins, Hilke E. Schlichting, and Re'em Sari 2007 The Astronomical Journal 133 2389-2392 doi: 10.1086/513718|
|Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Tony Diaz|
|Deposited On:||02 Nov 2009 17:43|
|Last Modified:||26 Dec 2012 11:30|
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