The Self-Similarity of Shear-dominated Viscous Stirring | Zendy

Benjamin F. Collins | Zendy; Hilke E. Schlichting | Zendy; Re’em Sari | Zendy

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The Self-Similarity of Shear-dominated Viscous Stirring

Author(s) -

Benjamin F. Collins,

Hilke E. Schlichting,

Re’em Sari

Publication year - 2007

Publication title -

the astronomical journal

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 2.61

H-Index - 271

eISSN - 1538-3881

pISSN - 0004-6256

DOI - 10.1086/513718

Subject(s) - eccentricity (behavior) , planetesimal , classical mechanics , physics , self similarity , population , shearing (physics) , mechanics , statistical physics , distribution function , boltzmann equation , distribution (mathematics) , mathematical analysis , geometry , mathematics , planet , astrophysics , quantum mechanics , demography , sociology , political science , law , thermodynamics

We examine the growth of eccentricities of a population of particles withinitially circular orbits around a central massive body. Successive encountersbetween pairs of particles increase the eccentricities in the disk on average.As long as the epicyclic motions of the particles are small compared to theshearing motion between Keplerian orbits, there is no preferred scale for theeccentricities. The simplification due to this self-similarity allows us tofind an analytic form for the distribution function; full numericalintegrations of a disk with 200 planetesimals verify our analyticalself-similar distribution. The shape of this non-equilibrium profile isidentical to the equilibrium profile of a shear-dominated population whosemutual excitations are balanced by dynamical friction or Epstein gas drag.Comment: 8 pages, 2 figure

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