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