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A.N. Youdin, J. Goodman (Princeton University)
Planetesimal formation by either the gravitational instability or collisional agglomeration mechanism faces serious obstacles. Controversy exists over whether particle-stirring turbulence, which opposes gravitational collapse, or the inefficiency of sticking, particularly at extreme ratios of kinetic to binding energy, poses the more formidable hurdle. We present results on secular instabilities which concentrate particles in the absence of self-gravity when space densities are well below the Roche limit. This growth in turn could seed more rapid gravitational instabilities.
We examine local normal modes of a Keplerian disk in which two fluids, representing gas and uniformly-sized solids, are coupled by a drag force directly proportional to relative velocity (as in Epstein's or Stokes' law). Our 3D model is laminar, contains no vertical stratification, and self-gravity is neglected. We work in the well-coupled limit where the particle stopping time is less than the orbital time. We find two varieties of axisymmetric unstable modes, both of which grow more slowly than the dynamical time. One is an overstable epicyclic oscillation that only grows for large vertical wavenumbers, while the secular mode is robustly unstable over a wide range of radial and vertical wavenumbers. The eigenfunctions exhibit substantial particle density perturbations. Growth rates increase as drag approaches marginal coupling, and also depend on the ratio of particle to gas density. Simpler systems in which motion is 2D, or rotation is ignored, are found to be stable because of the constraints imposed by gas incompressibility. Pending future study of stratified and/or viscous models, growth rates in our idealized model should not be taken literally. We therefore emphasize the physics behind this growth mechanism.
AY and JG acknowledge support from NASA Origins grant NAG5-1164.
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Bulletin of the American Astronomical Society, 36 #2
© 2004. The American Astronomical Soceity.