Streaming Instabilities in Protoplanetary Disks

Interpenetrating streams of solids and gas in a Keplerian disk produce alocal, linear instability. The two components mutually interact via aerodynamicdrag, which generates radial drift and triggers unstable modes. The secularinstability does not require self-gravity, yet it generates growing particledensity perturbations that could seed planetesimal formation. Growth rates areslower than dynamical, but faster than radial drift, timescales. Growth rates,like streaming velocities, are maximized for marginal coupling (stopping timescomparable dynamical times). Fastest growth occurs when the solid to gasdensity ratio is order unity and feedback is strongest. Curiously, growth isstrongly suppressed when the densities are too nearly equal. The relationbetween background drift and wave properties is explained by analogy withHoward's semicircle theorem. The three-dimensional, two-fluid equationsdescribe a sixth order (in the complex frequency) dispersion relation. Aterminal velocity approximation allows simplification to an approximate cubicdispersion relation. To describe the simplest manifestation of thisinstability, we ignore complicating (but possibly relevant) factors likevertical stratification, dispersion of particle sizes, turbulence, andself-gravity. We consider applications to planetesimal formation and compareour work to other studies of particle-gas dynamics.Comment: 26 pages, 8 figures, submitted to Ap