Streaming instability

Abstract: Four stages in the accretion of planetesimals are described. The initial stage is the condensation of dust particles from the gaseous solar nebula as it cools. These dust particles settle into a thin disk which is gravitationally unstable. A first generation of planetesimals, whose radii range up to about 0.1 km, form from the dust disk by direct gravitational collapse to solid densities on a time scale of the order of 1 year. The resulting disk, composed of first-generation planetesimals, is still gravitationally unstable, and the planetesimals are grouped into clusters containing approximately 10,000 members. The contraction of these clusters is controlled by the rate at which gas drag damps their internal rotational and random kinetic energies. On a time scale of a few thousand years, the clusters contract to form a second generation of planetesimals having radii of the order of 5 km. Further coalescence of planetesimals proceeds by direct collisions which seem capable of producing growth at a rate of the order of 15 cm per year at 1 AU.

Abstract: Interpenetrating streams of solids and gas in a Keplerian disk produce a local, linear instability. The two components mutually interact via aerodynamic drag, which generates radial drift and triggers unstable modes. The secular instability does not require self-gravity, yet it generates growing particle-density perturbations that could seed planetesimal formation. Growth rates are slower than dynamical but faster than radial drift timescales. Growth rates, like streaming velocities, are maximized for marginal coupling (stopping times comparable to dynamical times). Fastest growth occurs when the solid-to-gas density ratio is order unity and feedback is strongest. Curiously, growth is strongly suppressed when the densities are too nearly equal. The relation between background drift and wave properties is explained by analogy with Howard's semicircle theorem. The three-dimensional, two-fluid equations describe a sixth-order (in the complex frequency) dispersion relation. A terminal velocity approximation allows simplification to an approximate cubic dispersion relation. To describe the simplest manifestation of this instability, we ignore complicating (but possibly relevant) factors such as vertical stratification, dispersion of particle sizes, turbulence, and self-gravity. We consider applications to planetesimal formation and compare our work to other studies of particle-gas dynamics.

Abstract: The formation of planetesimals, the kilometer-sized planetary precursors, is still a puzzling process. Considerable progress has been made over the past years in the physical description of the first stages of planetesimal formation, owing to extensive laboratory work. This review examines the experimental achievements and puts them into the context of the dust processes in protoplanetary disks. It has become clear that planetesimal formation starts with the growth of fractal dust aggregates, followed by compaction processes. As the dust-aggregate sizes increase, the mean collision velocity also increases, leading to the stalling of the growth and possibly to fragmentation, once the dust aggregates have reached decimeter sizes. A multitude of hypotheses for the further growth have been proposed, such as very sticky materials, secondary collision processes, enhanced growth at the snow line, or cumulative dust effects with gravitational instability. We will also critically review these ideas.