The physical mechanism of the streaming instability, and whether it works in vortices

A major hurdle in planet formation theory is that we do not understand how pebbles congregate into planetesimals. A promising way to overcome this metre-scale barrier involves a mechanism called the streaming instability (SI). This hydrodynamic instability gathers the pebbles into clumps so dense that they collapse gravitationally and form planetesimals.

Unfortunately, the mechanism responsible for the onset of this instability remains mysterious. This makes it hard to evaluate the value of the SI as a planetesimal formation theory: how robust is the mechanism, how does it saturate, etc.

Fortunately, some significant progress has been made recently: J. Squire and P. Hopkins showed that the SI is a Resonant Drag Instability (RDI) involving inertial waves. In the first part of this talk, we build on their insight to produce a clear physical picture of how the SI develops.

Like all RDIs, the SI is built on a feedback loop: in the ‘forward action’, an inertial wave concentrates pebbles into clumps; in the ‘backward reaction’, those drifting pebble clumps excite an inertial wave. Each process breaks into two mechanisms, a fast one and a slow one. At resonance, each forward mechanism can couple with a backward mechanism to close a feedback loop. Unfortunately, the fast-fast loop is stable, so the SI uses the fast-slow and slow-fast loops. Despite this last layer of complexity, we hope that our explanation will help understand how the SI works, in which conditions it can grow, how it manifests itself, and how it saturates.

Another problem is that the SI can only develop in regions containing a high density of similar-sized pebbles. Those conditions are met in large-scale vortices, but no one knows if the SI can feed on vorticial flows. Indeed, each instability can only grow in a few specific flows, and a priori the SI is active in Keplerian flows, not vortex flows. We answer this long-standing question in the second part of the talk.

To do so, we develop a simple pen-and-paper model of a pebble-laden vortex in a protoplanetary disc. We find that if the vortex is weak and anticyclonic, pebbles drift towards its centre. We then build a vortex analog of the shearing box to analyse the local linear stability of our pebble-laden vortex. We find that the pebbles’ drift powers an instability which closely resembles the SI. Indeed, both rely on the same resonance between the pebble drift and inertial waves. This result strengthens the case for vortex-induced planetesimal formation.