Resonant drag instabilities in protoplanetary discs: the streaming instability and new, faster growing instabilities

Abstract

We identify and study a number of new, rapidly growing instabilities of dust grains in protoplanetary discs, which may be important for planetesimal formation. The study is based on the recognition that dust–gas mixtures are generically unstable to a resonant drag instability (RDI), whenever the gas, absent dust, supports undamped linear modes. We show that the ‘streaming instability’ is an RDI associated with epicyclic oscillations; this provides simple interpretations for its mechanisms and accurate analytic expressions for its growth rates and fastest growing wavelengths. We extend this analysis to more general dust streaming motions and other waves, including buoyancy and magnetohydrodynamic oscillations, finding various new instabilities. Most importantly, we identify the disc ‘settling instability,’ which occurs as dust settles vertically into the mid-plane of a rotating disc. For small grains, this instability grows many orders of magnitude faster than the standard streaming instability, with a growth rate that is independent of grain size. Growth time scales for realistic dust-to-gas ratios are comparable to the disc orbital period, and the characteristic wavelengths are more than an order of magnitude larger than the streaming instability (allowing the instability to concentrate larger masses). This suggests that in the process of settling, dust will band into rings then filaments or clumps, potentially seeding dust traps, high-metallicity regions that in turn seed the streaming instability, or even overdensities that coagulate or directly collapse to planetesimals.