The coexistence of the streaming instability and the vertical shear instability in protoplanetary disks

Planetesimal formation thresholds explored in two-dimensional global models

¹ Centre for Star and Planet Formation, Globe Institute, University of Copenhagen, Øster Voldgade 5–7, 1350 Copenhagen, Denmark
e-mail: urs.schafer@sund.ku.dk
² Lund Observatory, Department of Astronomy and Theoretical Physics, Lund University, Box 43, 22100 Lund, Sweden

Received: 28 March 2022
Accepted: 16 August 2022

Abstract

The streaming instability is a promising mechanism to induce the formation of planetesimals. Nonetheless, this process has been found in previous studies to require either a dust-to-gas surface density ratio or a dust size that is enhanced compared to observed values. Employing two-dimensional global simulations of protoplanetary disks, we show that the vertical shear instability and the streaming instability in concert can cause dust concentration that is sufficient for planetesimal formation for lower surface density ratios and smaller dust sizes than the streaming instability in isolation, and in particular under conditions that are consistent with observational constraints. This is because dust overdensities forming in pressure bumps induced by the vertical shear instability act as seeds for the streaming instability and are enhanced by it. While our two-dimensional model does not include self-gravity, we find that strong dust clumping and the formation (and dissolution) of gravitationally unstable overdensities can be robustly inferred from the evolution of the maximum or the mean dust-to-gas volume density ratio. The vertical shear instability puffs up the dust layer to an average mid-plane dust-to-gas density ratio that is significantly below unity. We therefore find that reaching a mid-plane density ratio of one is not necessary to trigger planetesimal formation via the streaming instability when it acts in unison with the vertical shear instability.