The vertical shear instability in poorly ionised, magnetized protoplanetary discs

TL;DR

This paper develops a local linear theory to analyze how non-ideal MHD effects influence the vertical shear instability in protoplanetary discs, revealing conditions under which VSI can develop despite magnetic suppression.

Contribution

It introduces analytical criteria for VSI occurrence considering non-ideal MHD effects and applies them to realistic disc models, highlighting the role of dust grain size.

Findings

VSI can develop within ~10au in protoplanetary discs.

Magnetic fields may suppress VSI, but non-ideal effects can enable it.

VSI onset depends on dust grain size beyond 10au.

Abstract

Protoplanetary discs should exhibit a weak vertical variation in their rotation profiles. Typically this `vertical shear' issues from a baroclinic effect driven by the central star's radiation field, but it might also arise during the launching of a magnetocentrifugal wind. As a consequence, protoplanetary discs are subject to a hydrodynamical instability, the `vertical shear instability' (VSI), whose breakdown into turbulence could transport a moderate amount of angular momentum and facilitate, or interfere with, the process of planet formation. Magnetic fields may suppress the VSI, however, either directly via magnetic tension or indirectly through magnetorotational turbulence. On the other hand, protoplanetary discs exhibit notoriously low ionisation fractions, and non-ideal effects, if sufficiently dominant, may come to the VSI's rescue. In this paper we develop a local linear theory that explores how non-ideal MHD influences the VSI, while also launching additional diffusive shear instabilities. We derive a set of analytical criteria that establish when the VSI prevails, and then show how it can be applied to a realistic global model of a protoplanetary disc. Our calculations suggest that within ~10au the VSI should have little trouble emerging in the main body of the disk, but beyond that, and in the upper regions of the disc, its onset depends sensitively on the size of the preponderant dust grains.