On the Vertical Shear Instability in Magnetized Protoplanetary Disks

TL;DR

This paper investigates how magnetic fields and resistivity influence the vertical shear instability in protoplanetary disks, revealing magnetic stabilization effects and conditions under which hydrodynamic behavior is restored.

Contribution

It provides the first linear analysis of VSI in magnetized, resistive protoplanetary disks, highlighting magnetic stabilization and the interplay with MRI.

Findings

Magnetism dampens VSI, especially surface modes.

Ohmic resistivity can revive VSI modes.

VSI dominates over MRI for certain resistivity and plasma beta conditions.

Abstract

The vertical shear instability (VSI) is a robust phenomenon in irradiated protoplanetary disks (PPDs). While there is extensive literature on the VSI in the hydrodynamic limit, PPDs are expected to be magnetized and their extremely low ionization fractions imply that non-ideal magneto-hydrodynamic (MHD) effects should be properly considered. To this end, we present linear analyses of the VSI in magnetized disks with Ohmic resistivity. We primarily consider toroidal magnetic fields, which are likely to dominate the field geometry in PPDs. We perform vertically global and radially local analyses to capture characteristic VSI modes with extended vertical structures. To focus on the effect of magnetism, we use a locally isothermal equation of state. We find that magnetism provides a stabilizing effect to dampen the VSI, with surface modes, rather than body modes, being the first to vanish with increasing magnetization. Subdued VSI modes can be revived by Ohmic resistivity, where sufficient magnetic diffusion overcome magnetic stabilization, and hydrodynamic results are recovered. We also briefly consider poloidal fields to account for the magnetorotational instability (MRI), which may develop towards surface layers in the outer parts of PPDs. The MRI grows efficiently at small radial wavenumbers, in contrast to the VSI. When resistivity is considered, we find the VSI dominates over the MRI for Ohmic Els\"{a}sser numbers $\lesssim 0.09$ at plasma beta parameter $\beta_Z \sim 10^4$.