On the Vertical Shear Instability in Magnetized Protoplanetary Disks

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 Elsässer numbers $\lesssim 0.09$ at plasma beta parameter ${\beta }_Z\sim 10^4$.

17 pages, 11 figures, accepted for publication in MNRAS

References in corpus (24)

• Gas- and dust evolution in protoplanetary disks
• Particle Stirring in Turbulent Gas Disks: Including Orbital Oscillations
• Closed-form expressions for particle relative velocities induced by turbulence
• Towards planetesimals: dense chondrule clumps in the protoplanetary nebula
• Global simulations of protoplanetary disks with ohmic resistivity and ambipolar diffusion
• A Three-Dimensional View of Turbulence: Constraints on Turbulent Motions in the HD 163296 Protoplanetary Disk using DCO${}^{+}$
• Magnetic fields in protoplanetary disks
• Hall-effect Controlled Gas Dynamics in Protoplanetary Disks: II. Full 3D Simulations toward the Outer Disk
• Global Simulations of the Inner Regions of Protoplanetary Disks with Comprehensive Disk Microphysics
• Measuring turbulent motion in planet-forming disks with ALMA: A detection around DM Tau and non-detections around MWC 480 and V4046 Sgr
• Convective Overstability in radially stratified accretion disks under thermal relaxation
• Vertical shear instability in accretion disc models with radiation transport
• Radiation Hydrodynamical Turbulence In Protoplanetary Disks: Numerical Models and Observational Constraints
• On the Linear Stability of Weakly-Ionized, Magnetized Planar Shear Flows
• Convective overstability in accretion disks: 3D linear analysis and nonlinear saturation
• Baroclinic Vorticity Production in Protoplanetary Disks; Part II: Vortex Growth and Longevity
• Particle dynamics in discs with turbulence generated by the vertical shear instability
• Gas and dust dynamics in starlight-heated protoplanetary disks
• On the vertical-shear instability in astrophysical discs
• Global Hydromagnetic Simulations of Protoplanetary Disks with Stellar Irradiation and Simplified Thermochemistry
• Dust settling against hydrodynamic turbulence in protoplanetary discs
• High Resolution Parameter Study of the Vertical Shear Instability
• Magnetohydrodynamics of Protostellar Disks
• Magnetohydrodynamics of protoplanetary discs

Cited by in corpus (5)

• Global Three-Dimensional Simulations of Outer Protoplanetary Disks with Ambipolar Diffusion
• Turbulence in outer protoplanetary disks: MRI or VSI?
• The vertical shear instability in poorly ionised, magnetized protoplanetary discs
• The saturation of the VSI in protoplanetary disks via parametric instability
• Dust ring and gap formation by gas flow induced by low-mass planets embedded in protoplanetary disks $\mathrm{I}$. Steady-state model