The outer regions of protoplanetary disks (PPDs) can host both the magnetorotational instability (MRI) and the vertical shear instability (VSI), yet global simulations have almost always studied them separately. Cui & Bai (2022) combined them for the first time in global 3D non-ideal magnetohydrodynamic simulations with ambipolar diffusion and instantaneous cooling, finding that VSI turbulence dominates for strong ambipolar diffusion, co-exists with the MRI at intermediate ionization, and is overwhelmed by the MRI at weak ambipolar diffusion, with angular momentum transport dominated by magnetized disk winds and robust spontaneous magnetic-flux concentration into annular substructures. Their own analysis, however, identified a set of connected open issues that must be resolved before turbulence, accretion, and substructure formation in outer PPDs are characterized under realistic conditions: finite cooling times and shallower temperature gradients, restricted azimuthal domains that may hide vortex formation, the missing dust response to magnetic flux concentration, and unresolved parametric sub-cascades. To date no study has combined the VSI and the MRI under realistic thermodynamics: subsequent work has either dropped the magnetic field (radiation-hydrodynamic or high-resolution hydrodynamic VSI studies, multifluid-dust VSI studies) or dropped the VSI (magnetized wind-launching disk and Rossby-wave-instability studies), so the combined problem remains open.

Background

Protoplanetary disks (PPDs) are the gas-and-dust birthplaces of planets. A central unsolved problem of disk dynamics is how orbital angular momentum is transported inward so that gas can accrete onto the young star. Two candidate instabilities operate in the cool, weakly ionized outer disk (beyond roughly 10 au). The first is the magnetorotational instability (MRI), which taps the free energy of differential rotation in a conducting, magnetized gas: magnetohydrodynamic (MHD) turbulence whose effective viscous transport is conventionally measured by the Shakura–Sunyaev parameter α\alpha, the dimensionless ratio of turbulent stress to gas pressure. Because PPD gas is weakly ionized, non-ideal MHD effects matter; in the outer disk the dominant one is ambipolar diffusion, the drift of magnetic fields relative to neutrals tied only to trace ions, parameterized by the ambipolar Elsässer number AmAm (the ratio of ion–neutral collision frequency to orbital frequency). Strong ambipolar diffusion (small AmAm) severely weakens MRI turbulence, while simultaneously magnetized disk winds can carry away angular momentum from the disk surface. The second instability, the vertical shear instability (VSI), is purely hydrodynamic: because an irradiated, flared disk is warmer at the surface than the midplane, orbital speed varies with height, and this vertical shear drives overturning motions once gas cools fast enough (the linear body modes saturate as radially propagating inertial-wave 'corrugation modes', coherent vertical oscillations). Analytic work (Cui & Lin 2021; Latter & Kunz 2022) showed that in magnetized, poorly ionized gas the two instabilities compete: ideal MHD favors the MRI (its modes grow faster by a factor of order R/HR/H, the radius-to-scale-height ratio), while strong ambipolar diffusion damps the MRI and can rescue the VSI. Before 2022, global 3D simulations had studied each instability in isolation: Cui & Bai (2021) simulated ambipolar-diffusion-dominated outer disks with MRI turbulence, magnetized winds, and spontaneous concentration of vertical magnetic flux into axisymmetric rings (also called zonal flows), while the VSI literature used locally isothermal hydrodynamic codes. Cui & Bai (2022) performed the first global 3D non-ideal MHD simulations in which both instabilities operate (with instantaneous cooling, temperature profile T∝r−qTT\propto r^{-q_T} with qT=1q_T=1, and a restricted azimuthal wedge). They found: VSI dominance at Am=0.1Am=0.1 (δv/cs∼0.02\delta v/c_s\sim0.02–0.030.03; here δv\delta v is the turbulent velocity dispersion, csc_s the sound speed), with the hydrodynamic and magnetic turbulent-stress contributions to α\alpha at Reynolds α∼10−4\alpha\sim10^{-4} and Maxwell α∼10−3\alpha\sim10^{-3} respectively; coexistence at Am=1Am=1; and MRI dominance at Am=10Am=10 (α\alpha up to a few ×10−2\times10^{-2}); wind-dominated angular-momentum transport in all models; and robust magnetic flux concentration and annular substructures at Am≤1Am\le1, attributed primarily to ambipolar diffusion rather than advection. The authors themselves flagged what remains unresolved, and these connected issues define this problem. Realistic irradiated disks have shallower temperature gradients (qT≈1/2q_T\approx1/2) and finite cooling times, both of which weaken the VSI, so whether the VSI–MRI interplay and its transport partition survive realistic thermodynamics is unknown. The azimuthal wedge may suppress non-axisymmetric Rossby wave instability (RWI, disruption of pressure bumps into vortices) and magnetic tension may resist vortex roll-up. Dust — the raw material of planets — was omitted, so its clumping at flux-concentration pressure maxima (found in MRI-only local simulations by Xu & Bai 2022) and its collisional velocities under non-Kolmogorov combined turbulence are untested. No mechanistic theory explains the formation, maintenance, and radial propagation of the magnetic flux sheets. Finally, an inertial-wave parametric instability (a secondary instability in which a VSI corrugation wave parametrically excites pairs of smaller-scale inertial waves, initiating a turbulent cascade; studied analytically by Cui & Latter 2022) was unresolved at the simulations' resolution, leaving its macroscopic transport impact uncertain.

Problem Statement

Characterize turbulence, angular-momentum transport, and substructure formation in ambipolar-diffusion-dominated outer protoplanetary disks in which both the VSI and the MRI operate, under realistic conditions, replacing the idealizations of Cui & Bai (2022) with physical fidelity. This objective spans the following linked aspects of that question, following the limitations and future directions discussed by the source work: (1) global 3D non-ideal MHD simulations with ambipolar diffusion, net poloidal flux, finite cooling times, and a realistic shallower temperature gradient (qT≈1/2q_T\approx1/2), set up — as in the source work — so that the disk is conducive to both instabilities, and quantifying the resulting turbulent velocities and Reynolds/Maxwell α\alpha values, the partition between magnetized-wind and viscous accretion, whether the VSI in fact survives finite cooling and the shallower gradient (throughout the disk, only in surface layers, or not at all), and whether spontaneous magnetic-flux concentration and annular substructures survive; (2) relaxation of the azimuthal-wedge restriction to a full 2π2\pi domain to determine whether Rossby-wave-instability vortices arise in the combined VSI+MRI state and how magnetic tension interacts with vortex roll-up; (3) incorporation of dust particles to determine whether dust clumps at flux-concentration pressure maxima in the presence of VSI turbulence (testing, in 3D global magnetized models, the MRI-only local result of Xu & Bai 2022) and how the combined, non-Kolmogorov turbulence modifies grain collisional velocities; and (4) the resolution regimes in which the inertial-wave parametric instability attacking VSI corrugation modes alters the macroscopic turbulence and transport of the combined state. Together these aspects frame one empirical question — what does outer-disk turbulence actually look like when both instabilities operate under realistic thermodynamics, geometry, and dust content — in which each 'whether' clause asks what the combined state does under those conditions, whatever the sign of the answer. These aspects are independently resolvable sub-questions of the one objective.

References

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