[Paper Review] The baroclinic instability in the context of layered accretion. Self-sustained vortices and their magnetic stability in local compressible unstratified models of protoplanetary disks

Wladimir Lyra, Hubert Klahr|Max Planck Institute for Plasma Physics|Nov 2, 2010

Astrophysics and Star Formation Studies26 references54 citations

TL;DR

This study investigates baroclinic instability (BI) in magnetized, compressible, unstratified shearing box models of protoplanetary disks, finding that BI-generated vortices are rapidly destroyed by magnetic instabilities—particularly the magneto-elliptical instability—when magnetic fields are well-coupled to the gas. The MRI dominates over BI in growth rate and saturation, rendering BI ineffective in magnetized active zones, but vortices may survive only in weakly ionized dead zones where magnetic coupling is low.

ABSTRACT

Turbulence and angular momentum transport in accretion disks remains a topic of debate. With the realization that dead zones are robust features of protoplanetary disks, the search for hydrodynamical sources of turbulence continues. A possible source is the baroclinic instability (BI), which has been shown to exist in unmagnetized non-barotropic disks. We present shearing box simulations of baroclinicly unstable, magnetized, 3D disks, in order to assess the interplay between the BI and other instabilities, namely the magneto-rotational instability (MRI) and the magneto-elliptical instability. We find that the vortices generated and sustained by the baroclinic instability in the purely hydrodynamical regime do not survive when magnetic fields are included. The MRI by far supersedes the BI in growth rate and strength at saturation. The resulting turbulence is virtually identical to an MRI-only scenario. We measured the intrinsic vorticity profile of the vortex, finding little radial variation in the vortex core. Nevertheless, the core is disrupted by an MHD instability, which we identify with the magneto-elliptic instability. This instability has nearly the same range of unstable wavelengths as the MRI, but has higher growth rates. In fact, we identify the MRI as a limiting case of the magneto-elliptic instability, when the vortex aspect ratio tends to infinity (pure shear flow). We conclude that vortex excitation and self-sustenance by the baroclinic instability in protoplanetary disks is viable only in low ionization, i.e., the dead zone. Our results are thus in accordance with the layered accretion paradigm. A baroclinicly unstable dead zone should be characterized by the presence of large-scale vortices whose cores are elliptically unstable, yet sustained by the baroclinic feedback. As magnetic fields destroy the vortices and the MRI outweighs the BI, the active layers are unmodified.

Motivation & Objective

• To assess whether baroclinic instability (BI) can generate and sustain large-scale vortices in magnetized, compressible, local models of protoplanetary disks.
• To determine the interplay between BI, the magneto-rotational instability (MRI), and the magneto-elliptical instability in vortex stability.
• To evaluate the role of magnetic fields, resistivity, and field geometry (vertical, azimuthal, zero-net flux) in disrupting or preserving BI-driven vortices.
• To test whether the layered accretion paradigm remains viable when BI is considered as a potential turbulence source in the dead zone.
• To isolate the conditions under which BI can lead to self-sustained vortices in the absence of strong MRI activity.

Proposed method

• Performed local, compressible, unstratified simulations using the Pencil Code in the shearing box approximation.
• Incorporated a linearized entropy gradient to drive baroclinic instability, enabling vortex generation and feedback via buoyancy.
• Used a compressible hydrodynamic framework allowing for spiral density wave excitation and angular momentum transport measurement.
• Varied magnetic field strength, geometry (vertical, azimuthal, zero-net flux), and resistivity to isolate the effects of MRI and magneto-elliptical instability.
• Tracked vortex evolution, magnetic field growth, and turbulence saturation levels via time-resolved diagnostics including enstrophy, kinetic and magnetic energy, and α-parameter.
• Identified the magneto-elliptical instability as a dominant disruption mechanism by analyzing unstable wavelength ranges and channel flow formation in vortex cores.

Experimental results

Research questions

• RQ1 Can baroclinic instability sustain large-scale vortices in 3D magnetized, compressible, unstratified protoplanetary disk models?
• RQ2 How does the magneto-elliptical instability affect the stability of BI-generated vortices compared to the MRI?
• RQ3 What role does magnetic field strength, geometry, and resistivity play in the survival or destruction of baroclinically driven vortices?
• RQ4 Does the MRI suppress the BI in magnetically coupled regions, and can the BI persist only in weakly coupled, low-ionization zones?
• RQ5 To what extent do vortex cores exhibit radial inhomogeneity in vorticity, and how does this affect their susceptibility to magnetic instabilities?

Key findings

• Baroclinically generated vortices are rapidly destroyed when magnetic fields are included, with the MRI dominating in growth rate and saturation amplitude.
• The magneto-elliptical instability, which has nearly the same unstable wavelength range as the MRI, grows faster and disrupts vortices via channel flows that stretch and destroy their spatial coherence.
• The MRI is identified as a limiting case of the magneto-elliptical instability when the vortex aspect ratio tends to infinity (pure shear flow).
• A strong vertical magnetic field leads to rapid growth of magnetic fields inside the vortex core, triggering channel flows that destroy the vortex within a few orbital times.
• Resistivity quenches both the MRI and magneto-elliptical instability when the magnetic Reynolds number of the longest box wavelength is near unity (Re_M ≲ 2), allowing vortex survival until MRI develops.
• Constant azimuthal and zero-net-flux magnetic fields also lead to vortex destruction via the magneto-elliptical instability, indicating the instability is robust across field configurations.