The baroclinic instability in the context of layered accretion
Self-sustained vortices and their magnetic stability in local compressible unstratified models of protoplanetary disks
Max-Planck-Institut für Astronomie, Königstuhl 17, 69117
2 American Museum of Natural History, Department of Astrophysics, Central Park West at 79th Street, New York, NY 10024-5192, USA
Accepted: 29 November 2010
Context. 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.
Aims. We aim to verify the existence of the baroclinic instability in 3D magnetized disks, as well as its interplay with other instabilities, namely the magneto-rotational instability (MRI) and the magneto-elliptical instability.
Methods. We performed local simulations of non-isothermal accretion disks with the Pencil Code. The entropy gradient that generates the baroclinic instability is linearized and included in the momentum and energy equations in the shearing box approximation. The model is compressible, so excitation of spiral density waves is allowed and angular momentum transport can be measured.
Results. 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 isolated its effect on the vortex, finding that a strong but unstable vertical magnetic field leads to channel flows inside the vortex, which stretch it apart. When the field is decreased or resistivity is used, we find that the vortex survives until the MRI develops in the box. The vortex is then destroyed by the strain of the surrounding turbulence. Constant azimuthal fields and zero net flux fields also lead to vortex destruction. Resistivity quenches both instabilities when the magnetic Reynolds number of the longest vertical wavelength of the box is near unity.
Conclusions. 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. Since magnetic fields destroy the vortices and the MRI outweighs the BI, the active layers are unmodified.
Key words: accretion, accretion disks / hydrodynamics / instabilities / magnetohydrodynamics (MHD) / turbulence / methods: numerical
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