The baroclinic instability in the context of layered accretion

Abstract

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.

Vortices in stratified protoplanetary disks

“…We observe that the vortex re-organizes in a vortical structure with a turbulent core that can survive till the end of the simulation. The results we found are consistent with those of Lesur & Papaloizou (2010) and Lyra & Klahr (2011) who found the emergence of vertical motions inside the vortices when their aspect ratio satisfies χ < 4.…”

“…This requires strong enough perturbations of the disk whose origin can only be speculated. It is unlikely that they could be created by the magneto-rotational instability in the vicinity of the deadzone since this instability tends to inhibit vortex formation (Lyra & Klahr 2011). However, they could be due to another hydrodynamical instability such as the linear version of the baroclinic instability proposed by Klahr & Hubbard (2014).…”

“…We fixe the nature of the thermal transfer to thermal relaxation with a cooling time τ = 1. Previous 3D simulations (Lesur & Papaloizou 2010;Lyra & Klahr 2011) were carried out using Boussinesq approximation and constant radial stratification. Here we use a fully compressible code first in an vertically unstratified configuration and then in a non-uniformly stratified configuration.…”

“…They studied the dependence of vortex amplification as a function of the entropy gradient, the thermal transfer efficiency and the numerical resolution of the computations. Lyra & Klahr (2011) also investigated numerically the growth of the subcritical baroclinic instability in a magnetic disk; they concluded that baroclinic vortices are destroyed by the magneto-rotational instability and can only survive in the dead zone of the protoplanetary disks.…”

Quasi-steady vortices in protoplanetary disks

“…They can be produced by different instabilities, like the Rossby waves instability (RWI, Lovelace et al 1999;Li et al 2000Li et al , 2001 or by what is now known as convective overstability (see Klahr & Bodenheimer 2003;Petersen et al 2007a,b;Lyra & Klahr 2011), in 2D and 3D flows, but the vortex structure is strongly dependent on the initial conditions. Vortex models can avoid this bias, as the widely used elliptical vortex (Kida 1981;Goodman et al 1987;Chavanis 2000).…”