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Register a new userVortices in stratified protoplanetary disks : From baroclinic instability to vortex layers
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Large scale vortices could play a key role in the evolution of protoplanetary disks, particularly in the dead-zone where no turbulence associated with magnetic field is expected. Their possible formation by the subcritical baroclinic instability is a complex issue due to the vertical structure of the disk and to the elliptical instability.} {In two-dimensional disks the baroclinic instability is studied as a function of the thermal transfer efficiency. In three-dimensional disks we explore the importance of radial and vertical stratification on the processes of vortex formation and amplification.} {Numerical simulations are performed using a fully compressible hydrodynamical code based on a second order finite volume method. We assume a perfect gas law in inviscid disk models in which heat transfer is due to either relaxation or diffusion.} {In 2D, the baroclinic instability with thermal relaxation leads to the formation of large-scale vortices, which are unstable with respect to the elliptic instability. In the presence of heat diffusion, hollow vortices are formed which evolve into vortical structures with a turbulent core. In 3D, the disk stratification is found to be unstable in a finite layer which can include the mid-plane or not. When the unstable layer contains the mid-plane, the 3D baroclinic instability with thermal relaxation is found to develop first in the unstable layer as in 2D, producing large-scale vortices. These vortices are then stretched out in the stable layer, creating long-lived columnar vortical structures extending through the height of the disk. They are also found to be the source of internal vortex layers that develop across the whole disk along baroclinic critical layer surfaces, and form new vortices in the upper region of the disk.} {In three-dimensional disks, vortices can survive for a very long time if the production of vorticity by...
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We consider the radial migration of vortices in two-dimensional isothermal gaseous disks. We find that a vortex core, orbiting at the local gas velocity, induces velocity perturbations that propagate away from the vortex as density waves. The resulting spiral wave pattern is reminiscent of an embedded planet. There are two main causes for asymmetries in these wakes: geometrical effects tend to favor the outer wave, while a radial vortensity gradient leads to an asymmetric vortex core, which favors the wave at the side that has the lowest density. In the case of asymmetric waves, which we always find except for a disk of constant pressure, there is a net exchange of angular momentum between the vortex and the surrounding disk, which leads to orbital migration of the vortex. Numerical hydrodynamical simulations show that this migration can be very rapid, on a time scale of a few thousand orbits, for vortices with a size comparable to the scale height of the disk. We discuss the possible effects of vortex migration on planet formation scenarios.
Under the right conditions, the streaming instability between imperfectly coupled dust and gas is a powerful mechanism for planetesimal formation as it can concentrate dust grains to the point of gravitational collapse. In its simplest form, the streaming instability can be captured by analyzing the linear stability of unstratified disk models, which represent the midplane of protoplanetary disks. We extend such studies by carrying out vertically-global linear stability analyses of dust layers in protoplanetary disks. We find the dominant form of instability in stratified dust layers is one driven by the vertical gradient in the rotation velocity of the dust-gas mixture, but also requires partial dust-gas coupling. These vertically-shearing streaming instabilities grow on orbital timescales and occur on radial length scales $sim10^{-3}H_mathrm{g}$, where $H_mathrm{g}$ is the local pressure scale height. The classic streaming instability, associated with the relative radial drift between dust and gas, occur on radial length scales $sim10^{-2}H_mathrm{g}$, but have much smaller growth rates than vertically-shearing streaming instabilities. Including gas viscosity is strongly stabilizing and leads to vertically-elongated disturbances. We briefly discuss the potential effects of vertically-shearing streaming instabilities on planetesimal formation.
In this work, we study how the dust coagulation/fragmentation will influence the evolution and observational appearances of vortices induced by a massive planet embedded in a low viscosity disk by performing global 2D high-resolution hydrodynamical simulations. Within the vortex, due to its higher gas surface density and steeper pressure gradients, dust coagulation, fragmentation and drift (to the vortex center) are all quite efficient, producing dust particles ranging from micron to $sim 1.0 {rm cm}$, as well as overall high dust-to-gas ratio (above unity). In addition, the dust size distribution is quite non-uniform inside the vortex, with the mass weighted average dust size at the vortex center ($sim 4.0$ mm) being a factor of $sim10$ larger than other vortex regions. Both large ($sim$ mm) and small (tens of micron) particles contribute strongly to affect the gas motion within the vortex. As such, we find that the inclusion of dust coagulation has a significant impact on the vortex lifetime and the typical vortex lifetime is about 1000 orbits. After the initial gaseous vortex is destroyed, the dust spreads into a ring with a few remaining smaller gaseous vortices with a high dust concentration and a large maximum size ($sim$ mm). At late time, the synthetic dust continuum images for the coagulation case show as a ring inlaid with several hot spots at 1.33 mm band, while only distinct hot spots remain at 7.0 mm.
Protoplanetary disks often appear as multiple concentric rings in dust continuum emission maps and scattered light images. These features are often associated with possible young planets in these disks. Many non-planetary explanations have also been suggested, including snow lines, dead zones and secular gravitational instabilities in the dust. In this paper we suggest another potential origin. The presence of copious amounts of dust tends to strongly reduce the conductivity of the gas, thereby inhibiting the magneto-rotational instability, and thus reducing the turbulence in the disk. From viscous disk theory it is known that a disk tends to increase its surface density in regions where the viscosity (i.e. turbulence) is low. Local maxima in the gas pressure tend to attract dust through radial drift, increasing the dust content even more. We investigate mathematically if this could potentially lead to a feedback loop in which a perturbation in the dust surface density could perturb the gas surface density, leading to increased dust drift and thus amplification of the dust perturbation and, as a consequence, the gas perturbation. We find that this is indeed possible, even for moderately small dust grain sizes, which drift less efficiently, but which are more likely to affect the gas ionization degree. We speculate that this instability could be triggered by the small dust population initially, and when the local pressure maxima are strong enough, the larger dust grains get trapped and lead to the familiar ring-like shapes. We also discuss the many uncertainties and limitations of this model.
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 Els{a}sser numbers $lesssim 0.09$ at plasma beta parameter $beta_Z sim 10^4$.
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