Vortex stretching in self-gravitating protoplanetary discs

Vortex stretching in self-gravitating protoplanetary discs 

Authors: 

Regaly et al 

Abstract:
Horseshoe-shaped brightness asymmetries of several transitional discs are thought to be caused by large-scale vortices. Anticyclonic vortices are efficiently collect dust particles, therefore they can play a major role in planet formation. Former studies suggest that the disc self-gravity weakens vortices formed at the edge of the gap opened by a massive planet in discs whose masses are in the range of 0.01 less than M_disc/M_* less than 0.1. Here we present an investigation on the long-term evolution of the large-scale vortices formed at the viscosity transition of the discs' dead zone outer edge by means of two-dimensional hydrodynamic simulations taking disc self-gravity into account. We perform a numerical study of low mass, 0.001 less than M_disc/M_* less than 0.01, discs, for which cases disc self-gravity was previously neglected. The large-scale vortices are found to be stretched due to disc self-gravity even for low-mass discs with M_disc/M_*>=0.005 where initially the Toomre Q-parameter was less than or equal 50 at the vortex distance. As a result of stretching, the vortex aspect ratio increases and a weaker azimuthal density contrast develops. The strength of the vortex stretching is proportional to the disc mass. The vortex stretching can be explained by a combined action of a non-vanishing gravitational torque caused by the vortex, and the Keplerian shear of the disc. Self-gravitating vortices are subject to significantly faster decay than non-self-gravitating ones. We found that vortices developed at sharp viscosity transitions of self-gravitating discs can be described by a GNG model as long as the disc viscosity is low, i.e. alpha_dz less than or equal to 10^-5.

Transient dynamics of large scale vortices in Keplerian disk

Transient dynamics of large scale vortices in Keplerian disk

Author:

Razdoburdin

Abstract:

The mechanism of transition from laminar state to turbulent state in Keplerian disks is still unknown. The most popular version today is generation of turbulence due to magnetorotational instability (MRI). However magnetohydrodynamic simulations give the value of Shakura-Sunyaev parameter more then an order of magnitude smaller rather than that found from observations. One way to solve this problem is the existence of an alternative or additional mechanism for generating turbulence. It can be the bypass mechanism, which is responsible for transition to turbulence in Couette and Poiseuille flows. This mechanism is based on the transient growth of linear perturbations in the flow with the subsequent transition to the nonlinear stage. In order to clarify the role of this mechanism in astrophysical disks first of all it is necessary to calculate the maximal possible growth factor of linear perturbations in the flow. In this paper the results of such calculations are presented for perturbations on different scales compared with the disk thickness. Qualitative description of mechanisms responsible for the growth will also be presented. It was found that the most rapidly growing shear harmonics have azimuthal wavelength of the order of the disk thickness. In addition, their initial form is always similar to the vortex perturbations with the same potential vorticity. It was shown that the vortices with azimuthal wavelength more than an order of magnitude in excess of the disc thickness, are still able to grow by dozens of times.

Slowly-growing gap-opening planets trigger weaker vortices

Slowly-growing gap-opening planets trigger weaker vortices

Authors:

Hammer et al

Abstract:

The presence of a giant planet in a low-viscosity disc can create a gap edge in the disc's radial density profile sharp enough to excite the Rossby Wave Instability. This instability may evolve into dust-trapping vortices that might explain the "banana-shaped" features in recently observed asymmetric transition discs with inner cavities. Previous hydrodynamical simulations of planet-induced vortices have neglected the timescale of hundreds to thousands of orbits to grow a massive planet to Jupiter-size. In this work, we study the effect of a giant planet's runaway growth timescale on the lifetime and characteristics of the resulting vortex. For two different planet masses (1 and 5 Jupiter masses) and two different disc viscosities (α=3×10−4 and 3×10−5), we compare the vortices induced by planets with several different growth timescales between 10 and 4000 planet orbits. In general, we find that slowly-growing planets create significantly weaker vortices with lifetimes and surface densities reduced by more than 50%. For the higher disc viscosity, the longest growth timescales in our study inhibit vortex formation altogether. Additionally, slowly-growing planets produce vortices that are up to twice as elongated, with azimuthal extents well above 180∘ in some cases. These unique, elongated vortices likely create a distinct signature in the dust observations that differentiates them from the more concentrated vortices that correspond to planets with faster growth timescales. We find that the low viscosities necessary for vortex formation likely prevent planets from growing quickly enough to trigger the instability in self-consistent models.

On the survival of zombie vortices in protoplanetary discs

On the survival of zombie vortices in protoplanetary discs

Authors:

Lesur et al

Abstract:

Recently it has been proposed that the zombie vortex instability (ZVI) could precipitate hydrodynamical activity and angular momentum transport in unmagnetized regions of protoplanetary discs, also known as ‘dead zones’. In this Letter we scrutinize, with high-resolution 3D spectral simulations, the onset and survival of this instability in the presence of viscous and thermal physics. First, we find that the ZVI is strongly dependent on the nature of the viscous operator. Although the ZVI is easily obtained with hyperdiffusion, it is difficult to sustain with physical (second order) diffusion operators up to Reynolds numbers as high as 107. This sensitivity is probably due to the ZVI's reliance on critical layers, whose characteristic length-scale, structure, and dynamics are controlled by viscous diffusion. Second, we observe that the ZVI is sensitive to radiative processes, and indeed only operates when the Peclet number is greater than a critical value ∼104, or when the cooling time is longer than ∼10Ω−1. As a consequence, the ZVI struggles to appear at R ≳ 0.3 au in standard 0.01 M⊙ T Tauri disc models, though younger more massive discs provide a more hospitable environment. Together these results question the prevalence of the ZVI in protoplanetary discs.

Vortices in stratified protoplanetary disks

Vortices in stratified protoplanetary disks : from baroclinic instability to vortex layers

Authors:

Richard et al

Abstract:

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.

Dust Clumping via Vortices in Protoplanetary Disks

Dust capture and long-lived density enhancements triggered by vortices in 2D protoplanetary disks

Authors:

Surville et al

Abstract:

We study dust capture by vortices and its long-term consequences in global two-fluid inviscid disk simulations using a new polar grid code RoSSBi. We perform the longest integrations so far, several hundred disk orbits, at the highest resolution attainable in global simulations of disks with dust, namely 2048x4096 grid points. This allows to study the dust evolution well beyond vortex dissipation. We vary a wide range of parameters, most notably the dust-to-gas ratio in the initial setup varies in the range 10−3 to 0.1. Irrespective of the initial dust-to-gas ratio we find rapid concentration of the dust inside vortices, reaching dust-to-gas ratios of order unity inside the vortex. We present an analytical model that describes very well the dust capture process inside vortices, finding consistent results for all dust-to-gas ratios. A vortex streaming instability develops which causes invariably vortex destruction. After vortex dissipation large-scale dust-rings encompassing a disk annulus form in most cases, which sustain very high dust concentration, approaching ratios of order unity. The rings are long lived lasting as long as the duration of the simulations. They also develop a streaming instability, which manifests itself in eddies at various scales within which the dust forms compact high density clumps. Such clumps would be unstable to gravitational collapse in absence of strong dissipation by viscous forces. When vortices are particularly long lived, rings do not form but dust clumps inside vortices become then long lived features and would likely undergo collapse by gravitational instability. Rings encompass almost an Earth mass of solid material, while even larger masses of dust do accumulate inside vortices in the earlier stage. We argue that rapid planetesimal formation would occur in the dust clumps inside the vortices as well as in the post-vortex ring.

Vortex formation in protoplanetary discs induced by the vertical shear instability

Vortex formation in protoplanetary discs induced by the vertical shear instability

Authors:

Richard et al

Abstract:

We present the results of 2D and 3D hydrodynamic simulations of idealized protoplanetary discs that examine the formation and evolution of vortices by the vertical shear instability (VSI). In agreement with recent work, we find that discs with radially decreasing temperature profiles and short thermal relaxation time-scales, are subject to the axisymmetric VSI. In three dimensions, the resulting velocity perturbations give rise to quasi-axisymmetric potential vorticity perturbations that break-up into discrete vortices, in a manner that is reminiscent of the Rossby wave instability. Discs with very short thermal evolution time-scales (i.e. {\tau} less than 0.1 local orbit periods) develop strong vorticity perturbations that roll up into vortices that have small aspect ratios ({\chi} less than 2) and short lifetimes (~ a few orbits). Longer thermal time-scales give rise to vortices with larger aspect ratios (6 less than {\chi} less than 10), and lifetimes that depend on the entropy gradient. A steeply decreasing entropy profile leads to vortex lifetimes that exceed the simulation run times of hundreds of orbital periods. Vortex lifetimes in discs with positive or weakly decreasing entropy profiles are much shorter, being 10s of orbits at most, suggesting that the subcritical baroclinic instability plays an important role in sustaining vortices against destruction through the elliptical instability. Applied to the outer regions of protoplanetary discs, where the VSI is most likely to occur, our results suggest that vortices formed by the VSI are likely to be short lived structures.

Toroidal Vortices Explain the Dust Migration Problem

Toroidal vortices as a solution to the dust migration problem

Authors:

Loren-Aguilar et al

Abstract:

In an earlier letter, we reported that dust settling in protoplanetary discs may lead to a dynamical dust-gas instability that produces global toroidal vortices. In this letter, we investigate the evolution of a dusty protoplanetary disc with two different dust species (1 mm and 50 cm dust grains), under the presence of the instability. We show how toroidal vortices, triggered by the interaction of mm grains with the gas, stop the radial migration of metre-sized dust, potentially offering a natural and efficient solution to the dust migration problem.

Planetesimal Formation Through Dust Trapping Vortices

Planetesimal formation in self-gravitating discs -- dust trapping by vortices

Authors:

Gibbons et al

Abstract:

The mechanism through which meter-sized boulders grow to km-sized planetesimals in protoplanetary discs is a subject of active research, since it is critical for planet formation. To avoid spiralling into the protostar due to aerodynamic drag, objects must rapidly grow from cm-sized pebbles, which are tightly coupled to the gas, to large boulders of 1-100m in diameter. It is already well known that over-densities in the gaseous component of the disc provide potential sites for the collection of solids, and that significant density structures in the gaseous component of the disc (e.g., spiral density waves) can trap solids efficiently enough for the solid component of the disc to undergo further gravitational collapse due to their own self-gravity. In this work, we employ the PENCIL CODE to conduct local shearing sheet simulations of massive self-gravitating protoplanetary discs, to study the effect of anticyclonic transient vortices, or eddies, on the evolution of solids in these discs. We find that these types of structures are extremely efficient at concentrating small and intermediate-sized dust particles with friction times comparable to, or less than, the local orbital period of the disc. This can lead to significant over-densities in the solid component of the disc, with density enhancements comparable to, and even higher, than those within spiral density waves; increasing the rate of gravitational collapse of solids into bound structures.

Vortex Formation and Evolution in Planet Harboring Disks under Thermal Relaxation

Vortex Formation and Evolution in Planet Harboring Disks under Thermal Relaxation

Authors:

Lobo Gomes et al

Abstract:

We study the evolution of planet-induced vortices in radially stratified disks, with initial conditions allowing for radial buoyancy. For this purpose we run global two dimensional hydrodynamical simulations, using the PLUTO code. Planet-induced vortices are a product of the Rossby wave instability (RWI) triggered in the edges of a planetary gap. In this work we assess the influence of radial buoyancy for the development of the vortices. We found that radial buoyancy leads to smoother planetary gaps, which generates weaker vortices. This effect is less pronounced for locally isothermal and quasi-isothermal (very small cooling rate) disks. We observed the formation of two generations of vortices. The first generation of vortices is formed in the outer wall of the planetary gap. The merged primary vortex induces accretion, depleting the mass on its orbit. This process creates a surface density enhancement beyond the primary vortex position. The second generation of vortices arise in this surface density enhancement, indicating that the bump in this region is sufficient to trigger the RWI. The merged secondary vortex is a promising explanation for the location of the vortex in the Oph IRS48 system. Finally, we observed a nonmonotonic behavior for the vortex lifetimes as a function of the thermal relaxation timescale, agreeing with previous studies. The birth times of the secondary vortices also display a nonmonotonic behavior, which is correlated with the growth time of the primary vortex and its induced accretion.

How Dust Collects into Rings in Protoplanetary Disks

Toroidal vortices and the conglomeration of dust into rings in protoplanetary discs

Authors:

Loren-Aguilar et al

Abstract:

We identify a new hydrodynamical instability in protoplanetary discs that may arise due to variations in the dust-to-gas ratio and may lead to concentration of dust grains within a disc. The instability can arise due to dust settling, which produces a vertical compositional entropy gradient. The entropy gradient drives a baroclinic instability that is capable of creating toroidal gas vortices that gather dust into rings. Such dust rings are potentially observable via continuum emission of the dust or scattered light. Indeed, this instability may offer an explanation for the rings recently observed in the discs around the young stars HL Tau and TW Hya that does not rely on clearing by protoplanets. The instability may also have wider ramifications, potentially aiding dust agglomeration, altering the radial migration of larger planetesimals, and modifying angular momentum transport within a disc.

Survival and Structure of Dusty Vortices in Protoplanetary Disks

Survival and Structure of Dusty Vortices in Protoplanetary Discs

Authors:

Crnkovic-Rubsamen et al

Abstract:

We have studied the impact of dust feedback on the survival and structure of vortices in protoplanetary discs using 2-D shearing box simulations with Lagrangian dust particles. We consider dust with a variety of sizes (stopping time ts=10−2Ω−1−102Ω−1, from fully coupled with the gas to the decoupling limit. We find that a vortex is destroyed by dust feedback when the total dust-to-gas mass ratio within the vortex is larger than 30-50%, independent of the dust size. The dust distribution can still be asymmetric in some cases after the vortex has been destroyed. With smaller amounts of dust, a vortex can survive for at least 100 orbits, and the maximum dust surface density within the vortex can be more than 100 times larger than the gas surface density, potentially facilitating planetesimal formation. On the other hand, in these stable vortices, small (ts less than Ω−1) and large (ts greater than Ω−1) dust grains concentrate differently and affect the gas dynamics in different ways. The distribution of large dust is more elongated than that of small dust. Large dust (ts greater than Ω−1) concentrates in the centre of the vortex and feedback leads to turn-over in vorticity towards the centre, forming a quiescent region within an anticyclonic vortex. Such a turn-over is absent if the vortex is loaded with small grains. We demonstrate that, in protoplanetary discs where both large and small dust grains are present and under the right condition, the concentration of large dust towards the vortex centre can lead to a quiescent centre, repelling the small dust and forming a small dust ring around the vortex centre. Such anticorrelations between small and large dust within vortices may explain the discrepancy between ALMA and near-IR scattered light observations in the asymmetric region of transitional discs.

Particle Trapping in Protoplanetary Disk Vortices

PARTICLE TRAPPING AND STREAMING INSTABILITY IN VORTICES IN PROTOPLANETARY DISKS

Authors:

Raettig et al

Abstract:

We analyze the concentration of solid particles in vortices created and sustained by radial buoyancy in protoplanetary disks, e.g., baroclinic vortex growth. Besides the gas drag acting on particles, we also allow for back-reaction from dust onto the gas. This becomes important when the local dust-to-gas ratio approaches unity. In our two-dimensional, local, shearing sheet simulations, we see high concentrations of grains inside the vortices for a broad range of Stokes numbers, St. An initial dust-to-gas ratio of 1:100 can easily be reversed to 100:1 for St = 1.0. The increased dust-to-gas ratio triggers the streaming instability, thus counter-intuitively limiting the maximal achievable overdensities. We find that particle trapping inside vortices opens the possibility for gravity assisted planetesimal formation even for small particles (St = 0.01) and a low initial dust-to-gas ratio of 1:104, e.g., much smaller than in the previously studied magnetohydrodynamic zonal flow case.

Do Protoplanetary Disks Form With Vortices?

Are protoplanetary disks born with vortices? -- Rossby wave instability driven by protostellar infall

Authors:

Bae et al

Abstract:

We carry out two-fluid, two-dimensional global hydrodynamic simulations to test whether protostellar infall can trigger Rossby wave instability (RWI) in protoplanetry disks. Our results show that infall can trigger the RWI and generate vortices near the outer edge of the mass landing on the disk (i.e. centrifugal radius). We find that the RWI is triggered under a variety of conditions, although the details depend on the disk parameters and the infall pattern. The common key feature of triggering the RWI is the steep radial gradient of the azimuthal velocity induced by the local increase in density at the outer edge of the infall region. Vortices form when the instability enters the nonlinear regime. In our standard model where self-gravity is neglected, vortices merge together to a single vortex within ∼20 local orbital times, and the merged vortex survives for the remaining duration of the calculation (less than 170 local orbital times). The vortex takes part in outward angular momentum transport, with a Reynolds stress of ≲10−2. Our two-fluid calculations show that vortices efficiently trap dust particles with stopping times of the order of the orbital time, locally enhancing the dust to gas ratio for particles of the appropriate size by a factor of ∼40 in our standard model. When self-gravity is considered, however, vortices tend to be impeded from merging and may eventually dissipate. We conclude it may well have that protoplanetary disks have favorable conditions for vortex formation during the protostellar infall phase, which might enhance early planetary core formation.

Vortex Cycles at the Inner Edges of Dead Zones in Protoplanetary Disks

Vortex cycles at the inner edges of dead zones in protoplanetary disks

Authors:

Faure et al

Abstract:

In protoplanetary disks, the inner boundary between the turbulent and laminar regions is a promising site for planet formation because solids may become trapped at the interface itself or in vortices generated by the Rossby wave instability. The disk thermodynamics and the turbulent dynamics at that location are entwined because of the importance of turbulent dissipation on thermal ionization and, conversely, of thermal ionisation on the turbulence. However, most previous work has neglected this dynamical coupling and have thus missed a key element of the physics in this region. In this paper, we aim to determine how the the interplay between ionization and turbulence impacts on the formation and evolution of vortices at the interface between the active and the dead zones. Using the Godunov code RAMSES, we have performed a 3D magnetohydrodynamic global numerical simulation of a cylindrical model of an MRI--turbulent protoplanetary disk, including thermodynamical effects as well as a temperature-dependant resistivity. The comparison with an analogous 2D viscous simulation has been extensively used to help identify the relevant physical processes and the disk's long-term evolution. We find that a vortex formed at the interface, due to Rossby wave instability, migrates inward and penetrates the active zone where it is destroyed by turbulent motions. Subsequently, a new vortex emerges a few tens of orbits later at the interface, and the new vortex migrates inward too. The sequence repeats itself, resulting in cycles of vortex formation, migration, and disruption. This behavior is successfully reproduced using two different codes. In this paper, we characterize this vortex life cycle and discuss its implications for planet formation at the dead/active interface. Our simulations highlight the importance of thermodynamical processes for the vortex evolution at the dead zone inner edge.

Dust's Effects on Vortices in Protoplanetary Disks

Effects of dust feedback on vortices in protoplanetary disks

Authors:

Fu et al

Abstract:

We carried out two-dimensional high-resolution simulations to study the effect of dust feedback on the evolution of vortices induced by massive planets in protoplanetary disks. Various initial dust to gas disk surface density ratios (0.001 -- 0.01) and dust particle sizes (Stokes number 4×10−4 -- 0.16) are considered. We found that while dust particles migrate inwards, vortices are very effective in collecting them. When dust density becomes comparable to gas density within the vortex, a dynamical instability is excited and it alters the coherent vorticity pattern and destroys the vortex. This dust feedback effect is stronger with higher initial dust/gas density ratio and larger dust grain. Consequently, we found that the disk vortex lifetime can be reduced up to a factor of 10. We discuss the implications of our findings on the survivability of vortices in protoplanetary disks and planet formation.

The Stability of Vortices in Protoplanetary Disks

On the local stability of vortices in differentially rotating discs

Authors:

Railton et al

Abstract:

In order to circumvent the loss of solid material through radial drift towards the central star, the trapping of dust inside persistent vortices in protoplanetary discs has often been suggested as a process that can eventually lead to planetesimal formation. Although a few special cases have been discussed, exhaustive studies of possible quasi-steady configurations available for dust-laden vortices and their stability have yet to be undertaken, thus their viability or otherwise as locations for the gravitational instability to take hold and seed planet formation is unclear. In this paper we generalise and extend the well known Kida solution to obtain a series of steady state solutions with varying vorticity and dust density distributions in their cores, in the limit of perfectly coupled dust and gas. We then present a local stability analysis of these configurations, considering perturbations localised on streamlines. Typical parametric instabilities found have growthrates of 0.05ΩP, where ΩP is the angular velocity at the centre of the vortex. Models with density excess can exhibit many narrow parametric instability bands while those with a concentrated vorticity source display internal shear which significantly affects their stability. However, the existence of these parametric instabilities may not necessarily prevent the possibility of dust accumulation in vortices.

Evolution of Planet-Induced Vortices in Protoplanetary Disks

Long Term Evolution of Planet-Induced Vortices in Protoplanetary Disks

Authors:

Fu et al

Abstract:

Recent observations of large-scale asymmetric features in protoplanetary disks suggest that large-scale vortices exist in such disks. Massive planets are known to be able to produce deep gaps in protoplanetary disks. The gap edges could become hydrodynamically unstable to the Rossby wave/vortex instability and form large-scale vortices. In this study we examine the long term evolution of these vortices by carrying out high-resolution two dimensional hydrodynamic simulations that last more than 104 orbits (measured at the planet's orbit). We find that the disk viscosity has a strong influence on both the emergence and lifetime of vortices. In the outer disk region where asymmetric features are observed, our simulation results suggest that the disk viscous α needs to be low ∼10−5 - 10−4 to sustain vortices to thousands and up to 104 orbits in certain cases. The chance of finding a vortex feature in a disk then decreases with smaller planet orbital radius. For α∼10−3 or larger, even planets with masses of 5 Jupiter-masses will have difficulty either producing or sustaining vortices. We have also studied the effects of different disk temperatures and planet masses. We discuss the implications of our findings on current and future protoplanetary disk observations.