Excitation of Rossby wave instability and development of a large-scale vortex at the outer dead zone edge of protoplanetary discs is one of the leading theories that explains horseshoe-like brightness distribution in transition discs. Formation of such vortices requires a relatively sharp viscosity transition. Detailed modelling, however, indicates that viscosity transitions at the outer edge of the dead zone is relatively smooth. In this study, we present 2D global, non-isothermal, gas-dust coupled hydrodynamic simulations to investigate the possibility of vortex excitation at smooth viscosity transitions. Our models are based on a recently postulated scenario, wherein the recombination of charged particles on the surface of dust grains results in reduced ionisation fraction and in turn the turbulence due to magnetorotational instability. Thus, the alpha-parameter for the disc viscosity depends on the local dust-to-gas mass ratio. We found that the smooth viscosity transitions at the outer edge of the dead zone can become Rossby unstable and form vortices. A single large-scale vortex develops if the dust content of the disc is well coupled to the gas, however, multiple small-scale vortices ensue for the case of less coupled dust. As both type of vortices are trapped at the dead zone outer edge, they provide sufficient time for dust growth. The solid content collected by the vortices can exceed several hundred Earth masses, while the dust-to-gas density ratio within often exceeds unity. Thus, such vortices function as planetary nurseries within the disc, providing ideal sites for formation of planetesimals and eventually planetary systems.
Turbulent, two-dimensional, hydrodynamic flows are characterized by the emergence of coherent, long-lived vortices without a need to invoke special initial conditions. Vortices have the ability to sequester particles, with typical radii from about 1 mm to 10 cm, that are slightly decoupled from the gas. A generic feature of discs with surface density and effective temperature profiles that are decreasing, power-law functions of radial distance is that four vortex zones exist for a fixed particle size. In particular, two of the zones form an annulus at intermediate radial distances within which…
The formation of planetesimals via gravitational instability of the dust layer in a protoplanetary disks demands that there be local patches where dust is concentrated by a factor of $\sim$ a few $\times 10^3$ over the background value. Vortices in protoplanetary disks may concentrate dust to these values allowing them to be the nurseries of planetesimals. The concentration of dust in the cores of vortices increases the dust-gas ratio of the core compared to the background disk, creating a "heavy vortex." In this work, we show that these vortices are subject to an instability which we have cal…
We present the highest resolution study to date of super-Earths migrating in inviscid and low-viscosity discs, motivated by the connection to laminar, wind-driven models of protoplanetary discs. Our models unveil the critical role of vortices in determining the migration behaviour for partial gap-opening planets. Vortices form in pressure maxima at gap edges, and prevent the disc-feedback stopping of migration for intermediate planets in low-viscosity and inviscid discs, contrary to the concept of the `inertial limit' or `disc feedback' halting predicted from analytical models. Vortices may al…
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<=M_disc/M_*<=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 t…
We study the type III migration of a Saturn mass planet in low viscosity discs. The planet is found to experience cyclic episodes of rapid decay in orbital radius, each amounting to a few Hill radii. We find this to be due to the scattering of large- scale vortices present in the disc. The origin and role of vortices in the context of type III migration is explored. It is shown through numerical simulations and semi- analytical modelling that spiral shocks induced by a sufficiently massive planet will extend close to the planet orbital radius. The production of vortensity across shock tips res…
A massive planet in a protoplanetary disc will open a gap in the disc material. A steep gap edge can be hydrodynamically unstable, which results in the formation of vortices that can act as tracers for the presence of planets in observational results. However, in a viscous disc, the potential formation of these vortices is dependent on the timescale over which the massive planet accretes mass and with a sufficiently long timescale it is possible for no vortices to form. Hence, there is a connection between the presence of vortices and the growth timescale of the planet and it may therefore be …
Vortex formation through the Rossby wave instability (RWI) in protoplanetary discs has been invoked to play a role in planet formation theory, and suggested to explain the observation of large dust asymmetries in several transitional discs. However, whether or not vortex formation operates in layered accretion discs, i.e. models of protoplanetary discs including dead zones near the disc midplane --- regions that are magnetically inactive and the effective viscosity greatly reduced --- has not been verified. As a first step toward testing the robustness of vortex formation in layered discs, we …
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 lifet…
Gas rich dusty circumstellar discs observed around young stellar objects are believed to be the birthplace of planets and planetary systems. Recent observations revealed that large-scale horseshoe-like brightness asymmetries are present in dozens of transitional protoplanetary discs. Theoretical studies suggest that these brightness asymmetries bf could be caused by large-scale anticyclonic vortices triggered by the Rossby Wave Instability (RWI), which can be excited at the edges of the accretionally inactive region, the dead zone edge. Since vortices may play a key role in planet formation, i…
Young planets embedded in protoplanetary discs (PPDs) excite spiral density waves, which propagate, shock and deposit angular momentum in the disc. This results in gap opening around the planetary orbit, even for low (sub-thermal) mass planets, provided that the effective viscosity in the disc is low. The edges of these planet-induced gaps are known to be prone to emergence of observable vortices via the Rossby Wave Instability (RWI). We study timescales for the development of vortices driven by low mass planets in inviscid discs. We employ a recently developed semi-analytical theory of vorten…
Recent ALMA observations have found many protoplanetary discs with rings that can be explained by gap-opening planets less massive than Jupiter. Meanwhile, recent studies have suggested that protoplanetary discs should have low levels of turbulence. Past computational work on low-viscosity discs has hinted that these two developments might not be self-consistent because even low-mass planets can be accompanied by vortices instead of conventional double rings. We investigate this potential discrepancy by conducting hydrodynamic simulations of growing planetary cores in discs with various aspect…
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 distr…
Turbulent state of spectrally stable shear flows may be developed and sustained according to the bypass scenario of transition. If it works in non-magnetised boundless and homogeneous quasi-Keplerian flow, transiently growing shearing vortices should supply turbulence with energy. Employing the large shearing box approximation, as well as a set of global disc models, we study the optimal growth of the shearing vortices in such a flow in the whole range of azimuthal length-scales, $λ_y$, as compared to the flow scale-height, $H$. It is shown that with the account of the viscosity the highest po…
Resolved ALMA and VLA observations indicate the existence of two dust traps in the protoplanetary disc MWC 758. By means of 2D gas+dust hydrodynamical simulations post-processed with 3D dust radiative transfer calculations, we show that the spirals in scattered light, the eccentric, asymmetric ring and the crescent-shaped structure in the (sub)millimetre can all be caused by two giant planets: a 1.5-Jupiter mass planet at 35 au (inside the spirals) and a 5-Jupiter mass planet at 140 au (outside the spirals). The outer planet forms a dust-trapping vortex at the inner edge of its gap (at ~85 au)…
It is believed that large-scale horseshoe-like brightness asymmetries found in dozens of transitional protoplanetary discs are caused by anticyclonic vortices. These vortices can play a key role in planet formation, as mm-sized dust -- the building blocks of planets -- can be accumulated inside them. Anticyclonic vortices are formed by the Rossby wave instability, which can be excited at the gap edges opened by a giant planet or at sharp viscosity transitions of accretionally inactive regions. It is known that vortices are prone to stretching and subsequent dissolution due to disc self-gravity…
In two-dimensional forced Navier-Stokes turbulence, energy cascades to the largest scales in the system to form a pair of coherent vortices known as the Bose condensate. We show, both numerically and analytically, that the energy condensation saturates and the system reaches a statistically stationary state. The time scale of saturation is inversely proportional to the viscosity and the saturation energy level is determined by both the viscosity and the force. We further show that, without sufficient resolution to resolve the small-scale enstrophy spectrum, numerical simulations can give a spu…
Recent sub-millimeter observations show non-axisymmetric brightness distributions with a horseshoe-like morphology for more than a dozen transition disks. The most accepted explanation for the observed asymmetries is the accumulation of dust in large-scale vortices. Protoplanetary disks vortices can form by the excitation of Rossby-wave instability in the vicinity of a steep pressure gradient, which can develop at the edges of a giant planet carved gap or at the edges of an accretionally inactive zone. We studied the formation and evolution of vortices formed in these two distinct scenarios by…
Gap-opening planets can generate dust-trapping vortices that may explain some of the latest discoveries of high-contrast crescent-shaped dust asymmetries in transition discs. While planet-induced vortices were previously thought to have concentrated shapes, recent computational work has shown that these features naturally become much more elongated in the gas when simulations account for the relatively long timescale over which planets accrete their mass. In this work, we conduct two-fluid hydrodynamical simulations of vortices induced by slowly-growing Jupiter-mass planets in discs with very …
In this paper the migration of a 10 Earth-mass planetary core is investigated at the outer boundary of the dead zone of a protoplanetary disc by means of 2D hydrodynamic simulations done with the graphics processor unit version of the FARGO code. In the dead zone, the effective viscosity is greatly reduced due to the disc self-shielding against stellar UV radiation, X-rays from the stellar magnetosphere and interstellar cosmic rays. As a consequence, mass accumulation occurs near the outer dead zone edge, which is assumed to trap planetary cores enhancing the efficiency of the core-accretion s…
Type-II migration of giant planets has a speed proportional to the disc's viscosity for values of the alpha viscosity parameter larger than 1.e-4 . At lower viscosities previous studies, based on 2D simulations have shown that migration can be very chaotic and often characterized by phases of fast migration. The reason is that in low-viscosity discs vortices appear due to the Rossby-wave instability at the edges of the gap opened by the planet. Migration is then determined by vortex-planet interactions. Our aim is to study migration in low viscosity 3D discs. We performed numerical simulations…
As accretion in protoplanetary disks is enabled by turbulent viscosity, the border between active and inactive (dead) zones constitutes a location where there is an abrupt change in the accretion flow. The gas accumulation that ensues triggers the Rossby wave instability, that in turn saturates into anticyclonic vortices. It was suggested that the trapping of solids within them leads to a burst of planet formation on very short timescales. We perform two-dimensional global simulations of the dynamics of gas and solids in a non-magnetized thin protoplanetary disk with the Pencil Code. We use mu…
Protoplanetary disks composed of dust and gas are ubiquitous around young stars and are commonly recognized as nurseries of planetary systems. Their lifetime, appearance, and structure are determined by an interplay between stellar radiation, gravity, thermal pressure, magnetic field, gas viscosity, turbulence, and rotation. Molecules and dust serve as major heating and cooling agents in disks. Dust grains dominate the disk opacities, reprocess most of the stellar radiation, and shield molecules from ionizing UV/X-ray photons. Disks also dynamically evolve by building up planetary systems whic…
It is known that gap opening depends on the disc's viscosity; however, eccentricity damping formulas have only been derived at high viscosities, ignoring partial gap opening. We aim at obtaining a simple formula to model $e$-damping of the type-I regime in low viscosity discs, where even small planets may start opening partial. We perform high resolution 2D locally isothermal hydrodynamical simulations of planets with varying masses on fixed orbits in discs with varying aspect ratios and viscosities. We determine the torque and power felt by the planet to derive migration and eccentricity damp…
We study linear transient dynamics in a thin Keplerian disc employing a method based on variational formulation of optimisation problem. It is shown that in a shearing sheet approximation due to a prominent excitation of density waves by vortices the most rapidly growing shearing harmonic has azimuthal wavelength, $λ_y$, of order of the disc thickness, $H$, and its initial shape is always nearly identical to a vortex having the same potential vorticity. Also, in the limit $λ_y\gg H$ the optimal growth $G\propto (Ω/κ)^4$, where $Ω$ and $κ$ stand for local rotational and epicyclic frequencies, r…
The physical mechanism of angular momentum transport in poorly ionized regions of protoplanetary discs, the dead zones (DZs), is not understood. The presence of a DZ naturally leads to conditions susceptible to the Rossby wave instability (RWI), which produces vortices and spiral density waves that may revive the DZ and be responsible for observed large-scale disc structures. We present a series of two-dimensional hydrodynamic simulations to investigate the role of the RWI in DZs, including its impact on the long-term evolution of the disc and its morphology. The nonlinear RWI can generate Rey…
It has been suggested that the transition between magnetorotationally active and dead zones in protoplanetary disks should be prone to the excitation of vortices via Rossby wave instability (RWI). However, the only numerical evidence for this has come from alpha disk models, where the magnetic field evolution is not followed, and the effect of turbulence is parametrized by Laplacian viscosity. We aim to establish the phenomenology of the flow in the transition in 3D resistive-magnetohydrodynamical models. We model the transition by a sharp jump in resistivity, as expected in the inner dead zon…
High-resolution sub-mm observations of some protoplanetary discs reveal non-asixymmetric features, which can often be interpreted as dust concentrations in vortices that form at the edges of gaps carved out by the embedded planets. We use recent results on the timescale for the planet-driven vortex development in low-viscosity discs to set constraints on the mass and age of a planet producing the vortex. Knowledge of the age of the central star in a vortex-bearing protoplanetary disc system allows one to set a lower limit on the planetary mass at the level of several tens of $M_\oplus$. Also, …
Transition disks have dust-depleted inner regions and may represent an intermediate step of an on-going disk dispersal process, where planet formation is probably in progress. Recent millimetre observations of transition disks reveal radially and azimuthally asymmetric structures, where micron- and millimetre-sized dust particles may not spatially coexist. These properties can be the result of particle trapping and grain growth in pressure bumps originating from the disk interaction with a planetary companion. The multiple features observed in some transition disks, such as SR 21, suggest the …
Migration of giant planets in discs with low viscosity has been studied recently. The proportionality between migration speed and the disc's viscosity is broken by the presence of vortices that appear at the edges of the planet-induced gap. Our goal is to investigate vortex-driven migration in low-viscosity discs in the presence of radial advection of gas, as expected from angular momentum removal by magnetised disc winds. We performed three dimensional simulations using the grid-based code FARGOCA. We mimicked the effects of a disc wind by applying a synthetic torque on a surface layer of the…
Context. Transition disks typically appear in resolved millimeter observations as giant dust rings surrounding their young host stars. More accurate observations with ALMA have shown several of these rings to be in fact asymmetric: they have lopsided shapes. It has been speculated that these rings act as dust traps, which would make them important laboratories for studying planet formation. It has been shown that an elongated giant vortex produced in a disk with a strong viscosity jump strikingly resembles the observed asymmetric rings. Aims. We aim to study a similar behavior for a disk in wh…
Rossby wave instability (RWI) at dead zone boundaries may play an important role in planet formation. Viscous hydrodynamics results suggest RWI is excited only when the viscosity changes over a radial distance less than two density scale heights. However in the disks around Solar-mass T Tauri stars, it is not viscosity but magnetic forces that provide the accretion stress beyond about 10 AU, where surface densities are low enough so stellar X-rays and interstellar cosmic rays can penetrate. Here we aim to explore the conditions for RWI in the smooth transition with increasing distance, from re…
Context: Anticyclonic vortices are considered as a favourable places for trapping dust and forming planetary embryos. On the other hand, they are massive blobs that can interact gravitationally with the planets in the disc. Aims: We aim to study how a vortex interacts gravitationally with a planet which migrates toward it or a planet which is created inside the vortex. Methods: We performed hydrodynamical simulations of a viscous locally isothermal disc using GFARGO and FARGO-ADSG. We set a stationary Gaussian pressure bump in the disc in a way that RWI is triggered. After a large vortex is es…
