Recent observations revealed organised structures in protoplanetary disks, such as axisymmetric rings or horseshoe concen- trations evocative of large-scale vortices. These structures are often interpreted as the result of planet-disc interactions. However, these disks are also known to be unstable to the magneto-rotational instability (MRI) which is believed to be one of the dominant angular momentum transport mechanism in these objects. It is therefore natural to ask if the MRI itself could produce these structures without invoking planets. The nonlinear evolution of the MRI is strongly affected by the low ionisation fraction in protoplanetary disks. The Hall effect in particular, which is dominant in dense and weakly ionised parts of these objects, has been shown to spontaneously drive self- organising flows in shearing box simulations. Here, we investigate the behaviour of global MRI-unstable disc models dominated by the Hall effect and characterise their dynamics. We perform 3D unstratified Hall-MHD simulations of keplerian disks for a broad range of Hall, ohmic and ambipolar Elsasser numbers. We confirm the transition from a turbulent to an organised state as the intensity of the Hall effect is increased. We observe the formation of zonal flows, their number depending on the available magnetic flux and on the intensity of the Hall effect. For intermediate Hall intensity, the flow self-organises into long-lived magnetised vortices. Neither the addition of a toroidal field nor ohmic or ambipolar diffusion drastically change this picture in the range of parameters we have explored. The ability of these structures to trap dust particles in this configuration is demonstrated. We conclude that Hall-MRI driven organisation is a plausible scenario which could explain some of the structures found in recent observations.
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 dr…
Spiral arms have been observed in nearly a dozen protoplanetary discs in near-infrared scattered light and recently also in the sub-millimetre continuum. While one of the most compelling explanations is that they are driven by planetary or stellar companions, in all but one cases such companions have not yet been detected and there is even ambiguity on whether the planet should be located inside or outside the spirals. Here we use 3D hydrodynamic simulations to study the morphology of spiral density waves launched by embedded planets taking into account the vertical temperature gradient, a nat…
The aim of this paper is to study the vertical profile of small dust particles in protoplanetary discs in which angular momentum transport is due to MHD turbulence driven by the magnetorotational instability. We consider particle sizes that range from approximately 1 micron up to a few millimeters.We use a grid--based MHD code to perform global two-fluid simulations of turbulent protoplanetary discs which contain dust grains of various sizes. In quasi--steady state, the gravitational settling of dust particles is balanced by turbulent diffusion. Simple and standard models of this process fail …
Due to the gravitational influence of density fluctuations driven by magneto-rotational instability in the gas disk, planetesimals and protoplanets undergo diffusive radial migration as well as changes in other orbital properties. The magnitude of the effect on particle orbits can have important consequences for planet formation scenarios. We use the local-shearing-box approximation to simulate an ideal, isothermal, magnetized gas disk with vertical density stratification and simultaneously evolve numerous massless particles moving under the gravitational field of the gas and the host star. We…
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 amplificati…
The redistribution of angular momentum is a long standing problem in our understanding of protoplanetary disk (PPD) evolution. The magnetorotational instability (MRI) is considered a likely mechanism. We present the results of a study involving multifluid global simulations including Ohmic dissipation, ambipolar diffusion and the Hall effect in a dynamic, self-consistent way. We focus on the turbulence resulting from the non-linear development of the MRI in radially stratified PPDs and compare with ideal MHD simulations. In the multifluid simulations the disk is initially set up to transition …
Turbulence driven by magnetorotational instability (MRI) crucially affects the evolution of solid bodies in protoplanetary disks. On the other hand, small dust particles stabilize MRI by capturing ionized gas particles needed for the coupling of the gas and magnetic fields. To provide an empirical basis for modeling the coevolution of dust and MRI, we perform three-dimensional, ohmic-resistive MHD simulations of a vertically stratified shearing box with an MRI-inactive "dead zone" of various sizes and with a net vertical magnetic flux of various strengths. We find that the vertical structure o…
The planet-forming region of protoplanetary disks is cold, dense, and therefore weakly ionized. For this reason, magnetohydrodynamic (MHD) turbulence is thought to be mostly absent, and another mechanism has to be found to explain gas accretion. It has been proposed that magnetized winds, launched from the ionized disk surface, could drive accretion in the presence of a large-scale magnetic field. The efficiency and the impact of these surface winds on the disk structure is still highly uncertain. We present the first global simulations of a weakly ionized disk that exhibits large-scale magnet…
The magnetorotational instability (MRI) is the most promising mechanism by which angular momentum is efficiently transported outwards in astrophysical discs. However, its application to protoplanetary discs remains problematic. These discs are so poorly ionised that they may not support magnetorotational turbulence in regions referred to as `dead zones'. It has recently been suggested that the Hall effect, a non-ideal magnetohydrodynamic (MHD) effect, could revive these dead zones by enhancing the magnetically active column density by an order of magnitude or more. We investigate this idea by …
This chapter highlights the properties of turbulence and meso-scale flow structures in protoplanetary disks and their role in the planet formation process. Here we focus on the formation of planetesimals from a gravitational collapse of a pebble cloud. Large scale and long lived flow structures - vortices and zonal flows - are a consequence of weak magneto and hydrodynamic instabilities in the pressure and entropy stratified quasi-Keplerian shear flow interacting with the fast rotation of the disk. The vortices and zonal flows on the other hand are particle traps tapping into the radial pebble…
A previously unknown instability creates space-filling lattices of 3D vortices in linearly-stable, rotating, stratified shear flows. The instability starts from an easily-excited critical layer. The layer intensifies by drawing energy from the background shear and rolls-up into vortices that excite new critical layers and vortices. The vortices self-similarly replicate to create lattices of turbulent vortices. The vortices persist for all time. This self-replication occurs in stratified Couette flows and in the dead zones of protoplanetary disks where it can de-stabilize Keplerian flows.
Layered accretion is one of the inevitable ingredients in protoplanetary disks when disk turbulence is excited by magnetorotational instabilities (MRIs). In the accretion, disk surfaces where MRIs fully operate have a high value of disk accretion rate ($\dot{M}$), while the disk midplane where MRIs are generally quenched ends up with a low value of $\dot{M}$. Significant progress on understanding MRIs has recently been made by a number of dedicated MHD simulations, which requires improvement of the classical treatment of $α$ in 1D disk models. To this end, we obtain a new expression of $α$ by …
We conduct a comprehensive axisymmetric, local linear mode analysis of a stratified, differentially rotating disk permeated by a toroidal magnetic field which could provide significant pressure support. In the adiabatic limit, we derive a new stability criteria that differs from the one obtained for weak magnetic fields with a poloidal component and reduces continuously to the hydrodynamic Solberg-Høiland criteria. Three fundamental unstable modes are found in the locally isothermal limit. They comprise of overstable: (i) acoustic oscillations, (ii) radial epicyclic (acoustic-inertial) oscilla…
We report observations of resolved C2H emission rings within the gas-rich protoplanetary disks of TW Hya and DM Tau using the Atacama Large Millimeter Array (ALMA). In each case the emission ring is found to arise at the edge of the observable disk of mm-sized grains (pebbles) traced by (sub)mm-wave continuum emission. In addition, we detect a C3H2 emission ring with an identical spatial distribution to C2H in the TW Hya disk. This suggests that these are hydrocarbon rings (i.e. not limited to C2H). Using a detailed thermo-chemical model we show that reproducing the emission from C2H requires …
Excitation and propagation of waves in a thermally stratified disk with an arbitrary vertical temperature profile are studied. Previous analytical studies of three-dimensional waves had been focused on either isothermal or polytropic vertical disk structures. However, at the location in a protoplanetary disk where the dominant heating source is stellar irradiation, the temperature gradient may become positive in the vertical direction. We extend the analysis to study the effects of the vertical temperature structure on the waves that are excited at the Lindblad resonances. For a hotter disk at…
The Vertical Shear Instability is an axisymmetric effect suggested to drive turbulence in the magnetically inactive zones of protoplanetary accretion disks. Here we examine its physical mechanism in analytically tractable ``minimal models" in three settings that include a uniform density fluid, a stratified atmosphere, and a shearing-box section of a protoplanetary disk. Each of these analyses show that the vertical shear instability's essence is similar to the slantwise convective symmetric instability in the mid-latitude Earth atmosphere, in the presence of vertical shear of the baroclinic j…
The Streaming Instability (SI) is a mechanism to concentrate solids in protoplanetary disks. Nonlinear particle clumping from the SI can trigger gravitational collapse into planetesimals. To better understand the numerical robustness of the SI, we perform a suite of vertically-stratified 3D simulations with fixed physical parameters known to produce strong clumping. We vary the numerical implementation, namely the computational domain size and the vertical boundary conditions (vBCs), comparing newly-implemented outflow vBCs to the previously-used periodic and reflecting vBCs. We find strong pa…
High-resolution imaging of protoplanetary disks has unveiled a rich diversity of spiral structure, some of which may arise from disk-planet interaction. Using 3D hydrodynamics with $β$-cooling to a vertically-stratified background, as well as radiative-transfer modeling, we investigate the temperature rise in planet-driven spirals. In rapidly cooling disks, the temperature rise is dominated by a contribution from stellar irradiation, 0.3-3% inside the planet radius but always <0.5% outside. When cooling time equals or exceeds dynamical time, however, this is overwhelmed by hydrodynamic PdV wor…
Dust grains with sizes around (sub)mm are expected to couple only weakly to the gas motion in regions beyond 10 au of circumstellar disks. In this work, we investigate the influence of the spatial distribution of such grains on the (sub)mm appearance of magnetized protoplanetary disks. We perform non-ideal global 3D magneto-hydrodynamic stratified disk simulations including particles of different sizes (50 micron to 1 cm), using a Lagrangian particle solver. We calculate the spatial dust temperature distribution, including the dynamically coupled submicron-sized dust grains, and derive ideal c…
We present high-resolution computer simulations of dust dynamics and planetesimal formation in turbulence generated by the magnetorotational instability. We show that the turbulent viscosity associated with magnetorotational turbulence in a non-stratified shearing box increases when going from 256^3 to 512^3 grid points in the presence of a weak imposed magnetic field, yielding a turbulent viscosity of $α\approx0.003$ at high resolution. Particles representing approximately meter-sized boulders concentrate in large-scale high-pressure regions in the simulation box. The appearance of zonal flow…
Large-scale persistent vortices are known to form easily in 2D disks via the Rossby wave or the baroclinic instability. In 3D, however, their formation and stability is a complex issue and still a matter of debate. We study the formation of vortices by the Rossby wave instability in a stratified inviscid disk and describe their three dimensional structure, stability and long term evolution. Numerical simulations are performed using a fully compressible hydrodynamical code based on a second order finite volume method. We assume a perfect gas law and a non-homentropic adiabatic flow.The Rossby w…
We study dust transport in turbulent protoplanetary disks using three-dimensional global unstratified magnetohydrodynamic (MHD) simulations including Lagrangian dust particles. The turbulence is driven by the magnetorotational instability (MRI) with either ideal or non-ideal MHD that includes ambipolar diffusion (AD). In ideal MHD simulations, the surface density evolution (except for dust that drifts fastest), turbulent diffusion, and vertical scale height of dust can all be reproduced by simple one-dimensoinal and/or analytical models. However, in AD dominated simulations which simulate prot…
Recent years have seen growing interest in the streaming instability as a candidate mechanism to produce planetesimals. However, these investigations have been limited to small-scale simulations. We now present the results of a global protoplanetary disk evolution model that incorporates planetesimal formation by the streaming instability, along with viscous accretion, photoevaporation by EUV, FUV, and X-ray photons, dust evolution, the water ice line, and stratified turbulence. Our simulations produce massive (60-130 $M_\oplus$) planetesimal belts beyond 100 au and up to $\sim 20 M_\oplus$ of…
Our aim is to study the thermal and dynamical evolution of protoplanetary disks in global simulations, including the physics of radiation transfer and magneto-hydrodynamic (MHD) turbulence caused by the magneto-rotational instability. We develop a radiative transfer method based on the flux-limited diffusion approximation that includes frequency dependent irradiation by the central star. This hybrid scheme is implemented in the PLUTO code. The focus of our implementation is on the performance of the radiative transfer method. Using an optimized Jacobi preconditioned BiCGSTAB solver, the radiat…
The gas temperature in protoplanetary disks (PPDs) is determined by a combination of irradiation heating and accretion heating, with the latter conventionally attributed to turbulent dissipation. However, recent studies have suggested that the inner disk (a few AU) is largely laminar, with accretion primarily driven by magnetized disk winds, as a result of nonideal magnetohydrodynamic (MHD) effects from weakly ionized gas, suggesting an alternative heating mechanism by Joule dissipation. We perform local stratified MHD simulations including all three nonideal MHD effects (ohmic, Hall, and ambi…
Magneto-rotational instability (MRI) and gravitational instability (GI) are the two principle routes to turbulent angular momentum transport in accretion disks. Protoplanetary disks may develop both. This paper aims to reinvigorate interest in the study of magnetized massive protoplanetary disks, starting from the basic issue of stability. The local linear stability of a self-gravitating, uniformly magnetized, differentially rotating, three-dimensional stratified disk subject to axisymmetric perturbations is calculated numerically. The formulation includes resistivity. It is found that the red…
We carry out local three dimensional (3D) hydrodynamic simulations of planet-disk interaction in stratified disks with varied thermodynamic properties. We find that whenever the Brunt-Vaisala frequency (N) in the disk is nonzero, the planet exerts a strong torque on the disk in the vicinity of the planet, with a reduction in the traditional "torque cutoff". In particular, this is true for adiabatic perturbations in disks with isothermal density structure, as should be typical for centrally irradiated protoplanetary disks. We identify this torque with buoyancy waves, which are excited (when N i…
Large-scale vertical magnetic fields are believed to play a key role in the evolution of protoplanetary discs. Associated with non-ideal effects, such as ambipolar diffusion, they are known to launch a wind that could drive accretion in the outer part of the disc ($R> 1$ AU). They also potentially lead to self-organisation of the disc into large-scale axisymmetric structures, similar to the rings recently imaged by sub-millimetre or near-infrared instruments (ALMA and SPHERE). The aim of this paper is to investigate the mechanism behind the formation of these gaseous rings, but also to underst…
Radiation Hydrodynamics of Self-gravitating Protoplanetary Disks II. Accretion, Migration, Spin, and Internal Structure of GI Fragments
Institute for Advanced Study, Tsinghua University（清华大学高等研究院）；Shanghai Astronomical Observatory, Chinese Academy of Sciences（中国科学院上海天文台）；Department of Astronomy, Tsinghua University（清华大学天文系）
Ultraviolet spectra of protoplanetary disks trace distributions of warm gas at radii where rocky planets form. We combine HST-COS observations of H2 and CO emission from 12 classical T Tauri stars to more extensively map inner disk surface layers, where gas temperature distributions allow radially stratified fluorescence from the two species. We calculate empirical emitting radii for each species under the assumption that the line widths are entirely set by Keplerian broadening, demonstrating that the CO fluorescence originates further from the stars (r ~ 20 AU) than the H2 (r ~ 0.8 AU). This …
MHD turbulence plays a crucial role in the dust dynamics of protoplanetary discs. It affects planet formation, vertical settling and is one possible origin of the large scale axisymmetric structures, such as rings, recently imaged by ALMA and SPHERE. Among the variety of MHD processes, the magnetorotational instability (MRI) has raised particular interest since it provides a source of turbulence and potentially organizes the flow into radial structures. However, the weak ionization of discs prevents the MRI from being excited beyond 1 AU. The strong sedimentation of millimetre dust measured in…
Recent observations by the Atacama Large Millimeter/submillimeter Array (ALMA) of disks around young stars revealed distinct asymmetries in the dust continuum emission. In this work we want to study axisymmetric and non-axisymmetric structures, evocated by the magneto-rotational instability in the outer regions of protoplanetary disks. We combine the results of state-of-the-art numerical simulations with post-processing radiative transfer (RT) to generate synthetic maps and predictions for ALMA. We performed non-ideal global 3D MHD stratified simulations of the dead-zone outer edge using the F…
In the recent years, sub/mm observations of protoplanetary disks have discovered an incredible diversity of substructures in the dust emission. An important result was the finding that dust grains of mm size are embedded in very thin dusty disks. This implies that the dust mass fraction in the midplane becomes comparable to the gas, increasing the importance of the interaction between the two components there. We address this problem by means of numerical 2.5D simulations in order to study the gas and dust interaction in fully global stratified disks. To this purpose, we employ the recently de…
We perform local, vertically stratified shearing-box MHD simulations of protoplanetary disks (PPDs) at a fiducial radius of 1 AU that take into account the effects of both Ohmic resistivity and ambipolar diffusion (AD). The magnetic diffusion coefficients are evaluated self-consistently from a look-up table based on equilibrium chemistry. We first show that the inclusion of AD dramatically changes the conventional picture of layered accretion. Without net vertical magnetic field, the system evolves into a toroidal field dominated configuration with extremely weak turbulence in the far-UV ioniz…
We perform 3D stratified shearing-box MHD simulations on the gas dynamics of protoplanetary disks threaded by net vertical magnetic field Bz. All three non-ideal MHD effects, Ohmic resistivity, the Hall effect and ambipolar diffusion are included in a self-consistent manner based on equilibrium chemistry. We focus on regions toward outer disk radii, from 5-60AU, where Ohmic resistivity tends to become negligible, ambipolar diffusion dominates over an extended region across disk height, and the Hall effect largely controls the dynamics near the disk midplane. We find that around R=5AU, the syst…
While it is generally accepted that the magnetic field and its non-ideal effects play important roles during the stellar formation, simple models of pure hydrodynamics and angular momentum conservation are still widely employed in the studies of disk assemblage in the framework of the so-called "alpha-disk" model due to their simplicity. There has only been a few efforts trying to bridge the gap between a collapsing prestellar core and a developed disk. The goal of the present work is to revisit the assemblage of the protoplanetary disk (PPD), by performing 3D MHD simulations with ambipolar di…
Observations suggest that protoplanetary disks have moderate accretion rates onto the central young star, especially at early stages (e.g. HL Tau), indicating moderate disk turbulence. However, recent ALMA observations suggest that dust is highly settled, implying weak turbulence. Motivated by such tension, we carry out 3D stratified local simulations of self-gravitating disks, focusing on settling of dust particles in actively accreting disks. We find that gravitationally unstable disks can have moderately high accretion rates while maintaining a relatively thin dust disk for two reasons. Fir…
One of the most challenging steps in planet formation theory is the one leading to the formation of planetesimals of kilometre size. A promising scenario involves the existence of vortices able to concentrate a large amount of dust and grains in their centres. Up to now this scenario has been studied mostly in 2D razor thin disks. A 3D study including, simultaneously, the formation and resulting dust concentration of the vortices with vertical settling, was still missing. The Rossby wave instability self-consistently forms 3D vortices, which have the unique quality of presenting a large scale …
Though usually treated in isolation, the magnetorotational and gravitational instabilities (MRI and GI) may coincide at certain radii and evolutionary stages of protoplanetary discs and active galactic nuclei. Their mutual interactions could profoundly influence several important processes, such as accretion variability and outbursts, fragmentation and disc truncation, or large-scale magnetic field production. Direct numerical simulations of both instabilities are computationally challenging and remain relatively unexplored. In this paper, we aim to redress this neglect via a set of 3D vertica…
Astrophysical disks with localized radial structure, such as protoplanetary disks containing dead zones or gaps due to disk-planet interaction, may be subject to the non-axisymmetric Rossby wave instability (RWI) that lead to vortex-formation. The linear instability has recently been demonstrated in three-dimensional (3D) barotropic disks. It is the purpose of this study to generalize the 3D linear problem to include an energy equation, thereby accounting for baroclinity in three-dimensions. Linear stability calculations are presented for radially structured, vertically stratified, geometrical…
The Zombie Vortex Instability (ZVI) occurs in the dead zones of protoplanetary disks (PPDs) where perturbations excite baroclinic critical layers, generating "zombie" vortices and turbulence. In this work, we investigate ZVI with nonuniform vertical stratification; while ZVI is triggered in the stratified regions away from the midplane, the subsequent turbulence propagates into and fills the midplane. ZVI turbulence alters the background Keplerian shear flow, creating a steady-state zonal flow. Intermittency is observed, where the flow cycles through near-laminar phases of zonal flow punctuate…
