A high resolution fourth-order Padé scheme is used to simulate locally isothermal 3D disk turbulence driven by the vertical shear instability (VSI) using 268.4 M points. In the early non-linear period of axisymmetric VSI, angular momentum transport by vertical jets creates correlated N-shaped radial profiles of perturbation vertical and azimuthal velocity. This implies dominance of positive perturbation vertical vorticity layers and a recently discovered angular momentum staircase with respect to radius ($r$). These features are present in 3D in a weaker form. The 3D flow consists of vertically and azimuthally coherent turbulent shear layers containing small vortices with all three vorticity components active. Previously observed large persistent vortices in the interior of the domain driven by the Rossby wave instability are absent. We speculate that this is due to a weaker angular momentum staircase in 3D in the present simulations compared to a previous simulation. The turbulent viscosity parameter $α(r)$ increases linearly with $r$. At intermediate resolution, the value of $α(r)$ at midradius is close to that of a previous simulation. The specific kinetic energy spectrum with respect to radial wavenumber has a power law region with exponent $-1.84$, close to the value $-2$ expected for shear layers. The spectrum with respect to azimuthal wavenumber has a $-5/3$ region and lacks a $-5$ region reported in an earlier study. Finally, it is found that axisymmetric VSI has artifacts at late times, including a very strong angular momentum staircase, which in 3D is present weakly in the disk's upper layers.
Protoplanetary discs should exhibit a weak vertical variation in their rotation profiles. Typically this `vertical shear' issues from a baroclinic effect driven by the central star's radiation field, but it might also arise during the launching of a magnetocentrifugal wind. As a consequence, protoplanetary discs are subject to a hydrodynamical instability, the `vertical shear instability' (VSI), whose breakdown into turbulence could transport a moderate amount of angular momentum and facilitate, or interfere with, the process of planet formation. Magnetic fields may suppress the VSI, however, …
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…
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…
Turbulence in protoplanetary disks plays an important role in dust evolution and planetesimal formation. The vertical shear instability (VSI) is one of the candidate hydrodynamic mechanisms that can generate turbulence in the outer disk regions. The VSI requires rapid gas cooling in addition to vertical shear. A linear stability analysis suggests that the VSI may not operate around the midplane where gas cooling is inefficient. In this study, we investigate the nonlinear outcome of the VSI in disks with a linearly VSI-stable midplane region. We perform two-dimensional global hydrodynamical sim…
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…
We aim to directly trace the vertical location of the emitting surface of multiple molecular tracers in protoplanetary disks. Our sample of disks includes Elias 2-27, WaOph 6 and the sources targeted by the MAPS ALMA Large Program. The set of molecules studied include CO isotopologues in various transitions, HCN, CN, H2CO, HCO+, C2H and c-C3H2. The vertical emitting region is determined directly from the channel maps, implementing accurate masking of the channel emission to recover the vertical location of the emission surface even at large radial distances from the star and for low-SNR lines.…
Gravitational instability (GI) controls the dynamics of young massive protoplanetary discs. Apart from facilitating gas accretion on to the central protostar, it must also impact on the process of planet formation: directly through fragmentation, and indirectly through the turbulent concentration of small solids. To understand the latter process, it is essential to determine the dust dynamics in such a turbulent flow. For that purpose, we conduct a series of 3D shearing box simulations of coupled gas and dust, including the gas's self-gravity and scanning a range of Stokes numbers, from 0.001 …
The vertical shear instability (VSI) is a hydrodynamical instability that requires rapid gas cooling and has been suggested to operate in outer regions of protoplanetary disks. The VSI drives turbulence with strong vertical motions, which could regulate the dust growth and settling. However, dust growth and settling can regulate the VSI because dust depletion makes gas cooling inefficient in outer disk regions that are optically thin to their own thermal emission. In this study, we quantify this potentially stabilizing effects of dust evolution on the VSI based on the linear analysis. We const…
We study wakes and gap opening by low mass planets in gaseous protoplanetary disks threaded by net vertical magnetic fields which drive magnetohydrodynamical (MHD) turbulence through the magnetorotational instabilty (MRI), using three dimensional simulations in the unstratified local shearing box approximation. The wakes, which are excited by the planets, are damped by shocks similar to the wake damping in inviscid hydrodynamic (HD) disks. Angular momentum deposition by shock damping opens gaps in both MHD turbulent disks and inviscid HD disks even for low mass planets, in contradiction to the…
We investigate a massive ($\varSigma \sim 10000 g cm^{-2}$ at 1 AU) protoplanetary disc model by means of 3D radiation magnetohydrodynamics simulations. The vertical structure of the disc is determined self-consistently by a balance between turbulent heating caused by the MRI and radiative cooling. Concerning the vertical structure, two different regions can be distinguished: A gas-pressure dominated, optically thick midplane region where most of the dissipation takes place, and a magnetically dominated, optically thin corona which is dominated by strong shocks. At the location of the photosph…
Turbulence has a profound impact on the evolution of gas and dust in protoplanetary disks (PPDs), from driving the collisions and the diffusion of dust grains, to the concentration of pebbles in giant vortices, thus, facilitating planetesimal formation. The Vertical Shear Instability (VSI) is a hydrodynamic mechanism, operating in PPDs if the local rate of thermal relaxation is high enough. Previous studies of the VSI have, however, relied on the assumption of constant cooling rates, or neglected the finite coupling time between the gas particles and the dust grains. Here, we present the resul…
The dynamical evolution of protoplanetary disks is of key interest for building a comprehensive theory of planet formation and to explain the observational properties of these objects. Using the magnetohydrodynamics code Athena++, with an isothermal shearing box setup, we study the boundary between the active and dead zone, where the accretion rate changes and mass can accumulate. We quantify how the turbulence level is affected by the presence of a non uniform ohmic resistivity in the radial-x direction that leads to a region of inhibited turbulence (or dead zone). Comparing the turbulent act…
We use local numerical simulations to investigate the strength and nature of magnetohydrodynamic (MHD) turbulence in the outer regions of protoplanetary disks, where ambipolar diffusion is the dominant non-ideal MHD effect. The simulations include vertical stratification and assume zero net vertical magnetic flux. We employ a super time-stepping technique to ameliorate the Courant restriction on the diffusive time step. We find that in idealized stratified simulations, with a spatially constant ambipolar Elsasser number Am, turbulence driven by the magnetorotational instability (MRI) behaves i…
Vertical shear instability in two-moment radiation-hydrodynamical simulations of irradiated protoplanetary disks II. Secondary instabilities and stability regions
We carry out a series of local, vertically stratified shearing box simulations of protoplanetary disks that include ambipolar diffusion and a net vertical magnetic field. The ambipolar diffusion profiles we employ correspond to 30AU and 100AU in a minimum mass solar nebula (MMSN) disk model, which consists of a far-UV-ionized surface layer and low-ionization disk interior. These simulations serve as a follow up to Simon et al. (2013), in which we found that without a net vertical field, the turbulent stresses that result from the magnetorotational instability (MRI) are too weak to account for …
Context: Recent observations with the Atacama Large Millimeter Array (ALMA) have shown that the large dust aggregates observed at millimeter wavelengths settle to the midplane into a remarkably thin layer. Aims: We intend to find out if the geometric thinness of these layers is evidence against the vertical shear instability (VSI) operating in these disks. Methods: We performed hydrodynamic simulations of a protoplanetary disk with a locally isothermal equation of state, and let the VSI fully develop. We sprinkled dust particles and followed their motion as they got stirred up by the VSI. We d…
In recent years hydrodynamical (HD) models have become important to describe the gas kinematics in protoplanetary disks, especially in combination with models of photoevaporation and/or magnetic-driven winds. We focus on diagnosing the the vertical extent of the VSI at 203 cells per scale height and allude at what resolution per scale height we obtain convergence. Finally, we determine the regions where EUV, FUV and X-Rays are dominant in the disk. We perform global HD simulations using the PLUTO code. We adopt a global isothermal accretion disk setup, 2.5D (2 dimensions, 3 components) which c…
Theoretical models predict that the obscuration of stellar radiation by irregularities on the surface of a protoplanetary disk can cause self-generating waves traveling towards the star. However, this process is traditionally simulated using the 1+1D approach, the key approximations of which - vertical hydrostatic equilibrium of the disk and vertical diffusion of IR radiation - can distort the picture. This article presents a two-dimensional radiative hydrodynamic model of the evolution of an axially symmetric gas and dust disk. Within this model, but using simplified assumptions from 1+1D mod…
We explore the linear stability of astrophysical discs exhibiting vertical shear, which arises when there is a radial variation in the temperature or entropy. Such discs are subject to a "vertical-shear instability", which recent nonlinear simulations have shown to drive hydrodynamic activity in the MRI-stable regions of protoplanetary discs. We first revisit locally isothermal discs using the quasi-global reduced model derived by Nelson et al. (2013). This analysis is then extended to global axisymmetric perturbations in a cylindrical domain. We also derive and study a reduced model describin…
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…
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…
It has recently been shown that the inner region of protoplanetary disks (PPDs) is governed by wind-driven accretion, and the resulting accretion flow showing complex vertical profiles. Such complex flow structures are further enhanced due to the Hall effect, especially when the background magnetic field is aligned with disk rotation. We investigate how such flow structures impact global dust transport via Monte-Carlo simulations, focusing on two scenarios. In the first scenario, the toroidal magnetic field is maximized in the miplane, leading to accretion and decretion flows above and below. …
We characterize magnetically driven accretion at radii between 1 au and 100 au in protoplanetary discs, using a series of local non-ideal magnetohydrodynamic (MHD) simulations. The simulations assume a Minimum Mass Solar Nebula (MMSN) disc that is threaded by a net vertical magnetic field of specified strength. Confirming previous results, we find that the Hall effect has only a modest impact on accretion at 30 au, and essentially none at 100 au. At 1-10 au the Hall effect introduces a pronounced bi-modality in the accretion process, with vertical magnetic fields aligned to the disc rotation s…
Context: Vertically hydrostatic protoplanetary disk models are based on the assumption that the main heating source, stellar irradiation, does not vary much with time. However, it is known that accreting young stars are variable sources of radiation. This is particularly evident for outbursting sources such as EX Lupi and FU Orionis stars. Aim: We investigate how such outbursts affect the vertical structure of the outer regions of the protoplanetary disk, in particular their appearance in scattered light at optical and near-infrared wavelengths. Methods: We employ the 3D FARGOCA radiation-hydr…
We analyze a sample of 12 HST-selected edge-on protoplanetary disks for which the vertical extent of the emission layers can be constrained directly. We present ALMA high angular resolution continuum images (0.1arcsec) of these disks at two wavelengths, 0.89mm and 2.06mm (respectively ALMA bands 7 and 4), supplemented with archival band 6 data (1.33mm) where available. For most sources, the millimeter continuum emission is more compact than the scattered light, both in the vertical and radial directions. Six sources are resolved along their minor axis in at least one millimeter band, providing…
Elias 2-27 is a young star that hosts an extended, bright and inclined disk of dust and gas. The inclination and extreme flaring of the disk make Elias 2-27 an ideal target to study the vertical distribution of molecules, particularly CN. We directly trace the emission of CN in Elias 2-27 and compare it to previously published CO isotopologue data. CN $N = 3-2$ emission is analyzed in two different transitions $J = 7/2 - 5/2$ and $J = 5/2 - 3/2$, for which we detect two hyperfine group transitions. The vertical location of CN emission is traced directly from the channel maps, following geometr…
Protoplanets can produce structures in protoplanetary disks via gravitational disk-planet interactions. Once detected, such structures serve as signposts of planet formation. Here we investigate the kinematic signatures in disks produced by multi-Jupiter mass ($M_{\rm J}$) planets using 3D hydrodynamics and radiative transfer simulations. Such a planet opens a deep gap, and drives transonic vertical motions inside. Such motions include both a bulk motion of the entire half-disk column, and turbulence on scales comparable to and smaller than the scale height. They significantly broaden molecula…
As the earliest stage of planet formation, massive, optically thick, and gas rich protoplanetary disks provide key insights into the physics of star and planet formation. When viewed edge-on, high resolution images offer a unique opportunity to study both the radial and vertical structures of these disks and relate this to vertical settling, radial drift, grain growth, and changes in the midplane temperatures. In this work, we present multi-epoch HST and Keck scattered light images, and an ALMA 1.3 mm continuum map for the remarkably flat edge-on protoplanetary disk SSTC2DJ163131.2-242627, a y…
Various physical processes that ensue within protoplanetary disks -- including vertical settling of icy/rocky grains, radial drift of solids, planetesimal formation, as well as planetary accretion itself -- are facilitated by hydrodynamic interactions between H/He gas and high-$Z$ dust. The Stokes number, which quantifies the strength of dust-gas coupling, thus plays a central role in protoplanetary disk evolution, and its poor determination constitutes an important source of uncertainty within the theory of planet formation. In this work, we present a simple model for dust-gas coupling, and d…
High spatial resolution CO observations of mid-inclination (30-75°) protoplanetary disks offer an opportunity to study the vertical distribution of CO emission and temperature. The asymmetry of line emission relative to the disk major axis allows for a direct mapping of the emission height above the midplane, and for optically-thick, spatially-resolved emission in LTE, the intensity is a measure of the local gas temperature. Our analysis of ALMA archival data yields CO emission surfaces, dynamically-constrained stellar host masses, and disk atmosphere gas temperatures for the disks around: HD …
Turbulent transport driven by secular shear instabilities can lead to enhanced vertical mixing in hot Jupiter atmospheres, impacting their cloudiness, chemistry and overall vertical structure. We discuss the turbulent regime expected and evaluate theoretical uncertainties on the strength of the vertical mixing (i.e, $K_{\rm zz}$ values). We focus our work on three well-studied hot Jupiters with a hierarchy of atmospheric temperatures: HD189733b ($T_{\rm eq} \simeq 1200$K), HD209458b ($T_{\rm eq} \simeq 1450$K) and Kepler7b ($T_{\rm eq} \simeq 1630$K). $K_{\rm zz}$ uncertainties are large. They…
The streaming instability for solid particles in protoplanetary disks is re-examined assuming the familiar alpha ($α$) model for isotropic turbulence. Turbulence always reduces the growth rates of the streaming instability relative to values calculated for globally laminar disks. While for small values of the turbulence parameter, $α< 10^{-5}$, the wavelengths of the fastest-growing disturbances are small fractions of the local gas vertical scale height $H$, we find that for moderate values of the turbulence parameter, i.e., $α\sim 10^{-5}-10^{-3}$, the lengthscales of maximally growing distur…
Observations have revealed that the elemental abundances of carbon and oxygen in the warm molecular layers of some protoplanetary disks are depleted compared to those is the interstellar medium by a factor of ~10-100. Meanwhile, little is known about nitrogen. To investigate the time evolution of nitrogen, carbon, and oxygen elemental abundances in disks, we develop a one-dimensional model that incorporates dust settling, turbulent diffusion of dust and ices, as well as gas-ice chemistry including the chemistry driven by stellar UV/X-rays and the galactic cosmic rays. We find that gaseous CO i…
Vertical shear instability in two-moment radiation-hydrodynamical simulations of irradiated protoplanetary disks I. Angular momentum transport and turbulent heating
We explore whether protoplanetary disks with self-shadowing from puffed up inner rims exhibit observable features in scattered light images. We use both self-consistent hydrostatic equilibrium calculations and parameterized models to produce the vertically puffed up inner rims. We find that, in general, the transition between the shadowed and flared regions occurs in a smooth manner over a broad radius range, and no sudden jump exists at the outer edge of the shadow in either the disk temperature or density structures. As a result, a puffed up rim cannot create sharp ring/arc/spiral-arm-like f…
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…
Protoplanetary disks around young stars are the sites of planet formation. While the dust mass can be estimated using standard methods, determining the gas mass - and thus the amount of material available to form giant planets - has proven to be very difficult. Hydrogen deuteride (HD) is a promising alternative to the commonly-used gas mass tracer, CO. We aim to examine the robustness of HD as tracer of the disk gas mass, specifically the effect of gas mass on the HD FIR emission and its sensitivity to the vertical structure. Deuterium chemistry reactions relevant for HD were implemented in th…
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…
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 …
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…
Aims: We investigate the evolution of protoplanetary discs (PPDs hereafter) with magnetically driven disc winds and viscous heating. Methods: We consider an initially massive disc with ~0.1 Msun to track the evolution from the early stage of PPDs. We solve the time evolution of surface density and temperature by taking into account viscous heating and the loss of the mass and the angular momentum by the disc winds within the framework of a standard alpha model for accretion discs. Our model parameters, turbulent viscosity, disc wind mass loss, and disc wind torque, which are adopted from local…
The mechanisms of angular momentum transport and level of turbulence in protoplanetary disks (PPDs) are crucial for understanding many aspects of planet formation. In the recent years, it has been realized that the magneto-rotational instability (MRI) tends to be suppressed in PPDs due to non-ideal MHD effects, and the disk is largely laminar with accretion driven by magnetized disk winds. In parallel, several hydrodynamical mechanisms have been identified that likely also generate vigorous turbulence and drive disk accretion. We study the interplay between MHD winds in PPDs with the vertical …
There is considerable interest in hydrodynamic instabilities in dead zones of protoplanetary disks as a mechanism for driving angular momentum transport and as a source of particle-trapping vortices to mix chondrules and incubate planetesimal formation. We present simulations with a pseudo-spectral anelastic code and with the compressible code Athena, showing that stably stratified flows in a shearing, rotating box are violently unstable and produce space-filling, sustained turbulence dominated by large vortices with Rossby numbers of order 0.2-0.3. This Zombie Vortex Instability (ZVI) is obse…
High-angular resolution observations at sub-millimeter/millimeter wavelengths of disks surrounding young stars have shown that their morphology is made of azimuthally-symmetric or point-symmetric substructures, in some cases with spiral arms, localized spur- or crescent-shaped features. The majority of theoretical studies with the aim of interpreting the observational results have focused on disk models with planets, under the assumption that the disk substructures are due to the disk-planet interaction. However, so far only in very few cases exoplanets have been detected in these systems. Fur…
