The magnetorotational instability (MRI) is believed to be responsible for most of the angular momentum transport in accretion discs. However, molecular dissipation processes may drastically change the efficiency of MRI turbulence in realistic astrophysical situations. The physical origin of this dependency is still poorly understood as linear and quasi linear theories fail to explain it. In this paper, we look for the link between molecular dissipation processes and MRI transport of angular momentum in non stratified shearing box simulations including a mean vertical field. We show that magnetic helicity is unimportant in the model we consider. We perform a spectral analysis on the simulations tracking energy exchanges in spectral space when turbulence is fully developed. We find that the energy exchanges are essentially direct (from large to small scale) whereas some non linear interactions appear to be non local in spectral space. We speculate that these non local interactions are responsible for the correlation between turbulent transport and molecular dissipation. We argue that this correlation should then disappear when a significant scale separation is achieved and we discuss several methods by which one can test this hypothesis.
We studied dynamical balances in magnetorotational instability (MRI) turbulence with a net vertical field in the shearing box model of disks. Analyzing the turbulence dynamics in Fourier (${\bf k}$-)space, we identified three types of active modes that define turbulence characteristics. These modes have lengths similar to the box size, i.e., lie in the small wavenumber region in Fourier space labeled the vital area and are: (i) the channel mode - uniform in the disk plane with the smallest vertical wavenumber,(ii) the zonal flow mode - azimuthally and vertically uniform with the smallest radia…
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…
We investigate the formation of hot coronae and vertical outflows in accretion disks by magneto-rotational turbulence. We perform local three-dimensional (3D) MHD simulations with the vertical stratification by explicitly solving an energy equation with various effective ratios of specific heats, gamma. Initially imposed weak vertical magnetic fields are effectively amplified by magnetorotational instability (MRI) and winding due to the differential rotation. In the isothermal case (gamma=1), the disk winds are mainly driven by the Poynting flux associated with the MHD turbulence and show quas…
The generation of spiral density waves by MRI in accretion discs
Helmholtz-Zentrum Dresden-Rossendorf（德累斯顿-罗斯多夫亥姆霍兹中心）；Abastumani Astrophysical Observatory（阿巴斯图马尼天文台）；Faculty of Exact and Natural Sciences, Tbilisi State University（第比利斯国立大学理学院）；LyRIDS, ECE-Paris Engineering School（巴黎ECE工程学院LyRIDS）；LUTH, UMR 8102 CNRS, Observatoire de Paris-Meudon（巴黎-默东天文台CNRS联合研究实验室）
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…
Turbulence driven by magnetorotational instability (MRI) affects planetesimal formation by inducing diffusion and collisional fragmentation of dust particles. We examine conditions preferred for planetesimal formation in MRI-inactive "dead zones" using an analytic dead-zone model based on our recent resistive MHD simulations. We argue that successful planetesimal formation requires not only a sufficiently large dead zone (which can be produced by tiny dust grains) but also a sufficiently small net vertical magnetic flux (NVF). Although often ignored, the latter condition is indeed important si…
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…
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…
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…
The magneto-rotational instability (MRI) is one of the most important processes in sufficiently ionized astrophysical disks. Grid-based simulations, especially those using the local shearing box approximation, provide a powerful tool to study the ensuing nonlinear turbulence. On the other hand, while meshless methods have been widely used in both cosmology, galactic dynamics, and planet formation they have not been fully deployed on the MRI problem. We present local unstratified and vertically stratified MRI simulations with two meshless MHD schemes: a recent implementation of SPH MHD (Price20…
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 study the role of ambipolar diffusion (AD) on the non-linear evolution of the MRI in protoplanetary disks using the strong coupling limit, which applies when the electron recombination time is much shorter than the orbital time. The effect of AD in this limit is characterized by the dimensionless number Am, the frequency of which neutral particles collide with ions normalized to the orbital frequency. We perform three-dimensional unstratified shearing-box simulations of the MRI over a wide range of Am as well as different magnetic field strengths and geometries. The saturation level of the …
We investigate linear dynamics of non-axisymmetric perturbations in incompressible, vertically stratified Keplerian discs with a weak vertical magnetic field in the shearing box approximation. Perturbations are decomposed into shearing waves whose evolution is followed via numerical integration of the linearized ideal MHD equations. There are two basic modes in the system -- inertia-gravity waves and magnetic mode, which displays the magnetorotational instability (MRI). As distinct from previous studies, we introduce `eigenvariables' characterizing each (counter-propagating) component of the i…
(abriged) MRI turbulence is a leading mechanism for the generation of an efficient turbulent transport of angular momentum in an accretion disk through a turbulent viscosity effect. It is believed that the same process could also transport large-scale magnetic fields in disks, reshaping the magnetic structures in these objects. This process, known as turbulent resistivity, has been suggested and used in several accretion-ejection models and simulations to produce jets. Still, the efficiency of MRI-driven turbulence to transport large-scale magnetic fields is largely unknown. We investigate thi…
This paper studies the response of a thin accretion disk to an external radial magnetic field. Our focus is on protoplanetary disks (PPDs), which are exposed during their later evolution to an intense, magnetized wind from the central star. A radial magnetic field is mixed into a thin surface layer, is wound up by the disk shear, and is pushed downward by a combination of turbulent mixing and ambipolar and Ohmic drift. The toroidal field reaches much greater strengths than the seed vertical field that is usually invoked in PPD models, even becoming superthermal. Linear stability analysis indic…
The outer protoplanetary disks (PPDs) can be subject to the magnetorotational instability (MRI) and the vertical shear instability (VSI). While both processes can drive turbulence in the disk, existing numerical simulations have studied them separately. In this paper, we conduct global 3D non-ideal magnetohydrodynamic (MHD) simulations for outer PPDs with ambipolar diffusion and instantaneous cooling, and hence conductive to both instabilities. Given the range of ambipolar Elsässer numbers ($Am$) explored, it is found that the VSI turbulence dominates over the MRI when ambipolar diffusion is s…
Accretion disks are likely threaded by external vertical magnetic flux, which enhances the level of turbulence via the magnetorotational instability (MRI). Using shearing-box simulations, we find that such external magnetic flux also strongly enhances the amplitude of banded radial density variations known as zonal flows. Moreover, we report that vertical magnetic flux is strongly concentrated toward low-density regions of the zonal flow. Mean vertical magnetic field can be more than doubled in low-density regions, and reduced to nearly zero in high density regions in some cases. In ideal MHD,…
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…
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…
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…
Short-period super-Earth-sized planets are common. Explaining how they form near their present orbits requires understanding the structure of the inner regions of protoplanetary discs. Previous studies have argued that the hot inner protoplanetary disc is unstable to the magneto-rotational instability (MRI) due to thermal ionization of potassium, and that a local gas pressure maximum forms at the outer edge of this MRI-active zone. Here we present a steady-state model for inner discs accreting viscously, primarily due to the MRI. The structure and MRI-viscosity of the inner disc are fully coup…
The destabilising effect of Hall diffusion in a Keplerian disc allows the MRI to occur for much lower ionisation levels than would otherwise be possible. However, simulations suggest that the consequences for the saturated state are not as significant as suggested by the linear instability. Close inspection reveals that that the simulations have not yet probed the Hall-dominated regime. Here we revisit the effect of Hall diffusion on the MRI and the implications for the extent of MHD turbulence in protoplanetary discs. We conduct a local stability analysis for a vertical, weak magnetic field s…
A magnetic disc wind is an important mechanism that may be responsible for driving accretion and structure formation in protoplanetary discs. Recent numerical simulations have shown that these winds can take either the traditional `hourglass' symmetry about the mid-plane, or a `slanted' symmetry dominated by a mid-plane toroidal field of a single sign. The formation of this slanted symmetry state has not previously been explained. We use radially local 1D vertical shearing box simulations to assess the importance of large-scale MRI channel modes in influencing the formation and morphologies of…
Non-ideal magnetohydrodynamical effects play a crucial role in determining the mechanism and efficiency of angular momentum transport as well as the level of turbulence in protoplanetary disks (PPDs), which are key to understanding PPD evolution and planet formation. It was shown in our previous work that at 1 AU, the magnetorotational instability (MRI) is completely suppressed when both Ohmic resistivity and ambipolar diffusion (AD) are taken into account, resulting in a laminar flow with accretion driven by magnetocentrifugal wind. In this work, we study the radial dependence of the laminar …
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 …
We report new global ideal MHD simulations for thin accretion disks (with thermal scale height H/R=0.1 and 0.05) threaded by net vertical magnetic fields. Our computations span three orders of magnitude in radius, extend all the way to the pole, and are evolved for more than one viscous time over the inner decade in radius. Static mesh refinement is used to properly resolve MRI. We find that:(1) inward accretion occurs mostly in the upper magnetically dominated regions of the disk, similar to the predictions from some previous analytical work and the "coronal accretion" in previous GRMHD simul…
[abridged] We present a 1+1D global magnetically-driven disk accretion model that captures the essence of the MRI-driven accretion, without resorting to 3D global non-ideal MHD simulations. The gas dynamics is assumed to be solely controlled by the MRI and hydrodynamic instabilities. For given stellar and disk parameters, the Shakura-Sunyaev viscosity parameter $α$ is determined self-consistently under the framework of viscously-driven accretion from detailed considerations of the MRI with non-ideal MHD effects (Ohmic resistivity and ambipolar diffusion), accounting for disk heating by stellar…
Close-in super-Earths are the most abundant exoplanets known. It has been hypothesized that they form in the inner regions of protoplanetary discs, out of the dust that may accumulate at the boundary between the inner region susceptible to the magneto-rotational instability (MRI) and an MRI-dead zone further out. In Paper I we presented a model for the viscous inner disc which includes heating due to both irradiation and MRI-driven accretion; thermal and non-thermal ionization; dust opacities; and dust effects on ionization. Here we examine how the inner disc structure varies with stellar, dis…
Debris discs are commonly swathed in gas which can be observed in UV, in fine structure lines in FIR, and in resolved maps of CO emission. Carbon and oxygen are overabundant in such gas, but it is severely depleted in hydrogen. As a consequence, its ionisation fraction is remarkably high, suggesting magnetohydrodynamic (MHD) processes may be important. In particular, the gas may be subject to the magnetorotational instability (MRI), and indeed recent modelling of $β$ Pictoris requires an anomalous viscosity to explain the gas's observed radial structure. In this paper we explore the possibilit…
During the final growth phase of giant planets, accretion is thought to be controlled by a surrounding circumplanetary disk. Current astrophysical accretion disk models rely on hydromagnetic turbulence or gravitoturbulence as the source of effective viscosity within the disk. However, the magnetically-coupled accreting region in these models is so limited that the disk may not support inflow at all radii, or at the required rate. Here, we examine the conditions needed for self-consistent accretion, in which the disk is susceptible to accretion driven by magnetic fields or gravitational instabi…
Angular momentum transport in accretion discs is often believed to be due to magnetohydrodynamic turbulence mediated by the magnetorotational instability. Despite an abundant literature on the MRI, the parameters governing the saturation amplitude of the turbulence are poorly understood and the existence of an asymptotic behavior in the Ohmic diffusion regime is not clearly established. We investigate the properties of the turbulent state in the small magnetic Prandtl number limit. Since this is extremely computationally expensive, we also study the relevance and range of applicability of the …
The mechanism behind angular momentum transport in protoplanetary disks, and whether this transport is turbulent in nature, is a fundamental issue in planet formation studies. Recent ALMA observations have suggested that turbulent velocities in the outer regions of these disks are less than ~5-10% of the sound speed, contradicting theoretical predictions of turbulence driven by the magnetorotational instability (MRI). These observations have generally been interpreted to be consistent with a large-scale laminar magnetic wind driving accretion. Here, we carry out local, shearing box simulations…
We explore in situ formation and subsequent evolution of close-in super-Earths and mini-Neptunes. We adopt a steady-state inner protoplanetary gas disc structure that arises from viscous accretion due to the magneto-rotational instability (MRI). We consider the evolution of dust in the inner disc, including growth, radial drift and fragmentation, and find that dust particles that radially drift into the inner disc fragment severely due to the MRI-induced turbulence. This result has two consequences: (1) radial drift of grains within the inner disc is quenched, leading to an enhancement of dust…
We consider the evolution of accretion discs that contain some turbulence within a disc dead zone, a region about the disc midplane of a disc that is not sufficiently ionised for the magneto-rotational instability (MRI) to drive turbulence. In particular, we determine whether additional sources of turbulence within a dead zone are capable of suppressing gravo-magneto (GM) disc outbursts that arise from a rapid transition from gravitationally produced to MRI produced turbulence. With viscous $α$ disc models we consider two mechanisms that may drive turbulence within the dead zone. First, we exa…
MRI-triggered instability at the inner dead zone edge: disc evolution and burst modes tied to magnetic field strengths
Max Planck Institute for Astronomy (MPIA)（马克斯·普朗克天文学研究所）；Department of Astrophysics, University of Vienna（维也纳大学天体物理系）；Fakultät für Physik und Astronomie, Universität Heidelberg（海德堡大学物理与天文学院）
