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 radial wavenumber and (iii) the rest modes. The rest modes comprise those harmonics in the vital area whose energies reach more than $50 \%$ of the maximum spectral energy. The rest modes individually are not so significant compared to the channel and zonal flow modes, however, the combined action of their multitude is dominant over these two modes. These three mode types are governed by interplay of the linear and nonlinear processes, leading to their interdependent dynamics. The linear processes consist in disk flow nonmodality-modified classical MRI with a net vertical field. The main nonlinear process is transfer of modes over wavevector angles in Fourier space - the transverse cascade. The channel mode exhibits episodic bursts supplied by linear MRI growth, while the nonlinear processes mostly oppose this, draining the channel energy and redistributing it to the rest modes. As for the zonal flow, it does not have a linear source and is fed by nonlinear interactions of the rest modes.
We investigate magnetohydrodynamic turbulence driven by the magnetorotational instability (MRI) in Keplerian disks with a nonzero net azimuthal magnetic field using shearing box simulations. As distinct from most previous studies, we analyze turbulence dynamics in Fourier (${\bf k}$-) space to understand its sustenance. The linear growth of MRI with azimuthal field has a transient character and is anisotropic in Fourier space, leading to anisotropy of nonlinear processes in Fourier space. As a result, the main nonlinear process appears to be a new type of angular redistribution of modes in Fou…
Dust Concentration at the Boundary Between Steady Super/Sub-Keplerian Flow Created by Inhomogeneous Growth of MRI
如何在原行星盘中的微小尘埃颗粒螺旋到中心恒星之前产生星子是行星系统形成理论中最具挑战性的问题之一。在我们之前的论文Kato et al.（2009）中，我们已经表明，通过磁旋转不稳定性（MRI）的非均匀激发，在盘中创建了由超开普勒区域和亚开普勒区域组成的稳定角速度分布。这种非均匀的MRI激励在具有相对低的电离度的盘的一部分中是合理预期的。在本文中，我们表明，通过三维电阻MHD模拟与测试粒子的这种径向结构的角速度确实导致防止螺旋的尘埃粒子，并进一步他们的积累在边界的超开普勒和次开普勒区域。以尘埃粒子为实验粒子，模拟了尘埃粒子在非均匀磁共振成像中的运动。在最有利的情况下（在磁盘区域中具有相对较大的MRI稳定区域部分的米级尘埃颗粒），我们发现尘埃浓度在超/亚开普勒流动边界附近达到峰值，并且峰值尘埃密度是初始值的10，000倍。峰值密度高到足以使随后的引力不稳定性发生，这表明在磁盘的弱电离区域通过非均匀激发的MRI形成星子的可能途径。
The magnetorotational (MRI) dynamo has long been considered one of the possible drivers of turbulent angular momentum transport in astrophysical accretion disks. However, various numerical results suggest that this dynamo may be difficult to excite in the astrophysically relevant regime of magnetic Prandtl number (Pm) significantly smaller than unity, for reasons currently not well understood. The aim of this article is to present the first results of an ongoing numerical investigation of the role of both linear and nonlinear dissipative effects in this problem. Combining a parametric explorat…
Observations of distorted discs have highlighted the ubiquity of warps in a variety of astrophysical contexts. This has been complemented by theoretical efforts to understand the dynamics of warp evolution. Despite significant efforts to understand the dynamics of warped discs, previous work fails to address arguably the most prevalent regime -- nonlinear warps in Keplerian discs for which there is a resonance between the orbital, epicyclic and vertical oscillation frequencies. In this work, we implement a novel nonlinear ring model, developed recently by Fairbairn and Ogilvie, as a framework …
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 investigate sustenance and dependence on magnetic Prandtl number (${\rm Pm}$) for magnetorotational instability (MRI)-driven turbulence in astrophysical Keplerian disks with zero net magnetic flux using standard shearing box simulations. We focus on the turbulence dynamics in Fourier space, capturing specific/noncanonical anisotropy of nonlinear processes due to disk flow shear. This is a new type of nonlinear redistribution of modes over wavevector orientations in Fourier space -- the nonlinear transverse cascade -- which is generic to shear flows and fundamentally different from usual dir…
The magnetorotational instability (MRI) is thought to be a powerful source of turbulence in Keplerian accretion disks. Motivated by recent laboratory experiments, we study the MRI driven by an azimuthal magnetic field in an electrically conducting fluid sheared between two concentric rotating cylinders. By adjusting the rotation rates of the cylinders, we approximate angular velocity profiles $ω\propto r^{q}$. We perform direct numerical simulations of a steep profile close to the Rayleigh line $q \gtrsim -2 $ and a quasi-Keplerian profile $q \approx -3/2$ and cover wide ranges of Reynolds ($R…
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…
The Magnetorotational Instability (MRI) has long been considered a plausibly ubiquitous mechanism to destabilize otherwise stable Keplerian flows to support radially outward transport of angular momentum. Such an efficient transport process would allow fast accretion in astrophysical objects such as stars and black holes to release copious kinetic energy that powers many of the most luminous sources in the universe. But the standard MRI under a purely vertical magnetic field has heretofore never been directly measured despite numerous efforts over more than a decade. Here we report an unambigu…
We compare transport statistics of elongated incompressible shearing boxes for different Reynolds and magnetic Prandtl numbers, $Re$ and $Pm$, and aspect ratios, $L_z/L_x$. We find that at fixed aspect ratio $L_z/L_x=4$ and $Re = 10,000$, the turbulent stresses for $Pm \lesssim 1$ do not show considerable variation and follow a power law $\sim Pm^{3/2}$ for $Pm > 1$. This is qualitatively consistent with previous results based on net imposed flux and small box $L_z/L_x \sim 1$ simulations but the power law exponent is different. The saturated level of stresses, the ratio of Maxwell stress to t…
We model the vertical structure of magnetized accretion disks subject to viscous and resistive heating, and irradiation by the central star. We apply our formalism to the radial structure of magnetized accretion disks threaded by a poloidal magnetic field dragged during the process of star formation developed by Shu and coworkers. We consider disks around low mass protostars, T Tauri, and FU Orionis stars. We consider two levels of disk magnetization, $λ_{sys} = 4$ (strongly magnetized disks), and $λ_{sys} = 12$ (weakly magnetized disks). The rotation rates of strongly magnetized disks have la…
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…
We conduct a linear analysis of axisymmetric magnetorotational instability (MRI) in a magnetized cylindrical Taylor-Couette (TC) flow for its standard version (SMRI) with a purely axial background magnetic field and two further types -- helically modified SMRI (H-SMRI) and helical MRI (HMRI) -- in the presence of combined axial and azimuthal magnetic fields. This study is intended as preparatory for upcoming large-scale liquid sodium MRI experiments planned within the DRESDYN project at Helmholtz-Zentrum Dresden-Rossendorf, so we explore these instability types for typical values of the main p…
We explore the pulsationally driven orbital mass ejection mechanism for Be star disc formation using isothermal, 3D magnetohydrodynamic (MHD) and hydrodynamic simulations. Non-radial pulsations are added to a star rotating at 95\% of critical as an inner boundary condition that feeds gas into the domain. In MHD, the initial magnetic field within the star is weak. The hydrodynamics simulation has limited angular momentum transport, resulting in repeating cycles of mass accumulation into a rotationally-supported disc at small radii followed by fall-back onto the star. The MHD simulation, convers…
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…
The observations and simulations have revealed that large-scale magnetic field and outflows can exist in the inner regions of an advection-dominated accretion disc where the resistive diffusion may also be important. In the present paper, the roles of large-scale magnetic field and outflows in the structure of resistive advection-dominated accretion discs are explored by assuming that the accretion flow is radially self-similar. In the non-ideal magnetohydrodynamic (MHD) approximation, the results show that the angular velocity is always sub-Keplerian when both the outflow and the large-scale …
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…
We show for the first time that sustained turbulence is possible at low magnetic Prandtl number for Keplerian flows with no mean magnetic flux. Our results indicate that increasing the vertical domain size is equivalent to increasing the dynamical range between the energy injection scale and the dissipative scale. This has important implications for a large variety of differentially rotating systems with low magnetic Prandtl number such as protostellar disks and laboratory experiments.
A Spatially Resolved Vertical Temperature Gradient in the HD 163296 Disk
我们分析敏感，亚弧秒分辨率ALMA科学验证观测的CO发射线在原行星盘主办的年轻，孤立的Ae星HD 163296。观测到的12 CO J=3-2发射线的空间形态在盘的长轴上是不对称的; 12 CO J=2-1线的特征是不太明显，但类似的不对称。~（12）CO及其主要同位素的J=2-1发射没有分辨的空间不对称性。我们将这种行为与盘中垂直温度梯度和分层分子结构的直接特征联系起来。这是证明使用玩具模型和更复杂的计算假设非局部热力学平衡（非LTE）条件。一个模型磁盘结构的开发，以再现独特的空间形态的12 CO J=3-2线，以及J=2-1的CO同位素的排放假设与星际介质的相对丰度一致。该模型盘结构具有τ =1的12 CO发射线的发射表面，其相对于盘中平面成大约15度的角度。此外，我们表明，这些数据的空间和光谱灵敏度可以区分模型，由于磁盘的垂直范围和其相关的径向压力梯度（在散装气体速度场的分数差约大于5%）的子开普勒气体速度。
