The Effect of the Hall Term on the Nonlinear Evolution of the Magnetorotational Instability. II. Saturation Level and Critical Magnetic Reynolds Number
The Effect of the Hall Term on the Nonlinear Evolution of the Magnetorotational Instability. II. Saturation Level and Critical Magnetic Reynolds Number
复制标题
霍尔项对磁旋转不稳定性非线性演化的影响。
DOI：
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发表时间：
2002
期刊：
影响因子：
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通讯作者：
J. Stone
中科院分区：
文献类型：
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作者：
T. Sano;J. Stone
使用局部三维 MHD 模拟和各种初始磁场几何形状研究弱电离吸积盘中磁旋转不稳定性 (MRI) 的非线性演化，包括霍尔项和欧姆耗散的影响。当磁雷诺数 ReM == v/ηΩ（其中 vA 是阿尔芬速度，η 是磁扩散率，Ω 是角频率）最初大于临界值 ReM,crit 时，MRI 演变成 MHD 湍流，其中角动量通过麦克斯韦应力有效传输。然而，如果 ReM < ReM,crit，欧姆耗散会抑制 MRI，并且应力会降低几个数量级。临界值在 1-30 范围内，具体取决于初始字段配置。霍尔效应不会太大地改变临界磁雷诺数，但会将麦克斯韦应力的饱和水平提高几倍。我们表明，MRI 的饱和水平由 v/ηΩ 表征，其中 vAz 是沿场垂直分量的非线性区域中的阿尔文速度。湍流和显着传输的条件由 v/ηΩ ≳ 1 给出，并且该临界值与磁场的强度和几何形状或霍尔项的大小无关。如果吸积盘中的磁场强度可以通过观测来估计，并且磁雷诺数 v/ηΩ 大于约 30，则这意味着 MRI 正在吸积盘中运行。
The nonlinear evolution of the magnetorotational instability (MRI) in weakly ionized accretion disks, including the effect of the Hall term and ohmic dissipation, is investigated using local three-dimensional MHD simulations and various initial magnetic field geometries. When the magnetic Reynolds number, ReM ≡ v/ηΩ (where vA is the Alfvén speed, η is the magnetic diffusivity, and Ω is the angular frequency), is initially larger than a critical value ReM,crit, the MRI evolves into MHD turbulence in which angular momentum is transported efficiently by the Maxwell stress. If ReM < ReM,crit, however, ohmic dissipation suppresses the MRI, and the stress is reduced by several orders of magnitude. The critical value is in the range of 1-30 depending on the initial field configuration. The Hall effect does not modify the critical magnetic Reynolds number by much but enhances the saturation level of the Maxwell stress by a factor of a few. We show that the saturation level of the MRI is characterized by v/ηΩ, where vAz is the Alfvén speed in the nonlinear regime along the vertical component of the field. The condition for turbulence and significant transport is given by v/ηΩ ≳ 1, and this critical value is independent of the strength and geometry of the magnetic field or the size of the Hall term. If the magnetic field strength in an accretion disk can be estimated observationally and the magnetic Reynolds number v/ηΩ is larger than about 30, this would imply that the MRI is operating in the disk.