Angular Momentum Transport by Magnetohydrodynamic Turbulence in Accretion Disks: Gas Pressure Dependence of the Saturation Level of the Magnetorotational Instability
Angular Momentum Transport by Magnetohydrodynamic Turbulence in Accretion Disks: Gas Pressure Dependence of the Saturation Level of the Magnetorotational Instability
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DOI：
10.1086/382184
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发表时间：
2003-12
期刊：
影响因子：
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通讯作者：
T. Sano;S. Inutsuka;N. Turner;J. Stone
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文献类型：
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作者：
T. Sano;S. Inutsuka;N. Turner;J. Stone
利用三维MHD模拟研究了磁旋转不稳定性(MRI)的饱和程度。采用剪切盒近似，忽略重力的垂直分量，从而在盘的一小部分局部跟踪MRI的演化。我们着重讨论了应力饱和程度对气体压力的依赖关系，这是标准α圆盘模型中的一个关键假设。数值实验发现，在非线性区域，麦克斯韦应力的饱和程度与气体压力之间存在微弱的幂函数关系，气体压力越高，应力越大。虽然幂指数略依赖于初始场的几何形状，但应力和气体压力之间的关系与初始场强度无关，如果磁雷诺数至少为10，则不受欧姆耗散的影响。这种关系在绝热计算和近等温计算中是相同的，在绝热计算中，压力随时间增加，而在近等温计算中，压力随时间变化很小。在所研究的整个参数空间区域内，由核磁共振驱动的湍流具有许多特征比，例如麦克斯韦应力与磁压的比。我们还发现，在非线性区域中，密度的空间涨落幅度和应力的时间变异性由磁压与气压之比来表征。我们的数值结果与核磁共振成像的饱和程度由核磁共振成像的增长和通过重联产生的场的耗散之间的平衡的观点是定性一致的。然而，对压力-应力关系的定量解释可能需要在非稳定磁重联的理论理解方面取得进展。
The saturation level of the magnetorotational instability (MRI) is investigated using three-dimensional MHD simulations. The shearing box approximation is adopted and the vertical component of gravity is ignored, so that the evolution of the MRI is followed in a small local part of the disk. We focus on the dependence of the saturation level of the stress on the gas pressure, which is a key assumption in the standard α disk model. From our numerical experiments we find that there is a weak power-law relation between the saturation level of the Maxwell stress and the gas pressure in the nonlinear regime; the higher the gas pressure, the larger the stress. Although the power-law index depends slightly on the initial field geometry, the relationship between stress and gas pressure is independent of the initial field strength and is unaffected by ohmic dissipation if the magnetic Reynolds number is at least 10. The relationship is the same in adiabatic calculations, where pressure increases over time, and nearly isothermal calculations, where pressure varies little with time. Over the entire region of parameter space explored, turbulence driven by the MRI has many characteristic ratios such as that of the Maxwell stress to the magnetic pressure. We also find that the amplitudes of the spatial fluctuations in density and the time variability in the stress are characterized by the ratio of magnetic pressure to gas pressure in the nonlinear regime. Our numerical results are qualitatively consistent with an idea that the saturation level of the MRI is determined by a balance between the growth of the MRI and the dissipation of the field through reconnection. The quantitative interpretation of the pressure-stress relation, however, may require advances in the theoretical understanding of nonsteady magnetic reconnection.