原行星和黑洞吸积盘中的Angular Momentum输运：寄生模在MHD饱和中的作用Turbulence
Angular Momentum Transport in Protoplanetary and Black-Hole Accretion Disks: The Role of Parasitic Modes in the Saturation of MHD Turbulence
摘要：
磁旋转不稳定性（MRI）被认为是驱动天体物理盘中有效角动量输运的关键过程。理解它的非线性饱和构成了现代吸积盘理论的一个基本问题。吸积盘中物理条件的大的动力学范围使得仅用数值模拟来解决这个问题具有挑战性。我们分析的概念，（二次）寄生不稳定性是负责的饱和的MRI。我们的方法使我们能够探索耗散制度，相关的天体物理和实验室条件，超越了目前的数值模拟访问的制度。我们计算的频谱和物理结构的寄生模式，饲料的最快，准确的（主要）MRI模式时，其幅度是这样的，最快的寄生模式的增长一样快的MRI。我们认为，这个“饱和”的幅度提供了一个估计的磁场，可以由MRI产生的二次不稳定性抑制其增长显着之前。最近的工作表明，磁共振成像的饱和振幅主要取决于磁普朗特数。我们的研究结果表明，只要粘性效应不占主导地位的流体动力学，磁共振成像的饱和度只取决于埃尔萨瑟数$Λ_η$。我们计算应力和磁能密度之间的比率，$α_{\rm sat}β_{\rm sat}$，与主要MRI模式相关。我们发现，对于$Λ_η>1$，Kelvin-Helmholtz模是导致饱和和$α_{\rm sat}β_{\rm sat} = 0.4$的主要原因，而对于$Λ_η< 1$，撕裂模占主导地位，并导致$α_{\rm sat}β_{\rm sat} \simeq 0.5 \, Λ_η$ .围绕年轻恒星和致密天体的吸积盘的MRI模拟的几个特征可以根据我们的发现来解释。
英文摘要：
The magnetorotational instability (MRI) is considered a key process for driving efficient angular momentum transport in astrophysical disks. Understanding its non-linear saturation constitutes a fundamental problem in modern accretion disk theory. The large dynamical range in physical conditions in accretion disks makes it challenging to address this problem only with numerical simulations. We analyze the concept that (secondary) parasitic instabilities are responsible for the saturation of the MRI. Our approach enables us to explore dissipative regimes that are relevant to astrophysical and laboratory conditions that lie beyond the regime accessible to current numerical simulations. We calculate the spectrum and physical structure of parasitic modes that feed off the fastest, exact (primary) MRI mode when its amplitude is such that the fastest parasitic mode grows as fast as the MRI. We argue that this "saturation" amplitude provides an estimate of the magnetic field that can be generated by the MRI before the secondary instabilities suppress its growth significantly. Recent works suggest that the saturation amplitude of the MRI depends mainly on the magnetic Prandtl number. Our results suggest that, as long as viscous effects do not dominate the fluid dynamics, the saturation level of the MRI depends only on the Elsasser number $Λ_η$. We calculate the ratio between the stress and the magnetic energy density, $α_{\rm sat}β_{\rm sat}$, associated with the primary MRI mode. We find that for $Λ_η>1$ Kelvin-Helmholtz modes are responsible for saturation and $α_{\rm sat}β_{\rm sat} = 0.4$, while for $Λ_η< 1$ tearing modes prevail and $α_{\rm sat}β_{\rm sat} \simeq 0.5 \, Λ_η$. Several features of MRI simulations in accretion disks surrounding young stars and compact objects can be interpreted in terms of our findings.
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