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arXiv 1011.4643astro-ph.HE
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MRI湍流吸积盘的稳定性

Stability of MRI turbulent Accretion Disks

Hiroyuki R. Takahashi, Youhei Masada

摘要:

基于磁旋转不稳定性(MRI)和MRI驱动湍流的特点,我们利用“非标准”$α$ -处方建立了一个几何薄圆盘的定常模型。角动量输运的效率取决于磁普朗特数$Pm = ν/η$,其中$ν$和$η$是微观粘性扩散率和磁扩散率。在我们的圆盘模型中,Shakura-Sunyaev的$α$参数对磁普朗特数有幂律依赖性,即$α\propto Pm^δ$,其中$δ$是常数幂律指数。采用斯皮策的微观扩散系数,磁普朗特数成为一个减少的功能时,磁盘半径$δ> 0$。因此,角动量的传输效率和粘性加热速率在盘的外部较小,而这些受到指数$δ$的大小的影响。我们发现,随着$δ$指数的增大,盘的引力不稳定性增强。在$δ> 2/3$条件下,即使辐射压很小,盘模型最显著的特点是热不稳定性和长期不稳定性也能在盘的中部增长。在实际盘系统中,除非MRI驱动湍流的$Pm$依赖性相对较弱,否则很难维持稳定的质量吸积状态。

英文摘要:

Based on the characteristics of the magnetorotational instability (MRI) and the MRI-driven turbulence, we construct a steady model for a geometrically thin disk using "non-standard" $α$-prescription. The efficiency of the angular momentum transport depends on the magnetic Prandtl number, $Pm = ν/η$, where $ν$ and $η$ are the microscopic viscous and magnetic diffusivities. In our disk model, Shakura-Sunyaev's $α$-parameter has a power-law dependence on the magnetic Prandtl number, that is $α\propto Pm^δ$ where $δ$ is the constant power-law index. Adopting Spitzer's microscopic diffusivities, the magnetic Prandtl number becomes a decreasing function of the disk radius when $δ> 0$. The transport efficiency of the angular momentum and the viscous heating rate are thus smaller in the outer part of the disk, while these are impacted by the size of index $δ$. We find that the disk becomes more unstable to the gravitational instability for a larger value of index $δ$. The most remarkable feature of our disk model is that the thermal and secular instabilities can grow in its middle part even if the radiation pressure is negligibly small in the condition $δ> 2/3$. In the realistic disk systems, it would be difficult to maintain the steady mass accretion state unless the $Pm$-dependence of MRI-driven turbulence is relatively weak.

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