The magneto-rotational instability (MRI) is the most likely mechanism for transportation of angular momentum and dissipation of energy within hot, ionized accretion discs. This instability is produced through the interactions of a differentially rotating plasma with an embedded magnetic field. Like all substances in nature, the plasma in an accretion disc has the potential to become magnetically polarized when it interacts with the magnetic field. In this paper we study the effect of this magnetic susceptibility, parameterized by χm, on the MRI, specifically within the context of black hole accretion. We find from a linear analysis within the Newtonian limit that the minimum wavelength of the first unstable mode and the wavelength of the fastest growing mode are shorter in paramagnetic (χm > 0) than in diamagnetic (χm < 0) discs, all other parameters being equal. Furthermore, the magnetization parameter (ratio of gas to magnetic pressure) in the saturated state should be smaller when the magnetic susceptibility is positive than when it is negative. We confirm this latter prediction through a set of numerical simulations of magnetically polarized black hole accretion discs. We additionally find that the vertically integrated stress and mass accretion rate are somewhat larger when the disc is paramagnetic than when it is diamagnetic. If astrophysical discs are able to become magnetically polarized to any significant degree, then our results would be relevant to properly interpreting observations.

中文翻译：

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磁极化盘中的磁旋转不稳定性

磁旋转不稳定性 (MRI) 是热电离吸积盘内角动量传输和能量耗散的最可能机制。这种不稳定性是通过差分旋转等离子体与嵌入磁场的相互作用产生的。像自然界中的所有物质一样，吸积盘中的等离子体在与磁场相互作用时有可能发生磁极化。在本文中，我们研究了这种由 χm 参数化的磁化率对 MRI 的影响，特别是在黑洞吸积的背景下。我们从牛顿极限内的线性分析中发现，顺磁性 (χm > 0) 的第一不稳定模式的最小波长和增长最快的模式的波长比反磁性 (χm < 0) 圆盘中的短，所有其他参数都相同。此外，饱和状态的磁化参数（气体与磁压的比值）在磁化率为正时应小于在磁化率为负时。我们通过一组磁极化黑洞吸积盘的数值模拟来证实后一种预测。我们还发现，当圆盘顺磁性时，垂直整合的应力和质量吸积率比反磁性时要大一些。如果天体物理圆盘能够被磁极化到任何显着程度，那么我们的结果将与正确解释观测结果相关。磁化率为正时，饱和状态的磁化参数（气体与磁压之比）应小于负磁化率。我们通过一组磁极化黑洞吸积盘的数值模拟来证实后一种预测。我们还发现，当圆盘顺磁性时，垂直整合的应力和质量吸积率比反磁性时要大一些。如果天体物理圆盘能够被磁极化到任何显着程度，那么我们的结果将与正确解释观测结果相关。磁化率为正时，饱和状态的磁化参数（气体与磁压之比）应小于负磁化率。我们通过一组磁极化黑洞吸积盘的数值模拟来证实后一种预测。我们还发现，当圆盘顺磁性时，垂直整合的应力和质量吸积率比反磁性时要大一些。如果天体物理圆盘能够被磁极化到任何显着程度，那么我们的结果将与正确解释观测结果相关。我们还发现，当圆盘顺磁性时，垂直整合的应力和质量吸积率比反磁性时要大一些。如果天体物理圆盘能够被磁极化到任何显着程度，那么我们的结果将与正确解释观测结果相关。我们还发现，当圆盘顺磁性时，垂直整合的应力和质量吸积率比反磁性时要大一些。如果天体物理圆盘能够被磁极化到任何显着程度，那么我们的结果将与正确解释观测结果相关。