arXiv 2312.044002023-12-07physics.plasm-phastro-ph.HEastro-ph.SRphysics.flu-dyn

数值扩散率在全局吸积盘发电机MHD模拟中的作用

On the role of numerical diffusivity in MHD simulations of global accretion disc dynamos

C. J. Nixon, C. C. T. Pringle, J. E. Pringle

备注：: 20 pages, 6 figures, accepted for publication in the Journal of Plasma Physics

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AI总结：

本文指出全局吸积盘MHD模拟中β远大于1的矛盾可能源于数值磁扩散率，并通过线性剪切弱磁场精确解说明磁能放大受磁雷诺数限制。

摘要：

主要针对矮新星爆发的观测表明，高电离吸积盘中的反常黏性具有磁起源，并且要求等离子体β约为1。迄今为止，大多数吸积盘磁发电机模拟都采用了被称为shearing box（剪切盒）的局部近似。尽管这些模拟证明了自持发电机的可能性，但这些模型中产生的磁活动在β远大于1时达到饱和。这一长期存在的差异此前被归因于局部近似本身。最近已有研究尝试在与矮新星相关的参数下模拟全局吸积盘中的磁活动。这些研究同样得到β远大于1的数值。我们推测，这些模型与观测之间的矛盾可能由数值磁扩散率造成。作为一个教学性示例，我们给出了不可压缩流体在承受线性剪切和磁扩散时弱磁场演化的精确含时解。我们发现，初始磁能量能够被放大的最大倍数按磁雷诺数${\mathcal R}_{\rm m}^{2/3}$变化。我们估计，当前矮新星盘的全局数值模拟所具有的数值磁雷诺数，比矮新星盘中发现的物理值${\mathcal R}_{\rm m}\sim10^{10}$低约6个数量级。我们认为，鉴于当前计算能力的限制，期望利用数值MHD计算可观测吸积盘中真实的发电机作用，目前而言还为时尚早。

英文摘要：

Observations, mainly of outbursts in dwarf novae, imply that the anomalous viscosity in highly ionized accretion discs is magnetic in origin, and requires that the plasma $β\sim 1$. Until now most simulations of the magnetic dynamo in accretion discs have used a local approximation (known as the shearing box). While these simulations demonstrate the possibility of a self-sustaining dynamo, the magnetic activity generated in these models saturates at $β\gg 1$. This long-standing discrepancy has previously been attributed to the local approximation itself. There have been recent attempts at simulating magnetic activity in global accretion discs with parameters relevant to the dwarf novae. These too find values of $β\gg 1$. We speculate that the tension between these models and the observations may be caused by numerical magnetic diffusivity. As a pedagogical example, we present exact time-dependent solutions for the evolution of weak magnetic fields in an incompressible fluid subject to linear shear and magnetic diffusivity. We find that the maximum factor by which the initial magnetic energy can be increased depends on the magnetic Reynolds number as ${\mathcal R}_{\rm m}^{2/3}$. We estimate that current global numerical simulations of dwarf nova discs have numerical magnetic Reynolds numbers around 6 orders of magnitude less than the physical value found in dwarf nova discs of ${\mathcal R}_{\rm m} \sim 10^{10}$. We suggest that, given the current limitations on computing power, expecting to be able to compute realistic dynamo action in observable accretion discs using numerical MHD is, for the time being, a step too far.

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