Dynamical Instabilities in Discs

自从Shakura和Sunyaev（1973）的开创性论文建立了湍流吸积盘理论的基础以来已经有40年了，自从磁旋转不稳定性（MRI）作为盘湍流的根本原因建立以来已经有22年了（Balbus和Hawley 1991）。然而，椎间盘行为的主要特征仍然知之甚少。也许其中最引人注目的是一些光盘自发改变其发射轮廓的趋势。这可能会发生在各种各样的时间尺度上，这取决于圆盘中心体的质量和性质。一个著名的例子是所谓的矮新星（DN）。这些是吸积的白色矮星，其中系统在几周的时间尺度上经历周期性的爆发。其根本原因被认为是在与原子H的电离相关的温度下的辐射不透明度的复杂行为，然后导致从负扩散系数的作用的不稳定盘演化。这种不稳定性的解决方案是极限环行为，似乎与观察到的重复爆发。DN理论已经有几十年的历史了，并且有相当强的观测支持。这反过来又为人们可以理解湍流介质中的爆发现象的概念提供了理论支持。此外，通过不断地将吸积盘从其稳态轮廓中移出，DN还探索了α盘模型本身的基本原理，因此DN已成为吸积盘理论的基石。对黑洞候选者和其他致密X射线源的状态变化了解得少得多，这涉及到不同的非热硬X射线成分的出现，可能还有喷流和外流。数值磁共振成像模拟没有显示出这种趋势，但当然没有理由期望它们在这个阶段应该：矮新星不稳定性，例如，来自热物理，通常在数值模拟中被大大简化或完全忽略。然而，X射线源远不是不透明度应该影响稳定性的区域，并且目前还没有普遍接受的状态变化理论。在这个博士项目中，学生将进行系统的努力，其目标是将MRI的物理学与观察到的X射线状态变化联系起来。这项工作将由S.巴尔布斯和一位博士后研究员，W。波特将从领先的数值天体物理学家那里获得技术支持。最初的努力设想集中在粘性和欧姆电阻的作用，两个耗散过程与MHD湍流。有很好的数值证据表明，大规模湍流的行为对粘度或电阻率是否较大很敏感（Fromang等人，2007年）。此外，围绕致密物体的盘有一个显著的特征：当盘向内移动时，盘从电阻率主导转变为粘性主导的过渡半径（Balbus & Henri 2008）。这个半径在白色矮星盘中是不存在的，因为它们在全球范围内都是由磁引力主导的。初步工作表明，过渡半径的存在预示着不稳定的行为，这可能在其非线性解决方案中与极限环相似（Potter & Balbus 2014）。目标是确定在哪些条件下（如果有的话）存在不稳定性，以及任何不稳定性的非线性分辨率是什么。希望和期望是，非线性行为将被证明与观察到的X射线状态变化有关。在这个博士项目中，我想发展一个更深入的了解磁流体磁盘湍流的MRI调节。根据学生的兴趣，我们使用的方法可能涉及数值和分析技术的混合。

It has been forty years since the seminal paper of Shakura & Sunyaev (1973) established the basis of turbulent accretion disc theory and twenty-two years since the establishment of the magnetorotational instability (MRI) as the fundamental cause for disc turbulence (Balbus & Hawley 1991). Yet, major features of disc behaviour remain poorly understood. Perhaps the most dramatic of these is the tendency for some discs to spontaneously change their emission profile. This may occur over a wide variety of time scales, depending on the mass and the nature of the disk's central body. A famous example is the case of so-called dwarf novae (DN). These are accreting white dwarf stars in which the system undergoes periodic eruptions on a time scale of weeks. The root cause is thought to be the complex behaviour of the radiative opacity at temperatures associated with the ionisation of atomic H, which then results in an unstable disc evolution from the action of a negative diffusion coefficient. The resolution of this instability is limit cycle behaviour that appears to be associated with the observed repeating outbursts. DN theory is several decades old now, and enjoys rather strong observational support. This in turn gives theoretical support to the notion that one can understand outburst phenomena in turbulent media. Moreover, by constantly dislodging the disk from its steady-state profile, DN also probe the very fundamentals of the alpha disc model itself, and thus DN have become the cornerstone of accretion disc theory. Much less understood are state changes in black hole candidates and other compact X-ray sources, that involve the appearance of distinct nonthermal hard X-ray components and possibly jets and outflows. Numerical MRI simulations show no such tendencies, but of course there is no reason to expect that they should at this stage: dwarf novae instabilities, for example, arise from thermal physics that is generally drastically simplified or ignored altogether in numerical simulations. X-ray sources are far from a regime where opacity should influence stability however, and there is at no present no generally accepted theory for the state changes. In this DPhil project, the student will undertake a systematic effort whose goal is to connect the physics of the MRI with the observed X-ray state changes. The work will be supervised by Prof. S. Balbus and a postdoctoral research fellow, Dr. W. Potter. Technical support will be available from leading numerical astrophysicists. The initial effort is envisaged to focus on the role of viscosity and ohmic resistance, the two dissipation processes associated with MHD turbulence. There is good numerical evidence that the behaviour of the large scale turbulence is sensitive to whether the viscosity or resistivity is larger (Fromang et al. 2007). There is, moreover, a distinguishing feature of discs surrounding compact objects: a transition radius at which the disk goes from resistivity dominated to viscous dominated as one moves inward (Balbus & Henri 2008). This radius is not present in white dwarf discs, which are globally resistivity-dominated. Preliminary work suggests that the existence of the transition radius heralds unstable behaviour, which may, in its nonlinear resolution, bear similarities to limit cycles (Potter & Balbus 2014). The goal is to determine under which conditions (if any) there are instabilities, and what the nonlinear resolution of any instabilities is. The hope and expectation is that the nonlinear behaviour will prove to be connected with the observed X-ray state changes. In this PhD project, I would like to develop a much deeper understanding of MHD disk turbulence regulated by the MRI. Depending upon the interests of the student, the approach we use could involve a mixture of both numerical and analytic techniques.