Dynamical Instabilities in Discs

自从Shakura&Sunyaev(1973)的开创性论文奠定了湍流吸积盘理论的基础以来，已经走过了40个年头，而磁致旋转不稳定性(MRI)是导致盘湍流的根本原因(Balbus&Hawley，1991)，至今已有22年。然而，对椎间盘行为的主要特征仍然知之甚少。其中最具戏剧性的可能是一些光盘自发地改变其发射曲线的趋势。这可能会发生在各种各样的时间尺度上，这取决于磁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)。这些是积聚的白矮星，系统在几周的时间尺度上经历周期性的喷发。根本原因被认为是与H原子电离相关的温度下辐射不透明度的复杂行为，这随后导致了负扩散系数作用下的不稳定圆盘演化。这种不稳定性的解决办法是极限环行为，它似乎与观察到的反复爆发有关。DN理论至今已有几十年的历史，并得到了较强的观测支持。这反过来又为人们可以理解湍流介质中的突出现象这一概念提供了理论支持。此外，通过不断地使盘脱离其稳态轮廓，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。人们对候选黑洞和其他致密X射线源的状态变化知之甚少，这些变化涉及不同的非热硬X射线成分的出现，可能还包括喷流和流出。数值核磁共振模拟没有显示出这样的趋势，但当然也没有理由期望它们会在这个阶段出现：例如，矮新星不稳定性是由热物理引起的，而在数值模拟中，热物理通常被大大简化或完全忽略。然而，X射线源远不是不透明应该影响稳定性的区域，目前还没有关于状态变化的普遍接受的理论。在这个DPhil项目中，学生将进行一项系统的工作，其目标是将核磁共振的物理与观察到的X射线状态变化联系起来。这项工作将由S.Balbus教授和博士后研究员W.Potter博士监督。领先的数值天体物理学家将提供技术支持。最初的努力被设想集中在粘性和欧姆阻力的作用上，这是与MHD湍流相关的两个耗散过程。有很好的数值证据表明，大尺度湍流的行为对粘性或电阻率是否较大很敏感(Frong等人)。2007)。此外，围绕致密物体的圆盘有一个明显的特征：当一个圆盘向内移动时，圆盘从电阻率为主到粘性为主的转变半径(Balbus&Henri 2008)。这个半径在白矮星圆盘中不存在，因为白矮星圆盘是以全球电阻率为主的。初步工作表明，过渡半径的存在预示着不稳定行为，在其非线性解析中，它可能与极限环具有相似之处(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解决方案是什么。人们的希望和期望是，这种非线性行为将被证明与观测到的X射线状态变化有关。在这个博士项目中，我想对磁共振所调节的磁流体盘湍流有更深入的了解。根据学生的兴趣，我们使用的方法可能会涉及到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.