Numerical investigations of the inner regions of black hole accretion discs

对黑洞吸积的研究已经有54年的历史，可以追溯到Donald Lynden-Bell的开创性论文(1969，自然，223,690)，他在论文中提出，当时非常神秘的类星体和活跃的星系核是由大黑洞提供动力的，这些大黑洞以圆盘的形式从周围吸积气体。在接下来的半个世纪里，黑洞吸积盘的研究领域在许多方面都有了巨大的发展：观测、唯象模型、数值模拟和基本的MHD过程。特别是，Shakura和Sunyaev(1973，AA，24,347)提出的吸积盘的稳态模型已经成为理论和观测的基础标准。它结合了动力学和辐射物理学。由于Shakura-Sunyaev理论适用于垂直标度高度远小于径向感兴趣程度的“薄圆盘”，因此对此类(湍流)圆盘进行直接数值研究一直非常困难。事实上，该理论本身从未被直接验证过，尽管它被广泛使用。我们现在已经能够做到这一点，这在很大程度上是因为有了最先进的硬件和代码开发。在这篇旨在详细研究黑洞吸积盘最内缘附近的吸积流的论文中，我们将设置一组测试问题来明确地检验Shakura-Sunyaev理论，并更广泛地探索该理论是如何崩溃的，因为我们知道它在某个点上肯定会崩溃。进行这项工作的观测环境是快速增长的潮汐干扰事件(TDEs)领域。这是当一颗恒星接近其星系中心的一个大质量黑洞时发生的事件，以至于它被潮汐撕裂开来。虽然一些恒星碎片总是会逃逸，但也有一些会留下来，并在其后期演化阶段形成一个依赖于时间的吸积盘，其发射可能已经成熟，其中含有关于中央黑洞的信息。将用于研究这一问题的计算工具是雅典娜++代码，由詹姆斯·斯通教授和他在普林斯顿IAS的同事开发。本论文的第一部分将利用雅典娜++在全辐射模式下研究一组受控问题中的含时盘吸积问题。该代码值得注意的是，它是完全相对论的，MHD，并允许辐射自我一致地包括在内，而不仅仅是在后处理意义上。我们从斯通教授参与这个项目中受益匪浅，他同意亲自参与，这样在适当的集群上设置和运行代码的技术细节就可以以最高的效率完成。这项工作的影响是巨大的，对基本的盘面理论和观测都有影响，盘面光谱是计算本身不可分割的一部分。主要的应用将是TDES的光曲线。这包括诸如Lightman-Eardley不稳定性等问题，这是圆盘湍流和辐射加热之间的耦合，其在圆盘演化中的作用仍未完全了解。这项研究具有数值分辨率和辐射物理能力，可以在比以前的研究高得多的水平上研究这个问题。我们还将研究磁场几何形状的影响，特别是它在设定盘的整体演化行为中的作用，这对于理解MHD喷流何时从内部区域出现以及何时不出现是重要的。本论文的第二个主要部分将是对通常被认为是圆盘内缘的流动的研究。黑洞圆盘向着越来越小的半径向下延伸，直到在某个点上，仍然远离视界，圆形轨道变得不稳定。这个过渡半径被称为最内侧的稳定性

Black hole accretion studies have history spanning some 54 years, going back to Donald Lynden-Bell's seminal paper (1969, Nature, 223, 690) in which he put forth the case that the then deeply mysterious quasars and active galactic nuclei were being powered by large black holes accreting gas from their surroundings in the form of a disc. In the ensuing half century, the field of black hole accretion disc studies has grown enormously on many fronts: observational, phenomenological modelling, numerical simulations and fundamental MHD processes. In particular, a steady-state model of accretion discs developed by Shakura and Sunyaev (1973, AA, 24, 347) has become a bedrock standard for both theory and observations. It combines both dynamical and radiation physics. Because of Shakura-Sunyaev theory applies to "thin discs," in which the vertical scale height is much less than the radial extent of interest, direct numerical study of such (turbulent) discs has been very difficult. In fact, the theory itself has never been verified directly, even though it is widely used. We are now in a position where this has become possible, in no small part because of the availability of state-of-the-art hardware and code development. In this thesis, which is designed to be a detailed study of the accretion flow near the innermost edge of black hole accretion discs, we will set up a suite of test problems to explicitly test Shakura-Sunyaev theory as well to explore more generally how the theory breaks down, as we know it must at some point. The observational setting in which this will be done is the rapidly growing field of tidal disruption events, or TDEs. This is an event that occurs when a star approaches a massive black hole at the centre of its galaxy in such a way that it is tidally torn apart. While some stellar debris invariably escapes, some also remains behind, and in its later evolutionary stages forms a time-dependent accretion disc whose emission is potentially ripe with information about the central black hole. The computational tool that will be used to study this problem is the Athena ++ code, developed by Prof James Stone and his co-workers at the IAS in Princeton. The first part of this thesis will be to use Athena ++ in its full radiative mode to study time dependent disc accretion in a set of controlled problems. The code is remarkable in that it is fully relativistic, MHD, and allows radiation to be included self-consistently not just in a post-processing sense. We benefit greatly from the additional presence of Prof Stone on this project, who has agreed to become involved at a hands-on level, so that technical details of setting up and running the code on the appropriate cluster can be done with maximum efficiency. The impact of this work promises to be enormous, bearing upon both fundamental disc theory and observation, the disc spectrum being an integral part of the calculation itself. The primary application will be to the light curves of TDEs. This includes such problems as the Lightman-Eardley Instability, a coupling between the disc turbulence and the radiative heating whose role in disc evolution is still not fully understood. This study has the numerical resolution and radiation physics capabilities to investigate this problem at a far higher level than previous studies. We shall also investigate the effect of magnetic field geometry, especially its role in setting the overall evolutionary behaviour of the disc, which is important for understanding when an MHD jet emerges from the inner regions and when it does not. A second major part of this thesis will be the investigation of the flow within what is normally considered the inner edge of the disc. Black hole discs extend down toward smaller and smaller radii until at some point, still well outside of the event horizon, the circular orbits become unstable. This transition radius is known as the innermost stable