Numerical investigations of the inner regions of black hole accretion discs

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