Illuminating tidal disruption events with a time-dependent theory of relativistic accretion discs

At the centre of every large galaxy in the Universe lurks a supermassive black hole, weighing in at a mass ranging from millions to tens of billions that of the Sun. The study of these monsters is by necessity an indirect science, as a black hole itself emits no detectable radiation: if one wants to learn about the properties of black holes, one must understand in great detail their effect on their surroundings. Historically, the primary approach to inferring the existence of black holes and determining their properties has been through the detection and study of bright X-ray emitting accretion discs, in our Galaxy and at cosmological distances. The name accretion disc'' is given to the structures formed by gas as it spirals slowly into a black hole, never to return. Accretion discs are turbulent, and phenomenally bright, systems which can outshine entire galaxies. In this thesis I present my contributions to the field of accretion disc physics, in particular to the study of time-dependent and relativistic accretion discs.
One particularly interesting type of astrophysical black hole--accretion disc system, and the focus of much of this thesis, are called tidal disruption events. The stellar densities of galactic centres are high, and the orbits of individual stars are continuously perturbed by the combined gravitational interactions of the galaxy's stellar population. Very unfortunate stars can, on a rare occasion, be perturbed onto a near-radial orbit about the galaxy's central black hole. Should this orbit take the star within a critical separation called the tidal radius, the star's gravitational attraction to the black hole will become larger than its own self-gravity. Upon entering this region the star is destroyed, in its entirety, by the black hole's tidal gravitational force, scattering stellar debris onto a series of different orbits. Some fraction of this stellar debris subsequently rains back onto the supermassive black hole, and fuels an accretion disc which is observed as a bright flare from an otherwise quiescent galactic centre. These flares, which typically outshine their entire host galaxy, last for timescales of months-to-years and have been observed at frequencies across the entire electromagnetic spectrum. The current population of known tidal disruption events stands at roughly 40 sources, and their study is taking on a growing importance in the field of transient astronomy.
Tidal disruption events are intrinsically relativistic and time dependent accretion disc systems, and must therefore be described by a relativistic and time dependent theory. However, despite the great success of steady-state relativistic disc models, and the myriad practical uses found for Newtonian time-dependent disc theory, the theory of relativistic, time-dependent, accretion discs is a hugely under-explored field. In Chapter 2 of this thesis I derive and then present the first analytical and numerical solutions of the evolution equations describing relativistic thin discs. I show that these solutions represent much more than simple refinements of the Newtonian theory, and display a mathematically rich and physically interesting set of behaviours. The global properties of time-dependent relativistic discs are shown to be sensitive to the physical properties of the disc's very innermost regions, and in particular to the behaviour of the disc stress at the innermost stable circular orbit. The question of whether the dynamical disc stress vanishes at the innermost stable circular orbit of a black hole disc has a controversial history as old as the field of black hole accretion itself. In this thesis I develop and explore a number of observational probes that may have already offered insight into the answer to this long controversial question.
The solutions of the relativistic disc equations developed in Chapter 2 are put to the test in Chapter 3, where I develop models which describe the evolving luminosities observed from two tidal disruption events named ASASSN-14li and ASASSN-15lh. So named after the All Sky Automated Survey for SuperNovae which discovered them, ASASSN-14li and ASASSN-15lh show rather distinct observed properties, here chosen to span the broad range of observed tidal disruption event phenomenology. Despite their very different properties, the luminosity from both sources are extremely well described as resulting from evolving relativistic discs. In addition to providing an excellent description of the observations, the disc models measure and constrain the physical parameters of the tidal disruption event system. As a result of this analysis, observations of the luminosity emergent from tidal disruption events can be used as probes of the properties of the black holes at their hearts.
The numerical models of Chapter 3 are complimented by an asymptotic analysis of the emitted luminosity of relativistic thin discs. I demonstrate a profound dependence of the properties of tidal disruption event light curves on observing band. This dependence can be understood entirely analytically, and in particular the X-ray luminosity emergent from supermassive black hole discs is extremely simple to describe. I show that a simple power-law decay of the bolometric disc luminosity, when appropriately filtered by bandpass, is observed to be near-time-independent in the ultra-violet, while simultaneously exponentially decaying at X-ray energies. These particular properties are observed in numerous tidal disruption event light curves.
In Chapter 4 this analysis of the X-ray luminosity of relativistic thin discs is extended so as to model tidal disruption events from across the entire parameter space likely to be spanned by these remarkable objects. This includes the development of the first self-consistent models for the time evolution of hard state'' nonthermal X-ray emission from black hole accretion discs. By extending classical disc scaling relationships into the time-dependent regime, I highlight that time dependent accretion discs have a temperature profile which is far more sensitively dependent on their black hole and disc parameters than their steady state counterparts. This sensitive dependence of the temperature on system parameters, in particular the black hole mass, coupled with the exponential dependence of the X-ray luminosity on disc temperature results in diverse, quantitative predictions for the properties of a population of tidal disruption event sources. I compare these predictions to the current observed population of tidal disruption events, and demonstrate that, while we are in the early days of population studies, the initial evidence suggests that these predictions are in excellent accord with the data.
In addition to seeking to answer a number of questions of interest to the study of accretion disc physics and tidal disruption events, this thesis will, I hope, highlight a number of interesting avenues for further research. In Chapter 5 I highlight two areas in which I believe the analysis in this thesis can be refined, or extended, and some initial progress in those directions. The first of these is the future inclusion of the emission resulting from material within the innermost stable circular orbit of a black hole disc. Before the properties of the emission from this region can be understood, the underlying dynamical equations of motion describing the intra-ISCO inspiral must first be solved. I present a universal form of the discs inflow velocity in Chapter 5, in addition to explicit solutions of the full inspiralling trajectory of test particles. The solutions for maximally rotating Kerr black holes are, in particular, remarkably simple. Finally, I highlight how the late-time ultra-violet luminosity emergent from tidal disruption events represents potentially the most powerful probe of the properties of their black holes. In fact, strong constraints on a tidal disruption event's black hole mass can be placed with just a single measurement of its late-time luminosity. This opens up the possibility of utilising the full power of tidal disruption events as a probe of galactic dynamics. I conclude by presenting updated galactic scaling relationships which have been extended with the addition of 41 tidal disruption event black hole masses.

Advisor: Balbus, S