Stars are likely to form with non-zero initial angular momentum, and will consequently possess a substantial gaseous protostellar disc in the early phases of their evolution. At this early stage, the disc mass is expected to be comparable to the mass of the protostar. The disc’s self-gravity therefore plays an important role in the subsequent evolution of the system, regulating the accretion of matter onto the protostar, as well as being potentially capable of forming low mass stars and massive planets by disc fragmentation. The protostellar disc may later evolve into a protoplanetary disc, providing the feedstock for planet formation. Therefore, if the current stellar populations and exoplanetary systems are to be understood, an understanding of the evolution of protostellar discs is crucial, especially their earliest self-gravitating phases. I have used various methods of numerical simulation to probe the physics of self-gravitating protostellar discs and their constituents. When constructing a model for self-gravitating protostellar discs, including detailed thermodynamics and radiative transfer is essential. I have developed two distinct numerical techniques for incorporating radiative transfer into Smoothed Particle Hydrodynamics (SPH) simulations. The first allows the modelling of frequency-averaged radiative transfer during the SPH simulation, in effect approximating radiative SPH (RSPH) with only a marginal increase in runtime (around 6%). The second takes the output from SPH simulations, and creates synthetic, wavelength-dependent telescope images and spectra of SPH systems. This allows the direct construction of observables from SPH simulations, providing, for the first time, a direct connection between the output of SPH simulations and observations. I have used these numerical methods to analyse, in detail, the local angular momentum transport induced by self-gravity in protostellar discs, testing the robustness of the “pseudo-viscous” analytical approximation for local disc stresses. I confirm that semi-analytical disc modellers are justified in using the pseudo-viscous approximation in some cases, but I also outline the limits in which non-local transport effects causes the approximation to fail. Also, I have investigated the evolution of protostellar discs when perturbed by a secondary companion, in particular identifying whether such events will in general trigger a) a disc fragmentation event, or b) a stellar outburst event. For case a), I found no significant evidence that perturbation by a companion improves the possibility of disc fragmentation in compact discs - in case b), I found that stellar outburst events do indeed occur, but they are unlikely to be seen by observers due to their rare occurrence, as well as due to self-obscuration effects.

<p>We use numerical simulations to examine the fragmentation of protostellar discs via gravitational instability (GI), a proposed formation mechanism for gas-giant planets and brown dwarfs. To accurately model heating and cooling, we have implemented radiative transfer (RT) in the TreeSPH code Gasoline, using the flux-limited diffusion approximation coupled to photosphere boundary cooling. We present 3D radiation hydrodynamics simulations of discs that are gravitationally unstable in the inner 40 AU; these discs do not fragment because the cooling times are too long. In prior work, one of these discs was found to fragment; however, we demonstrate that this resulted from an over-estimate of the photosphere cooling rate. Fragmentation via GI does not appear to be a viable formation mechanism in the inner 40 AU.</p> <p>We also present simulations of GI in the outer regions of discs, near 100 AU, where we find GI to be a viable formation mechanism. We give a detailed framework that explains the link between cooling and fragmentation: spiral arms grow on a scale determined by the linear gravitational instability, have a characteristic width determined by the balance of heating and cooling, and fragment if this width is less than twice their Hill radius. This framework is consistent with the fragmentation and initial fragment masses observed in our simulations. We apply the framework to discs modelled with the commonly-used beta-prescription cooling and calculate the critical cooling rate for the first time, with results that are consistent with previous estimates measured from numerical experiments.</p> <p>RT is fundamentally important in the star formation process. Non-ionizing radiation heats the gas and prevents small-scale fragmentation. Ionizing radiation from massive stars is an important feedback mechanism and may disrupt giant molecular clouds. We present methods and tests for our implementation of ionizing radiation, using the Optically-Thin Variable Eddington Tensor method.</p> / Doctor of Philosophy (PhD)

In this thesis, I study numerical and semi-analytical models of self-gravitating protostellar discs, with the aim of furthering our understanding of the role of disc-self gravity in planet formation. At the time of writing, the ALMA era of observational astronomy is upon us. Therefore, I place my research into this context with synthetic images of both numerical and semi-analytical models. I begin with an examination into the apparent lack of convergence, with increasing resolution, of the fragmentation boundary in Smoothed Particle Hydrodynamics (SPH) simulations of a protostellar disc. I run a suite of SPH with different numerical implementations, and find that even very similar implementations can fundamentally change the final answer. I analyse a suite of SPH simulations that fragment to form gravitationally bound objects, with the motivation of informing future population synthesis model development. I find that fragment-fragment and fragment-disc interaction dominates the orbital evolution of the system even at very early times, and any attempt to produce a population of objects from the gravitational instability process must include these interactions. Before a disc fragments, it will go through a self-gravitating phase. If the disc cools globally on a timescale such that it is balanced by heating due to gravitational stresses, the disc will be in a state of quasi-equilibrium. So long as the disc mass is sufficiently low, and spirals are sufficiently tightly wound, then angular momentum transport can be described by the local approximation, for which there is an analytical description. Using this analytical description, I develop an existing 1D model into 3D, and examine a wide range of parameter space for which disc self-gravity produces significant non-axisymmetry. Using radiative transfer calculations coupled with synthetic observations, I determine that there is a very narrow range of parameter space in which a disc will have sufficiently large gravitational stresses so as to produce detectable spirals, but the stresses not be so large as to cause the disc to fragment. By developing a simple analytical prescription for dust, I show that this region of parameter space can be broadened considerably. However, it requires grains that are large enough to become trapped by pressure maxima in the disc, so I conclude that if self-gravitating spiral arms are detected in the continuum, it is likely that at least some grain growth has taken place.