Exploring the Variability of Accretion Discs with Stochastic Models
Across a large range of scales, accreting sources show a remarkable similarity in their observed variability. The theory of propagating fluctuations, in which stochastic fluctuations in the viscosity create corresponding fluctuations in the accretion rate which then propagate through the disc, is often used to explain these characteristic features in the variability. While this theory has been extensively explored analytically, there has thus far been little numerical work investigating the non-linear behaviour. In this thesis, I develop new numerical models for simulating variable accretion discs, and explore what the resultant simulations reveal about the physical origin of the variability. Firstly, I perform the most detailed 1D simulations of stochastic accretion discs, taking the analytic theory of propagating firmly into the non-linear regime. I find that the eponymous propagating fluctuations are present across a wide range of model parameters and that the model naturally produces variability with many of the same features as that observed in nature. Notably, the timescale on which the stochastic fluctuations in the viscosity occur is found to be closely related to the break frequency in the luminosity power spectral density (PSD), providing a possible observational probe for the magnetorotational instability (MRI). I then present a new 2D (vertically integrated) stochastic model for simulating variable accretion discs, generalising the previous work in 1D. This model has the potential to bridge the gap between constant viscosity models and those with full 3D magnetohydrodynamics (MHD), allowing for discs with realistic variability to be simulated with much less computational expensive. To explore the theory of propagating fluctuations in 2D, I then use this new model to run a series of simulations with varying model parameters. While many of the results from 1D translate well to 2D, I find that the presence of radial epicycles in 2D has an important effect on the local disc dynamics and thus on the local accretion rate in the disc. Further, there are suggestions that the expected log-normality of the observed luminosity (and the associated linear root mean square (rms)-flux relation) break down for sufficiently thin discs. Finally, I explore the classical thermal instability for radiation pressure dominated accretion discs by running 2D (vertically integrated) simulations of viscous discs. With these, I am able to explore the long duration behaviour of these systems, revealing interesting limit-cycle behaviour. I also apply the new 2D stochastic model, investigating the effect of stochastic viscosity on the nature of these outbursts.
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