A new stochastic model for simulating accretion disks in 2D: propagating fluctuations and epicyclic motion

Accretion occurs across a large range of scales and physical regimes. Despite this diversity in the physics, the observed properties show remarkably similarity. The theory of propagating fluctuations, in which random fluctuations within an accretion disk travel inwards and combine, has long been used to explain these phenomena. Recent numerical work has expanded on the extensive analytical literature but has been restricted to using the standard 1D diffusion equation for modelling the disk behaviour. I will present a novel numerical approach for 2D (vertically integrated), stochastically driven α-disk simulations, generalising existing 1D models. This is achieved through defining the α-parameter as a function of a stochastic random variable β. This new variable β is advected as a tracer field and stochastically evolved in time according to the Ornstein-Uhlenbeck process, in a manner motivated by the behaviour of the magnetorotational instability (MRI) dynamo.

Through a suite of long-duration simulations, we find that there are two key differences between the existing theory of propagating fluctuations and our new 2D simulations. Firstly, we find that the presence of epicyclic motion in 2D (which cannot be captured within the 1D diffusion equation) has an important impact on local disk dynamics. Secondly, while the theory of propagating fluctuations predicts log-normal light-curves, we find that this occurs only if the disk is sufficiently thick, with thinner disks producing normally distributed light-curves. We also find that these thinner disks are significantly less variable than thicker ones, providing a compelling explanation for the greater variability seen in the hard state vs the soft state of X-ray binaries. Additionally, our simulations show that the break frequency in the luminosity power spectrum is strongly dependent on the driving timescale of the stochastic evolution of β within the disk, providing a possible observational signature for probing the MRI dynamo. Finally, I will briefly consider the wide-ranging applications of our numerical model for use in other areas as an improvement over constant α-models.