Dynamical Instabilities in Discs

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It has been forty years since the seminal paper of Shakura & Sunyaev (1973) established the basis of turbulent accretion disc theory and twenty-two years since the establishment of the magnetorotational instability (MRI) as the fundamental cause for disc turbulence (Balbus & Hawley 1991). Yet, major features of disc behaviour remain poorly understood. Perhaps the most dramatic of these is the tendency for some discs to spontaneously change their emission profile. This may occur over a wide variety of time scales, depending on the mass and the nature of the disk's central body. A famous example is the case of so-called dwarf novae (DN). These are accreting white dwarf stars in which the system undergoes periodic eruptions on a time scale of weeks. The root cause is thought to be the complex behaviour of the radiative opacity at temperatures associated with the ionisation of atomic H, which then results in an unstable disc evolution from the action of a negative diffusion coefficient. The resolution of this instability is limit cycle behaviour that appears to be associated with the observed repeating outbursts. DN theory is several decades old now, and enjoys rather strong observational support. This in turn gives theoretical support to the notion that one can understand outburst phenomena in turbulent media. Moreover, by constantly dislodging the disk from its steady-state profile, DN also probe the very fundamentals of the alpha disc model itself, and thus DN have become the cornerstone of accretion disc theory. Much less understood are state changes in black hole candidates and other compact X-ray sources, that involve the appearance of distinct nonthermal hard X-ray components and possibly jets and outflows. Numerical MRI simulations show no such tendencies, but of course there is no reason to expect that they should at this stage: dwarf novae instabilities, for example, arise from thermal physics that is generally drastically simplified or ignored altogether in numerical simulations. X-ray sources are far from a regime where opacity should influence stability however, and there is at no present no generally accepted theory for the state changes. In this DPhil project, the student will undertake a systematic effort whose goal is to connect the physics of the MRI with the observed X-ray state changes. The work will be supervised by Prof. S. Balbus and a postdoctoral research fellow, Dr. W. Potter. Technical support will be available from leading numerical astrophysicists. The initial effort is envisaged to focus on the role of viscosity and ohmic resistance, the two dissipation processes associated with MHD turbulence. There is good numerical evidence that the behaviour of the large scale turbulence is sensitive to whether the viscosity or resistivity is larger (Fromang et al. 2007). There is, moreover, a distinguishing feature of discs surrounding compact objects: a transition radius at which the disk goes from resistivity dominated to viscous dominated as one moves inward (Balbus & Henri 2008). This radius is not present in white dwarf discs, which are globally resistivity-dominated. Preliminary work suggests that the existence of the transition radius heralds unstable behaviour, which may, in its nonlinear resolution, bear similarities to limit cycles (Potter & Balbus 2014). The goal is to determine under which conditions (if any) there are instabilities, and what the nonlinear resolution of any instabilities is. The hope and expectation is that the nonlinear behaviour will prove to be connected with the observed X-ray state changes. In this PhD project, I would like to develop a much deeper understanding of MHD disk turbulence regulated by the MRI. Depending upon the interests of the student, the approach we use could involve a mixture of both numerical and analytic techniques.