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Session 85 - Cataclysmic Variables and Accretion Disks.
Oral session, Wednesday, January 15
We examine the growth of the Velikhov-Chandrasekhar instability for an azimuthal field in a thin accretion disk. We assume periodic vertical boundary conditions and look for modes that vanish far from the corotation radius, thereby eliminating any dependence on artificial boundaries. In an inviscid and perfectly conducting fluid there are no solutions which are properly localized. If we modify the force equations to include radial diffusion, then we obtain a sixth order equation in the radial velocity, with solutions that contain a local instability. We obtain a similar result using magnetic resistivity instead. Finally we using both a diffusion coefficient and magnetic resistivity and gives a tenth order differential equation in u_r with reasonable asymptotic limits. The well behaved solutions include modes with arbitrarily large growth rates, but these modes have a negligible effect on transport. \vskip .1in We explore parameter space and look at the growth rate of instabilities contained within the disk. We found that the critical quantity in the final result is the ratio of the diffusion coefficient to the resistivity. We try various values of this quantity to determine which range of this ratio gives the largest transport effects. This involves actually integrating the modified force equations, changing Døver \eta then looking at the growth rates as a function of frequency. We conclude that the instability is formally nonlinear in the absence of resistivity or viscosity, but one can produce linear instabilities when includes diffusion, resistivity or both diffusion and resistivity into the force equations.
Program listing for Wednesday