Physics
Scientific paper
Oct 1998
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1998phdt........27c&link_type=abstract
Thesis (PHD). THE UNIVERSITY OF TEXAS AT AUSTIN , Source DAI-B 59/09, p. 4871, Mar 1999, 106 pages.
Physics
Magnetic Shearing
Scientific paper
We examine possible mechanisms for the transport of angular momentum across an azimuthal magnetic field in a thin accretion disk. We assume that these processes are a result of the magnetorotational instability, or MRI. In the first model, we assume periodic vertical boundary conditions and look for solutions for the radial velocity that vanish far from the corotation radius in all directions, thereby eliminating any dependence on artificial boundary conditions. In an inviscid and perfectly conducting fluid there are no solutions which are properly localized within a small region on r. We show that including radial diffusion and/or electrical resistivity into the force equations does not change this result. When these effects are added, however, we see that there exists a family of localized transient solutions, indicating the existence of a robust non-linear instability. These solutions are associated with local zeros in the radial group velocity, which represent a localized region of the disk which is stationary in r relative to the corotation point and is unrelated to global singularities in the complex plane. We discuss the properties of these 'quasi-modes'. In the second model, we extend the work to include vertical structure, with separate pressure and magnetic field scale heights. We then restrict the consideration to modes with no z-dependence, in order to examine the interaction between the Parker instability and local turbulence. We obtained a second order equation in r with an asymptotic expansion for large distances from the corotation point which could not be solved analytically. We analyzed the zeros in the radial group velocity and singularities of the equation to see if these had any physical significance. We found, similar to the study of the first model where we were looking at the effects of diffusion and resistivity, that some of the roots of the dispersion relation were complex and therefore may be associated with physical local instabilities.
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