1111.3138 (B. P. Pandey et al.)

Magnetorotational instability in magnetic diffusion dominated accretion discs    [PDF]

B. P. Pandey, Mark Wardle

We derive general stability criterion from local analysis of axisymmetric fluctuations in a diffusive disc threaded by both azimuthal and vertical magnetic field. We show that in the presence of ambipolar and Hall or, Ohm diffusion, such discs are always unstable to almost radial, axisymmetric fluctuations. The general stability criterion can be stated purely in terms of ambipolar and Hall diffusivities. We show that the disc is magnetorotationally unstable to axisymmetric fluctuations if the sum of scaled ambipolar and Hall diffusivities are larger than some numerical constant determined by the rotation profile of the disc. Thus, the stability of Hall-Ohm diffusion dominated disc require that the scaled Hall diffusion should exceed numerical constant whereas ambipolar-Ohm dominated disc requires a positive topological switch $g$ that carries the signature of disc field and wavevector. The topological factor $g$ plays dual role of not only assisting MRI in ambipolar-Ohm dominated disc but also making otherwise stable region in Hall-ambipolar diffusion plane unstable.

View original: http://arxiv.org/abs/1111.3138