Magnetorotational instability in magnetic diffusion dominated accretion discs

TL;DR

This paper derives a stability criterion for magnetorotational instability in partially ionized, diffusive accretion discs influenced by ambipolar and Hall diffusivities, revealing conditions under which the disc becomes unstable.

Contribution

It provides a new stability criterion based on ambipolar and Hall diffusivities, linking magnetic field geometry and wavevector obliqueness to MRI in diffusive discs.

Findings

Discs are always unstable to almost radial fluctuations.

Magnetic field geometry influences MRI stability.

The stability criterion depends on ambipolar and Hall diffusivities.

Abstract

We investigate the stability of partially ionised, differentially rotating, diffusive disc threaded by both azimuthal and vertical magnetic field. The general stability criterion of such a disc in the presence of axisymmetric fluctuations can be stated purely in terms of ambipolar and Hall diffusivities. It is shown that the disc is magnetorotationally unstable if the sum of scaled ambipolar and Hall diffusivities are larger than some numerical constant determined by the rotation profile of the disc. This criterion suggests that the diffusive discs are always unstable to almost radial fluctuations. The field geometry and obliqueness of wavevector (encapsulated together in 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.