Global theory of Balbus-Hawley instability

To understand the origin of turbulence in an accretion disk is an extraordinary challenge to theory. According to the Rayleigh criterion hydrodynamic turbulence does not arise in Keplerian disks. Although magnetic fields are known to suppress the turbulence, numerical supercomputer experiments more and more reveal a magnetic origin of the turbulent instability. With the well-known formulations of dynamo theory we have computed the relevant amplitude of the magnetic fields in order to produce the turbulence. Only the interplay of non rigid rotation and (weak) magnetic field causes the desired instability.

A sphere embedded in vacuum and threaded by a uniform external field yields the following stability diagram:



The diagramm shows neutral stability lines for different azimuthal wave numbers m. C_Om and Hartmann number Ha are normalized rotation rate and external magnetic field amplitude. Nonaxisymmetric modes are dominating for not too slow rotation and sufficiently strong magnetic field.

For a thin disk threaded by a uniform external magnetic field the neutral stability contours are:



Again for high Hartmann numbers the nonaxisymmetric modes are most easily excited.

AGN and quasars swallow up enormous amounts of gas and dust which is possible only due to the loss of angular momentum via turbulence. An accretion disk in the heart of a galaxy radiates with ultimate luminosity and is hot enough to blow up itself into a torus-like structure. Then a magnetic stability analysis is much more complicated than for the geometrically thin disks around stars.

	Turbulence			Group			Papers			AIP