Viscosity-alpha and dynamo-alpha for magnetically driven compressible turbulence in Kepler disks

For a given isotropic and homogeneous field of magnetic fluctuations both the viscosity-α as well as the dynamo-α have been computed for accretion disks on the basis of a quasilinear approximation with shear flow and density fluctuations (i.e. magnetic buoyancy) included. The resulting viscosity-α proves to be positive for sufficiently strong shear (i.e. the angular momentum transport is outwards) while the sign of the dynamo-α depends on the hemisphere. Again, for sufficiently strong shear it changes its sign, it is now negative for the upper disk plane and positive for the lower one. The current helicity 〈j′ · B′〉 also changes its sign with increasing shear. For a Kepler flow in the upper (lower) disk plane, the sign is positive (negative). In our turbulence model the current helicity of the fluctuations and the α-effect of dynamo theory are almost always out of phase; the signs of all the quantities are in perfect correspondence to the numerical simulations of Brandenburg (1998, 2000). The kinetic helicity has the same sign as the α-effect – not, as often assumed, the opposite one. The resulting ratio between the dynamo-α and the viscosityα reveals the dynamo-α amplitude as rather small compared with the turbulence intensity. This is in contrast to earlier results on the basis of a quantitative approximation but again is in agreement with recent results of numerical simulations.