Dynamo action in turbulent accretion discs around black holes – II. The mean magnetic field

The presence of strong differential rotation and vertical density gradients in thin accretion discs allows the generation of a large-scale, mean magnetic field by $\alpha\enspace \omega$ dynamo action. Analytic expressions for the preferred steady-state solutions are found, which when matched on to an exterior vacuum field show that the class of quadrupole modes ($B_\phi$ and Br even, and Bz odd functions of z) are most easily excited. The …