Accretion disc viscosity: a simple model for a magnetic dynamo

We develop here a simple physical model for the manner in which a magnetic dynamo might operate in an accretion disc and so provide an effective (magnetic) viscosity. In contrast to other dynamo models, the mechanism we discuss does not depend on the existence of some hydrodynamical small-scale turbulent flow hypothesized to be already present in a non-magnetic disc. Rather, the model we present depends on three well-established physical processes: the Parker instability, the Balbus–Hawley instability and magnetic field reconnection. The model gives rise to finite but non-stationary magnetic field configurations. For the set of parameters chosen here we find a time-averaged effective viscosity with Shakura–Sunyaev α-parameter around $$\alpha_\text {SS} \approx 0.4$$.