A simple model of globally magnetized accretion discs

Abstract

We present an analytic, quasi-local model for accretion discs threaded by net, vertical magnetic flux. In a simple slab geometry and ignoring stochastic mean-field dynamo effects, we calculate the large-scale field resulting from the balance between kinematic field amplification and turbulent diffusion. The ability of the disc to accumulate magnetic flux is sensitive to a single parameter dependent on the ratio of the vertical diffusion time to the Alfv\'en crossing time, and we show how the saturation levels of magnetorotational and other instabilities can govern disc structure and evolution. Under wide-ranging conditions, inflow is governed by large-scale magnetic stresses rather than internal viscous stress. We present models of such "magnetically boosted" discs and show that they lack a radiation pressure-dominated zone. Our model can account for "magnetically elevated" discs as well as instances of midplane outflow and field reversals with height that have been seen in some global simulations. Using the time-dependent features of our model, we find that the incorporation of global transport effects into disc structure can lead to steady or episodic "magnetically arrested discs" (MADs) that maximize the concentration of magnetic flux in their central regions.