On the role of resonant absorption in the electromotive force of dynamic disc dynamos

In zero-net flux accretion discs, magnetic fields are believed to arise through dynamo activity. In the common prototype for such processes, a toroidal field is induced from a weak poloidal field by differential rotation, while the poloidal field is regenerated from the toroidal field by the electromotive force (EMF). A major theoretical challenge is to describe the latter feedback provided by the EMF, which traditionally has been treated using kinematic mean-field theory. While such an approach might be successful at low magnetic Reynolds numbers and weak magnetic fields, a dynamic dynamo model where the velocity and the magnetic field destabilise through a magnetohydrodynamic instability might be more appropriate in parameter regimes of relevance to astrophysical discs.

In this seminar, an EMF that stems from three-dimensional waves on a neutrally stable background will be considered. This is believed to characterise non-linear lower branch disc dynamo states driven by the magnetorotational instability (MRI). Assuming that the background magnetic field is spatially varying, the system features a continuous Alfvén spectrum. Consequently, if the Doppler-shifted frequency of a neutral perturbation falls within this Alfvén continuum, the wave will be absorbed in narrow Alfvén resonant layers where its amplitude diverges. The details of this resonant absorption will be outlined during the talk, and to illustrate the feedback on the background state by such singular modes, an analytic expression for the EMF in the vicinity of Alfvén resonance will be presented. This expression is then applied to a one-dimensional global model of an accretion disc, which offers insight into the conditions under which a persistent EMF may be expected. Finally, the analysis is extended to a two-dimensional local disc model for which the resonant layers correspond to curves around which the wave dynamics is organised.

REFERENCE
Brynjell-Rahkola, M., & Ogilvie, G. I. (2025). Geophys. Astrophys. Fluid Dyn., 1–21.