Non-linear Galactic Dynamos and the Magnetic R\"{a}dler Effect

We show that the magnetic analogue of the R\"{a}dler effect of mean-field dynamo theory leads to a non-linear backreaction that quenches a large-scale galactic dynamo, and can result in saturation of the large-scale magnetic field at near-equipartition with turbulent kinetic energy density. In a rotating fluid containing small-scale magnetic fluctuations, anisotropic terms in the mean electromotive force are induced via the Coriolis effect and these terms lead to a reduction of the growth rate in a predominantly $\alpha\Omega$-type galactic dynamo (Chamandy & Singh 2017). By including the generation of small-scale magnetic fluctuations by turbulent tangling of the large-scale magnetic field, one obtains a negative feedback effect that quenches the dynamo and leads to the saturation of the large-scale field. This saturation mechanism is found to be competitive with the dynamical $\alpha$-quenching mechanism for realistic galactic parameter values. Furthermore, in the context of the dynamical $\alpha$-quenching model, a separate non-linear term is obtained which has the same form as the helicity flux term of Vishniac & Cho (2001), but which depends on the strength of small-scale magnetic fluctuations. We briefly discuss the observational implications of the magnetic R\"{a}dler effect for galaxies.