The role of diffusivity quenching in flux-transport dynamo models

In the nonlinear phase of a dynamo process, the back-reaction of the magnetic field upon the turbulent motion results in a decrease of the turbulence level and therefore in a suppression of both the magnetic field amplification (the α-quenching effect) and the turbulent magnetic diffusivity (the η-quenching effect). While the former has been widely explored, the effects of η-quenching in the magnetic field evolution have rarely been considered. In this work, we investigate the role of the suppression of diffusivity in a flux-transport solar dynamo model that also includes a nonlinear α-quenching term. Our results indicate that, although for α-quenching the dependence of the magnetic field amplification with the quenching factor is nearly linear, the magnetic field response to η-quenching is nonlinear and spatially nonuniform. We have found that the magnetic field can be locally amplified in this case, forming long-lived structures whose maximum amplitude can be up to 2.5 times larger at the tachocline and up to 2 times larger at the center of the convection zone than in models without quenching. However, this amplification leads to unobservable effects and to a worse distribution of the magnetic field in the butterfly diagram. Since the dynamo cycle period increases when the efficiency of the quenching increases, we have also explored whether the η-quenching can cause a diffusion-dominated model to drift into an advection-dominated regime. We have found that models undergoing a large suppression in η produce a strong segregation of magnetic fields that may lead to unsteady dynamo-oscillations. On the other hand, an initially diffusion-dominated model undergoing a small suppression in η remains in the diffusion-dominated regime.