Magnetic Quenching of Turbulent Diffusivity: Reconciling Mixing-length Theory Estimates with Kinematic Dynamo Models of the Solar Cycle

The turbulent magnetic diffusivity in the solar convection zone is one of the most poorly constrained ingredients of mean-field dynamo models. This lack of constraint has previously led to controversy regarding the most appropriate set of parameters, as different assumptions on the value of turbulent diffusivity lead to radically different solar cycle predictions. Typically, the dynamo community uses double step diffusivity profiles characterized by low values of diffusivity in the bulk of the convection zone. However, these low diffusivity values are not consistent with theoretical estimates based on mixing-length theory -- which suggest much higher values for turbulent diffusivity. To make matters worse, kinematic dynamo simulations cannot yield sustainable magnetic cycles using these theoretical estimates. In this work we show that magnetic cycles become viable if we combine the theoretically estimated diffusivity profile with magnetic quenching of the diffusivity. Furthermore, we find that the main features of this solution can be reproduced by a dynamo simulation using a prescribed (kinematic) diffusivity profile that is based on the spatiotemporal geometric-average of the dynamically quenched diffusivity. Here, we provide an analytic fit to the dynamically quenched diffusivity profile, which can be used in kinematic dynamo simulations. Having successfully reconciled the mixing-length theory estimated diffusivity profile with kinematic dynamo models, we argue that they remain a viable tool for understanding the solar magnetic cycle.