Delayed Babcock-Leighton dynamos in the diffusion-dominated regime

Context. Solar dynamo models of Babcock-Leighton type typically assume the rise of magnetic flux tubes to be instantaneous. The periods of solutions with high magnetic diffusivity are too short, and their active belts do not migrate correctly. Only the low-diffusivity regime with advective meridional flows is usually considered.
Aims: We here discuss these assumptions and apply a time delay in the source term of the azimuthally averaged induction equation. This delay is set to be the rise time of magnetic flux tubes, which are assumed to form at the tachocline. We study the effect of the delay, which adds a nonlinear temporal to the spacial nonlocality in the advective but particularly in the diffusive regime.
Methods: We have previously obtained the rise time as a function of rotation and the magnetic field strength at the bottom of the convection zone. These results allowed us to constrain the delay in the mean-field model we used in a parameter study.
Results: We identify an unknown family of solutions. These solutions show self-quenching and exhibit longer periods than their nondelayed counterparts. Additionally, we demonstrate that the nonlinear delay is responsible for the recovery of the equatorward migration of the active belts at high turbulent diffusivities.
Conclusions: By introducing a nonlinear temporal nonlocality (the delay) in a Babcock-Leighton dynamo model, we were able to obtain solutions that are quantitatively comparable to the solar butterfly diagram in the diffusion-dominated regime.