A stochastically forced time delay solar dynamo model: Self-consistent recovery from a maunder-like grand minimum necessitates a mean-field alpha effect

Fluctuations in the Sun's magnetic activity, including episodes of grand minima such as the Maunder minimum have important consequences for space and planetary environments. However, the underlying dynamics of such extreme fluctuations remain ill-understood. Here, we use a novel mathematical model based on stochastically forced, non-linear delay differential equations to study solar cycle fluctuations in which time delays capture the physics of magnetic flux transport between spatially segregated dynamo source regions in the solar interior. Using this model, we explicitly demonstrate that the Babcock-Leighton poloidal field source based on dispersal of tilted bipolar sunspot flux, alone, cannot recover the sunspot cycle from a grand minimum. We find that an additional poloidal field source effective on weak fields—e.g., the mean-field α effect driven by helical turbulence—is necessary for self-consistent recovery of the sunspot cycle from grand minima episodes.