The nature of grand minima and maxima from fully nonlinear flux transport dynamos

We aim to investigate the nature and occurrence characteristics of grand solar minimum and maximum periods, which are observed in the solar proxy records such as Be-10 and C-14, using a fully nonlinear Babcock-Leighton type flux transport dynamo including momentum and entropy equations. The differential rotation and meridional circulation are generated from the effect of turbulent Reynolds stress and are subjected to back-reaction from the magnetic field. To generate grand minimum-and maximum-like periods in our simulations, we used random fluctuations in the angular momentum transport process, namely the Lambda-mechanism, and in the Babcock-Leighton mechanism. To characterize the nature and occurrences of the identified grand minima and maxima in our simulations, we used the waiting time distribution analyses, which reflect whether the underlying distribution arises from a random or a memory-bearing process. The results show that, in the majority of the cases, the distributions of grand minima and maxima reveal that the nature of these events originates from memoryless processes. We also found that in our simulations the meridional circulation speed tends to be smaller during grand maximum, while it is faster during grand minimum periods. The radial differential rotation tends to be larger during grand maxima, while it is smaller during grand minima. The latitudinal differential rotation, on the other hand, is found to be larger during grand minima.