Studies of grand minima in sunspot cycles by using a flux transport solar dynamo model

We propose that grand minima in solar activity are caused by simultane- ous fluctuations in the meridional circulation and the Babcock-Leighton mechanism for the poloidal field generation in the flux transport dynamo model. We present the following results： （a） fluctuations in the meridional circulation are more effective in producing grand minima; （b） both sudden and gradual initiations of grand minima are possible; （c） distributions of durations and waiting times between grand minima seem to be exponential; （d） the coherence time of the meridional circulation has an effect on the number and the average duration of grand minima, with a coherence time of about 30 yr being consistent with observational data. We also study the occurrence of grand maxima and find that the distributions of durations and waiting times between grand maxima are also exponential, like the grand minima. Finally we address the question of whether the Babcock-Leighton mechanism can be operative during grand minima when there are no sunspots. We show that an a-effect restricted to the upper portions of the convection zone can pull the dynamo out of the grand minima and can match various observational requirements if the amplitude of this a-effect is suitably fine-tuned.

A possible explanation of the Maunder minimum from a flux transport dynamo model

We propose that the poloidal field at the end of the last sunspot cycle before the Maunder minimum fell to a very low value due to fluctuations in the Babcock-Leighton process. With this assumption, a flux transport dynamo model is able to explain various aspects of the historical records of the Maunder minimum remarkably well by suitably choosing the parameters of the model to give the correct growth time.

Subcritical dynamo and hysteresis in a Babcock-Leighton type kinematic dynamo model

In the Sun and Sun-like stars,it is believed that cycles of the large-scale magnetic field are produced due to the existence of differential rotation and helicity in the plasma flows in their convection zones(CZs).Hence,it is expected that for each star,there is a critical dynamo number for the operation of a large-scale dynamo.As a star slows down,it is expected that the large-scale dynamo ceases to operate above a critical rotation period.In our study,we explore the possibility of the operation of the dynamo in the subcritical region using the Babcock–Leighton type kinematic dynamo model.In some parameter regimes,we find that the dynamo shows hysteresis behavior,i.e.,two dynamo solutions are possible depending on the initial parameters—decaying solution if starting with weak field and strong oscillatory solution(subcritical dynamo)when starting with a strong field.However,under large fluctuations in the dynamo parameter,the subcritical dynamo mode is unstable in some parameter regimes.Therefore,our study supports the possible existence of subcritical dynamo in some stars which was previously demonstrated in a mean-field dynamo model with distributedαand MHD turbulent dynamo simulations.