Magnetic Flux Transport Simulations of Solar Surface Magnetic Distributions During a Grand Minimum

It is well known that magnetic activity on the Sun modulates from one cycle to the next. The most striking occurrence of this is called a grand minimum where magnetic activity all but disappears. The latest grand minimum occurred between the years 1645 and 1715 and is called the Maunder minimum. In this paper magnetic flux transport simulations are used to consider what type of surface magnetic field configurations may be produced both during and after a grand minimum depending on how the grand minimum occurs. It is shown that the surface configurations during and after a grand minimum strongly depend on the phase of the cycle in which the grand minimum starts and whether it lasts for an odd or even number of cycles. If the grand minimum starts around cycle minimum then a significant amount of large-scale magnetic flux may persist on the Sun at high latitudes during the grand minimum. In contrast, if it starts at cycle maximum during the grand minimum it is possible for there to be essentially zero large-scale magnetic flux over the entire surface of the Sun. It is shown that for a single grand minimum event the reversal of the polar fields at the presently observed time in the solar cycle is only reproduced if the event starts at cycle minimum and extends over an even number of cycles. In contrast, if the grand minimum runs for an odd number of cycles it is possible for there to be no reversal of the polar fields or for the reversals to occur at times inconsistent with our present understanding of the solar cycle. Consequences of the assumptions made in the modelling are discussed and the significance of the simulations for direct modelling of events such as the Maunder minimum are considered.