Nandy et al. in Nature, “The cause of the unusual minimum of sunspot cycle 23”

“The number of sunspots observed on the Sun’s surface varies periodically, going through successive maxima and minima. Following sunspot cycle 23, the Sun went into a prolonged minimum characterized by a very weak polar magnetic field and an unusually large number of days without sunspots. Sunspots are strongly magnetized regions generated by a dynamo mechanism that recreates the solar polar field mediated through plasma flows.” Nandy et al. “report results from kinematic dynamo simulations which demonstrate that a fast meridional flow in the first half of a cycle, followed by a slower flow in the second half, reproduces both characteristics of the minimum of sunspot cycle 23; they conclude that very deep minima are associated with weak polar fields.” Dibyendu Nandy, Andrés Muñoz-Jaramillo, Petrus C. H. Martens, “The unusual minimum of sunspot cycle 23 caused by meridional plasma flow variations,” Nature 471: 80–82, 03 March 2011.

“Starting with the pioneering telescopic observations of Galileo Galilei and Christopher Scheiner in the early seventeenth century, sunspots have been observed more or less continuously up to the present. Except for the period AD 1645–1715, known as the Maunder minimum, when hardly any sunspots were observed, the sunspot time series shows a cyclic variation going through successive epochs of maximum and minimum activity. A recently developed axisymmetric, kinematic solar dynamo model is used to solve the evolution equations for the toroidal and poloidal components of the solar magnetic field (see the figure). The effect of changing meridional flows on the nature of solar minima is studied by means of introducing fluctuations in the meridional flow. The simulations extend over 210 sunspot cycles corresponding to 1,860 solar years.”

“In the figure, v_n denotes flow speed during the minimum of sunspot cycle n, v_n−1 denotes the speed during the early, rising, part of cycle n, and v_n−v_n−1 denotes the change in flow speed between the declining and rising parts of the cycle. Cycle overlap is measured in days. Positive overlap denotes the number of days on which simulated sunspots from successive cycles erupted together, whereas negative overlap denotes the number of spotless days during a solar minimum. A good correlation between polar field strength versus v_n−v_n−1 has been found, with r = 0.87, P = 99.99%. Evidently, a change from fast to slow internal meridional flow results in deep solar minima. The model results are robust with respect to reasonable changes in the driving parameters.

“The physics of meridional-flow-mediated magnetic flux transport shows that a faster flow (v_n−1) before and during the first half of cycle n would sweep the poloidal field of the previous cycle quickly through the region of differential rotation responsible for toroidal field induction; this would allow less time for toroidal field amplification and would hence result in a sunspot cycle (n) which is not too strong. The fast flow, followed by a slower flow during the second half of cycle n and persisting to the early part of the next cycle, would also distance the two successive cycles, contributing to a higher number of spotless days during the intervening minimum. Moreover, a strong flow during the early half of cycle n would sweep both the positive and the negative polarity sunspots of cycle n (erupting at mid to high latitudes) to the polar regions; therefore, lower net flux would be available for cancelling the polar field of the old cycle and building the field of the new cycle, resulting in a relatively weak polar field strength at the minimum of cycle n. Nandy et al. believe that a combination of these effects contributes to the occurrence of deep minima such as that of solar cycle 23.”

“NASA’s recently launched Solar Dynamics Observatory will provide more precise constraints on the structure of the plasma flows deep in the solar interior, which could be useful for complementing and confirming the new simulations.”