2.4 Flows in the photosphere

In the currently widely popular flux transport dynamo models the strong polar fields prevalent around sunspot minimum are formed by the advection of following polarity flux from active regions by the poleward meridional flow. Changes in this flow may thus influence the would-be polar fields and thereby may serve as precursors of the upcoming cycle.

Such changes, on the other hand, are also associated with the normal course of the solar activity cycle, the overall flow at mid-latitudes being slower before and during maxima and faster during the decay phase. Therefore, it is just the cycle-to-cycle variation in this normal pattern that may be associated with the activity variations between cycles. In this respect it is of interest to note that the poleward flow in the late phases of cycle 23 seems to have had an excess speed relative to the previous cycle (Hathaway and Rightmire, 2010). If this were a latitude-independent amplitude modulation of the flow, then most flux transport dynamo models would predict a stronger than average polar field at the minimum, contrary to observations. On the other hand, in the surface flux transport model of Wang et al. (2009) an increased poleward flow actually results in weaker polar fields, as it lets less leading polarity flux to diffuse across the equator and cancel there. As the recent analysis by Muñoz-Jaramillo et al. (2010) has shown, the discrepancy resulted from the neglect of leading polarity flux in the Babcock–Leighton source term in flux transport dynamo models, and it can be remedied by substituting a pair of opposite polarity flux rings as source term instead of the α-term. With this correction, 2D flux transport and surface flux transport models agree in predicting a weaker polar field for faster meridional flow.

It is known from helioseismology that meridional flow speed fluctuations follow a characteristic latitudinal pattern associated with torsional oscillations and the butterfly diagram, consisting of a pair of axisymmetric bands of latitudinal flows converging towards the activity belts, migrating towards the equator, and accompanied by similar high-latitude poleward branches. This suggests interpreting the unusual meridional flow speeds observed during cycle 23 as an increased amplitude of this migrating modulation, rather than a change in the large-scale flow speed (Cameron and Schüssler, 2010). In this case, the flows converging on the activity belts tend to inhibit the transport of following polarities to the poles, again resulting in a lower than usual polar field, as observed (Jiang et al., 2010bJump To The Next Citation Point; note, however, that Švanda et al., 2007Jump To The Next Citation Point find no change in the flux transport in areas with increased flows). It is interesting to note that the torsional oscillation pattern, and thus presumably the associated meridional flow modulation pattern, was shown to be fairly well reproduced by a microquenching mechanism due to magnetic flux emerging in the active belts (Petrovay and Forgács-Dajka, 2002). Observational support for this notion has been provided by the seismic detection of locally increased flow modulation near active regions (Švanda et al., 2007). This suggests that stronger cycles may be associated with a stronger modulation pattern, introducing a nonlinearity into the flux transport dynamo model, as suggested by Jiang et al. (2010b).

In addition to a variation in the amplitude of migrating flow modulations, their migration speed may also influence the cycle. Howe et al. (2009) point out that in the current minimum the equatorward drift of the torsional oscillation shear belt corresponding to the active latitude of the cycle has been slower than in the previous minimum. They suggest that this slowing may explain the belated start of cycle 24.

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