Polar Flux, Cross‐equatorial Flux, and Dynamo‐generated Tachocline Toroidal Flux as Predictors of Solar Cycles

Abstract

We evaluate the skill of three solar cycle predictors, namely, polar magnetic flux, flux crossing the equator, and tachocline toroidal flux, using both observations and a calibrated dynamo model. Polar flux measurements are available only for the past three sunspot cycles, implying poor statistics. However, the correlation between observed north and south polar flux peaks, and peaks of the next sunspot cycle is r = 0.785. We find that the correlation between the observed cross-equatorial flux and the observed peak of the next solar cycle is also high, close to that of Cameron & Schussler, and the statistics are more reliable. Thus, the cross-equatorial flux is a better predictor of the next cycle than is the polar flux. From the dynamo model, the correlations with observed cycle peaks for polar flux, cross-equatorial flux, and toroidal flux are 0.48, 0.76, and 0.96, respectively. All these correlations decline when the northern and southern hemispheres are simulated separately, as well as with shortening of the averaging length in input data. A very high correlation between the model polar flux at the end of a cycle and the observed peak of that cycle implies that, within a calibrated flux transport dynamo, the polar flux follows the sunspot cycle, rather than being a precursor to it. With short-term averaging of input data, the polar and cross-equatorial fluxes retain much more short-term variability than does the toroidal flux. This is because the long traversal time of the input poloidal fields to the bottom of the convection zone in a mean-field model smooths out the short-term variability in the toroidal flux. The observed slowdown in meridional flow during 1996-2004 leads to a weaker polar flux, but a stronger cross-equatorial flux compared to the case with steady meridional flow. We infer that it is unlikely that both the cross-equatorial and the polar fluxes can be good predictors of solar cycle peaks.