2.2 Polar precursors

Direct measurements of the magnetic field in the polar areas of the Sun have been available from Wilcox Observatory since 1976 (Svalgaard et al., 1978Hoeksema, 1995). Even before a significant amount of data had been available for statistical analysis, solely on the basis of the Babcock–Leighton scenario of the origin of the solar cycle, Schatten et al. (1978) suggested that the polar field measurements may be used to predict the amplitude of the next solar cycle. Data collected in the four subsequent solar cycles have indeed confirmed this suggestion. As it was originally motivated by theoretical considerations, this polar field precursor method might also be a considered a model-based prediction technique. As, however, no particular detailed mathematical model is underlying the method, numerical predictions must still be based on empirical correlations – hence our categorization of this technique as a precursor method.

The shortness of the available direct measurement series represents a difficulty when it comes to finding empirical correlations to solar activity. This problem can to some extent be circumvented by the use of proxy data. For instance, Obridko and Shelting (2008) use H α synoptic maps to reconstruct the polar field strength at the source surface back to 1915. Spherical harmonic expansions of global photospheric magnetic measurements can also be used to deduce the field strength near the poles. The use of such proxy techniques permits a forecast with a sufficiently restricted error bar to be made, despite the shortness of the direct polar field data set.

The polar fields reach their maximal amplitude near minima of the sunspot cycle. In its most commonly used form, the polar field precursor method employs the value of the polar magnetic field strength (typically, the absolute value of the mean field strength poleward of 55° latitudes, averaged for the two hemispheres) at the time of sunspot minimum. It is indeed remarkable that despite the very limited available experience, forecasts using the polar field method have proven to be consistently in the right range for cycles 21, 22, and 23 (Schatten and Sofia, 1987Jump To The Next Citation PointSchatten et al., 1996Jump To The Next Citation Point).

View Image

Figure 7: Magnetic field strength in the Sun’s polar regions as a function of time. Blue solid: North; red dashed: (− 1)⋅South; thin black solid: average; heavy black solid: smoothed average. Strong annual modulations in the hemispheric data are due to the tilt of the solar equator to the Ecliptic. Data and figure courtesy of Wilcox Solar Observatory (see External Linkhttp://wso.stanford.edu/gifs/Polar.gif for updated version).

By virtue of the definition (2View Equation), the time of the minimum of R cannot be known earlier than 6 months after the minimum – indeed, to make sure that the perceived minimum was more than just a local dip in R, at least a year or so needs to elapse. This would suggest that the predictive value of polar field measurements is limited, the prediction becoming available 2 – 3 years before the upcoming maximum only.

To remedy this situation, Schatten and Pesnell (1993) introduced a new activity index, the “Solar Dynamo Amplitude” (SoDA) index, combining the polar field strength with a traditional activity indicator (the 10.7 cm radio flux F10.7). Around minimum, SoDA is basically proportional to the polar precursor and its value yields the prediction for F10.7 at the next maximum; however, it was constructed so that its 11-year modulation is minimized, so theoretically it should be rather stable, making predictions possible well before the minimum. That is the theory, anyway – in reality, SoDA based forecasts made more than 2 – 3 years before the minimum usually proved unreliable. It is then questionable to what extent SoDA improves the prediction skill of the polar precursor, to which it is more or less equivalent in those late phases of the solar cycle when forecasts start to become reliable.

Fortunately, however, the maxima of the polar field curves are often rather flat (see Figure 7View Image), so approximate forecasts are feasible several years before the actual minimum. Using the current, rather flat and low maximum in polar field strength, Svalgaard et al. (2005Jump To The Next Citation Point) have been able to predict a relatively weak cycle 24 (peak R value 75 ± 8) as early as 4 years before the sunspot minimum took place in December 2008! Such an early prediction is not always possible: early polar field predictions of cycles 22 and 23 had to be corrected later and only forecasts made shortly before the actual minimum did finally converge. Nevertheless, even the moderate success rate of such early predictions seems to indicate that the suggested physical link between the precursor and the cycle amplitude is real.

In addition to their above mentioned use in reconstructing the polar field strength, various proxies or alternative indices of the global solar magnetic field during the activity minimum may also be used directly as activity cycle precursors. H α synoptic charts are now available from various observatories from as early as 1870. As H α filaments lie on the magnetic neutral lines, these maps can be used to reconstruct the overall topology, if not the detailed map, of the large-scale solar magnetic field. Tlatov (2009Jump To The Next Citation Point) has shown that several indices of the polar magnetic field during the activity minimum, determined from these charts, correlate well with the amplitude of the incipient cycle.

High resolution Hinode observations have now demonstrated that the polar magnetic field has a strongly intermittent structure, being concentrated in intense unipolar tubes that coincide with polar faculae (Tsuneta et al., 2008). The number of polar faculae should then also be a plausible proxy of the polar magnetic field strength and a good precursor of the incipient solar cycle around the minimum. This conclusion was indeed confirmed by Li et al. (2002Jump To The Next Citation Point) and, more recently, by Tlatov (2009Jump To The Next Citation Point).

These methods offer a prediction over a time span of 3 – 4 years, comparable to the rise time of the next cycle. A significantly earlier prediction possibility was, however, suggested by Makarov et al. (1989Jump To The Next Citation Point) and Makarov and Makarova (1996) based on the number of polar faculae observed at Kislovodsk, which was found to predict the next sunspot cycle with a time lag of 5 – 6 years; even short term annual variations or “surges” of sunspot activity were claimed to be discernible in the polar facular record. This surprising result may be partly due to the fact that Makarov et al. considered all faculae poleward of 50 ° latitude. Bona fide polar faculae, seen on Hinode images to be knots of the unipolar field around the poles, are limited to higher latitudes, so the wider sample may consist of a mix of such “real” polar faculae and small bipolar ephemeral active regions. These latter are known to obey an extended butterfly diagram, as recently confirmed by Tlatov et al. (2010): the first bipoles of the new cycle appear at higher latitudes about 4 years after the activity maximum. It is not impossible that these early ephemeral active regions may be used for prediction purposes (cf. also Badalyan et al., 2001); but whether or not the result of Makarov et al. (1989) may be attributed to this is doubtful, as Li et al. (2002) find that even using all polar faculae poleward of 50° from the Mitaka data base, the best autocorrelation still results with a time shift of about 4 years only.

Finally, trying to correlate various solar activity parameters, Tlatov (2009Jump To The Next Citation Point) finds this surprising relation:

(n+1) (n) ( (n) (n)) R max = C1 + C2R max trev − tmax , C1 = 83 ± 11, C2 = 0.09 ± 0.02 , (12 )
where t(rne)v is the epoch of the polarity reversal in cycle n (typically, about a year after t(nm)ax). The origin of this curious relationship is unclear. In any case, the good correlation coefficient (r = 0.86, based on 12 cycles) and the time lag of ∼ 10 years make this relationship quite remarkable. For cycle 24 this formula predicts R(m2a4x)= 94 ± 14.
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