Figure 1: a) Butterfly diagram of the net (signed) magnetic flux density, averaged over longitude for each Carrington rotation. Sine latitude ranges from -1 (south pole) to +1 (north pole). Positive polarities appear white, negative polarities black, as defined by the color bar. For better contrast, the upper and lower cut offs have been set to . The actual maximum is , the minimum . b) The same for the total (unsigned) magnetic flux density (i.e. the average of the absolute values). The maximum is . | |
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Figure 2: Power level P_{p} vs. for significance levels p=0.9999 (solid line), p=0.999 (dotted), p=0.99 (dashed), and p=0.95 (dash-dotted). a) P_{p} for the net magnetic flux and the entire time series (cycles 21-23, N=3830). b) The same for the total magnetic flux. c) and d) Cycle 21 (N=1380). e) and f) Cycle 22 (N=1320). g) and h) Cycle 23 (N=940). | |
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Figure 3: a) FFT power density (in arbitrary but constant units) of the net (signed) magnetic flux vs. sine latitude and frequency. The frequency range is 1.1- (corresponding to periods 29- , indicated in white on the horizontal axis). Dotted contour lines represent the significance level, the labeled regions A-D are listed in Table 1. The color table has been normalized to the maximum power in the range 10- (see the color bar). b) The same for the total (unsigned) magnetic flux. | |
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Figure 4: a) The raw time series of the total magnetic flux density averaged over latitudes . b) The smoothed time series calculated with an averaging window of 6 months. c) The wavelet power spectrum of the raw time series, calculated with Morlet wavelets and nondimensional frequency 9 (cf. Sect. 2.2). It clearly shows enhanced power at the significance level (white contour lines) around a periodicity of (represented by the horizontal white line at 475 days) during all three cycles 21-23. The hatched areas indicate the "cone of influence'', where edge effects become important. d)- f) The same for latitudes . The wavelet power spectrum shows significant power around for cycles 22 and 23. | |
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Figure 5: a) FFT power density (in arbitrary but constant units) vs. sine latitude and frequency for the net (signed) magnetic flux. The frequency range is 30- (corresponding to periods 386- , indicated in white on the horizontal axis). Dotted contour lines represent the significance level. The labeled regions are listed in Table 2. b) The same for the total (unsigned) magnetic flux. | |
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Figure 6: a) Wavelet power spectrum of the total magnetic flux averaged over latitudes - . Morlet wavelets with nondimensional frequency 12 were applied. The Rieger period around is indicated by the horizontal white line. Significant power at the Rieger period is seen around 1981-1982. The white contour line corresponds to the significance level. b) The same for latitudes - . c) The same for latitudes - . Significant power at the Rieger period is seen for cycles 21 and 22. | |
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Figure 7: a) FFT power density (in arbitrary but constant units) vs. sine latitude and frequency for the net (signed) magnetic flux. The frequency range is 390- (corresponding to periods 29.7- , indicated in white on the horizontal axis). Dotted contour lines represent the significance level. The labeled regions are listed in Table 3. The two curves indicate the differential rotation laws for sunspots (right curve) and Doppler shifts (left curve). b) The same for the total (unsigned) magnetic flux. | |
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Figure 11: a) Wavelet power spectrum of the total magnetic flux averaged over latitudes - . Morlet wavelets with a nondimensional frequency of 120 were used to achieve a maximum frequency resolution. White contours indicate the significance level, hatched regions the cone of influence. The horizontal dashed lines represent the synodic rotation periods of sunspots at and , respectively. During cycle 21, most power is concentrated around a periodicity of , while cycle 22 shows dominant power around . During cycle 23, most power is concentrated around the periodicity of . b) The same for latitudes - . The period is prominent for cycles 21 and 22, while the 25.0- period occurs during all three cycles and is particularly pronounced during cycle 22. | |
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Figure 8: a) FFT power density vs. sine latitude and frequency for the net magnetic flux in cycle 21. The frequency range is 390- (corresponding to periods 29.7- , indicated in white). Dotted contour lines represent the significance level. The labeled regions are listed in Table 4. The two curves indicate the differential rotation laws for sunspots ( right curve) and Doppler shifts ( left curve). b) Same as a) for the total magnetic flux. c) Same as a) but for the second harmonic frequency range 780- (14.8- ). d) Same as c) but for the total magnetic flux. | |
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Figure 9: Same as Fig. 8 but for cycle 22. The labeled regions are listed in Table 5. | |
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Figure 10: Same as Fig. 8 but for cycle 23. The labeled regions are listed in Table 6. | |
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