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Astron. Astrophys. 322, 311-319 (1997)

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3. Data processing and results

Due to the observational evidence of a complex shape of the solar activity cycles, our study started by computing the average trends on several time-scales and the corresponding standard deviations. Data averages allow to examine maximum shape variability in the 11-year quasi-stationary trends while standard deviation values reveal dynamical phenomena along the cycle.

Fig. 1 (thin lines) illustrates the Rz averages on one-half, 1, 6 and 12 months, together with the ones for 51, 157, 204 and 455 days (periodicities obtained by Pap et al. 1990, and Bouwer 1992).

[FIGURE] Fig. 1. Rz averages (thin lines) on several time-scales together with the corresponding standard deviations (S.D., thick lines). Numbers on the abscissa axis represent the activity cycle enumeration (10 to 22, according to the Zürich one).

On a short time-scale ([FORMULA] days) the cycle shape (in particular, the maximum phase) is dominated by large fluctuations; conversely, on a large time-scale ([FORMULA] [FORMULA] months) only the quasi-stationary 11-year trend appears. Finally, on an intermediate time-scale (see panels for [FORMULA] days), two or more peaks emerge during the maximum phase of each solar cycle. In a similar way, the average trends of the 10.7- [FORMULA] radio flux have been computed (Fig. 2, thin lines). Again, on intermediate time-scales (see panels for [FORMULA] days) more than one peak occurs in the maximum activity phases; for example, the dataset for 155-day averages shows many peaks in cycle 20 and double-structured maximum phases in cycles 19, 21 and 22.

[FIGURE] Fig. 2. As for Fig. 1 but for the 10.7- [FORMULA] flux ([FORMULA]).

The average datasets seen as a whole (thin lines in Figs. 1 and 2) suggest that:

1. the shape of the maximum phase is double- or multi-structured (i.e., composed of several peaks);

2. only averages on intermediate time-scales highlight the maximum shape by performing a compromise between fluctuations of data and long-term 11-year behaviour of activity cycles;

3. double- or multi-structured maxima seem to be a common feature at all the atmospheric layers.

With this aim in mind, we looked at the standard deviation results (thick lines in Fig. 1 and 2) but we found that the standard deviation of monthly means with respect to the annual mean (denoted m/y in Fig. 3) reveals the presence of double-peak structures better. In fact double sharped peaks are found in the majority of the cycles (11, 16, 19, 21 and 22 for Rz; 19 and 22 for 10.7- [FORMULA] radio flux; 22 for 1-8 [FORMULA] X-ray flux and [FORMULA] flux). On the contrary, multi-structured maxima appear in cycles 10, 13 and 15 for Rz; in cycle 20 for the radio flux index and in cycles 20 and 21 for the grouped [FORMULA] flares. Large unresolved peaks appear in cycles 12, 14 and 17 for Rz and in cycle 21 for the radio flux. Multi-structured peaks during the maximum phase of solar activity indicates that a search for only two peaks, according to Gnevyshev's first results, could be misleading with regard to the causes of the phenomenon. Moreover, pure statistical artefacts (appearing in the form of minor peaks) cannot be excluded. On the other hand, the quasi-repetitivity of a dual pattern represents a valid indicator for the existence of dynamical variations overlapped on the long-term trend. On the ground of the previous observations we will pay attention to remove causes of its scarce evidence.

[FIGURE] Fig. 3. Standard deviation (SD) of monthly averages with respect to the annual average (m/y) for Rz, grouped [FORMULA] flare number, 10.7- [FORMULA] radio and 1-8 [FORMULA] X-ray background fluxes (in units of [FORMULA]).
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© European Southern Observatory (ESO) 1997

Online publication: June 30, 1998