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Astron. Astrophys. 345, 1006-1010 (1999)

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4. Features of the sunspot cycle

The time of the sunspot area maximum, [FORMULA], was given explicitly by the value of [FORMULA] for which [FORMULA], then we have

[EQUATION]

[EQUATION]

[FORMULA] is the rising time of a cycle. The value of the sunspot area at maximum, [FORMULA] is given by

[EQUATION]

Using Eqs. (3) to (5), we calculate values of [FORMULA] and [FORMULA] of each cycle, which are listed in Table 1 as well. Here, we define the cycle length T of a solar cycle as the difference between the starting points of two successive cycles, and the value of T of each cycle is listed in the table too. The starting time of the 23rd solar cycle, now known to be 1998 May, is regarded as the parametric value of the starting time [FORMULA] of the cycle.

The relationship of the rising time [FORMULA] and the maximum amplitude [FORMULA] is shown in Fig. 5. The thin line in the figure is the regression line of the form

[EQUATION]

[FIGURE] Fig. 5. Relationship of the rising time ([FORMULA]) and the maximum amplitude [FORMULA]. The thin curve is the regression line.

The figure shows that the shorter the rising time of a cycle is, the larger the maximum amplitude of the cycle is. In other words, cycles with large amplitude take less time to rise to maximum, similar to the so-called Waldmeier effect of the sunspot number. A weak correlation between cycle length and the rising time of solar cycles is found and shown in Fig. 6. The linear regression coefficient [FORMULA], and the line is

[EQUATION]

[FIGURE] Fig. 6. Correction between cycle length and the rising time of the solar cycles 12-22. The linear regression line is shown by the thin line.

The figure indicates that cycles that take a long time to get maximum amplitude tend to run a long time to get ended. The mean value of the rising time is 5.253 years for the 11 cycles, the average of the cycle length is 10.883 years. So on an average, the rising time is less than the falling time of a cycle. We define asymmetry of a cycle as [FORMULA]. Relation between asymmetry and [FORMULA] is shown in Fig. 7. There appears to be a upward trend with [FORMULA]. It shows that cycles with larger amplitude are more asymmetric.

[FIGURE] Fig. 7. Relation between the maximum amplitude [FORMULA] and asymmetry defined in the text. The thin line, i.e. the linear regression line shows a upward trend with a linear equation given in the text.

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© European Southern Observatory (ESO) 1999

Online publication: April 28, 1999
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