4.3 Cycle periods

The period of a sunspot cycle is defined as the elapsed time from the minimum preceding its maximum to the minimum following its maximum. This does not, of course, account for the fact that each cycle actually starts well before its preceding minimum and continues long after its following minimum. By this definition, a cycle’s period is dependent upon the behavior of both the preceding and following cycles. The measured period of a cycle is also subject to the uncertainties in determining the dates of minimum as indicated in the previous subsections. Nonetheless, the length of a sunspot cycle is a key characteristic and variations in cycle periods have been well studied. The average cycle period can be fairly accurately determined by simply subtracting the date for the minimum preceding cycle 1 from the date for the minimum preceding cycle 23 and dividing by the 22 cycles those dates encompass. This gives an average period for cycles 1 to 22 of 131.7 months – almost exactly 11 years.

The distribution of cycle periods depends upon the cycles used and the methods used to determine minima. Eddy (1977) noted that the cycle periods did not appear to be distributed normally. Wilson (1987) included cycle 8 to 20 and used the dates for minimum from the 13-month mean of the monthly sunspot numbers and found that a bimodal distribution best fit the data with short period (122 month) cycles and long period (140 month) cycles separated by a gap (the Wilson Gap) surrounding the mean cycle length of 132.8 months. However, Hathaway et al. (2002Jump To The Next Citation Point) used minima dates from the 24-month Gaussian smoothing of the International Sunspot number for cycles 1 to 23 and of the Group Sunspot Numbers for cycles –4 to 23 and found distributions that were consistent with a normal distributions about a mean of 131 months with a standard deviation of 14 months and no evidence of a gap. These cycle periods and their distributions are shown in Figure 22View Image.

View Image

Figure 22: The left panel shows cycle periods as functions of Cycle Number. Filled circles give periods determined from minima in the 13-month mean while open circles give periods determined from the 24-month Gaussian smoothing. Both measurements give a mean period of about 131 months with a standard deviation of about 14 months. The “Wilson Gap” in periods between 125 and 134 months from the 13-month mean is shown with the dashed lines. The right panel shows histograms of cycle periods centered on the mean period with bin widths of one standard deviation. The solid lines show the distribution from the 13-month mean while the dashed lines show the distribution for the 24-month Gaussian. The periods appear normally distributed and the “Wilson Gap” is well populated with the 24-month Gaussian smoothed data.

  Go to previous page Go up Go to next page