Occurrence Rate of Sunspots in Solar Cycles 12–25

Here, we have statistically investigated the averaged occurrence rate of sunspots during active days to test whether it is uniform across solar cycles, motivated by an intriguing observation that weak solar cycles tend to be preceded by solar minimum with numerous spotless days. The occurrence rate of sunspot in a particular month is defined by a ratio of the monthly sunspot number to the number of active days in the corresponding month. The cycle with a large number of spotless days becomes weak owing to either a small number of active days during solar cycle or a lower occurrence rate per day during active days of solar cycle, or even both. More specifically speaking, we have attempted to examine whether the averaged occurrence rate of sunspots during weak solar cycles differs from that of strong ones, and, if so, determine in what part of solar cycle the occurrence rate contributes to such changes in sunspot number. As a result, we find that the occurrence rate of sunspot averaged over the period from maximum of (i − 1)-th solar cycle to maximum of i-th solar cycle is negatively correlated with the number of spotless days, and is correlated with sunspot numbers. It is found that the averaged occurrence rate appears to more significantly correlate with the sunspot number when the sun is relatively more active compared to the period when the sun is relatively less active. It is also found that the averaged occurrence rate of sunspot does not correlate with length of solar cycle, nor length of ascending phase. Finally, we conclude by pointing out implications of our findings.