Maximum Sunspot Numbers and Active Days

Parameters associated with solar minimum have been studied to relate them to solar activity at solar maximum so that one could possibly predict behaviors of an upcoming solar cycle. The number of active days has been known as a reliable indicator of solar activity around solar minimum. Active days are days with sunspots reported on the solar disk. In this work, we have explored the relationship between the sunspot numbers at solar maximum and the characteristics of the monthly number of active days. Specifically, we have statistically examined how the maximum monthly sunspot number of a given solar cycle is correlated with the slope of the linear relationship between monthly sunspot numbers and the monthly number of active days for the corresponding solar cycle. We have calculated the linear correlation coefficient r and the Spearman rank-order correlation coefficient $r_s$ for data sets prepared under various conditions. Even though marginal correlations are found, they turn out to be insufficiently significant (r ~ 0.3). Nonetheless, we have confirmed that the slope of the linear relationship between monthly sunspot numbers and the monthly number of active days is less steep when solar cycles belonging to the "Modern Maximum" are considered compared with rests of solar cycles. We conclude, therefore, that the slope of the linear relationship between monthly sunspot numbers and the monthly number of active days is indeed dependent on the solar activity at its maxima, but that this simple relationship should be insufficient as a valid method to predict the following solar activity amplitude.