The relationships of solar flares with both sunspot and geomagnetic activity

The relationships between solar flare parameters (total importance, time duration, flare index, and flux) and sunspot activity (R-z) as well as those between geomagnetic activity (aa index) and the flare parameters can be well described by an integral response model with the response time scales of about 8 and 13 months, respectively. Compared with linear relationships, the correlation coefficients of the flare parameters with R-z, of aa with the flare parameters, and of aa with R-z based on this model have increased about 6%, 17%, and 47% on average, respectively. The time delays between the flare parameters with respect to R-z, aa to the flare parameters, and aa to R-z at their peaks in a solar cycle can be predicted in part by this model (82%, 47%, and 78%, respectively). These results may be further improved when using a cosine filter with a wider window. It implies that solar flares are related to the accumulation of solar magnetic energy in the past through a time decay factor. The above results may help us to understand the mechanism of solar flares and to improve the prediction of the solar flares.