Abstract The relationships between solar flare parameters (total importance, time duration, flare index, and flux) and sunspot activity (Rz ) as well as those between geomagnetic activity (aa index) and the flare parameters can be well described by an integral response model with response time scales of about eight and 13 months, respectively. Compared with linear relationships, the correlation coefficients of the flare parameters with Rz, of aa with the flare parameters, and of aa with Rz based on this model have increased about 6%, 17%, and 47% on average, respectively. The time delays between the flare parameters with respect to Rz , aa to the flare parameters, and aa to Rz 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.

Keywords Sun: activity—Sun: sunspots—Sun: flares—geomagnetic activity

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