Waiting-time distributions of solar eruptions and the evidence for sympathetic flares

In this study we have examined the waiting-time distributions of solar flares and CMEs as well as the evidence for sympathetic events. First, we considered GOES X-ray flares stronger than C1 class during the solar maximum between 1989 and 1991 and all LASCO CMEs from 1999 to 2001. The observed waiting-time distributions are found to be well represented by nonstationary Poisson probability function with time-varying mean occurrence rates, implying that independent events outnumber sympathetic ones. It is also found that there are no systematic relationships between peak fluxes of flares and their waiting-time distributions. The above findings support an idea that the solar corona is in a self-organized critical state. Second, we collected 48 pairs of near simultaneous flares whose positional information and Yohkoh soft X-ray telescope images are available. To select the active regions that probably have sympathetic flares, we have estimated the ratio R of actual flaring overlap time to random-coincidence overlap time for 38 active region pairs. We have then compared the waiting-time distributions for the two different groups of active region pairs (R > 1 and R < 1) with corresponding nonstationary Poisson distributions. As a result, we find a remarkable overabundance of short waiting times for the group with R > 1. This is the first time such strong statistical evidence has been found for the existence of sympathetic flares.