The Origin of the Solar Flare Waiting-Time Distribution

It was recently pointed out that the distribution of times between solar flares (the flare waiting-time distribution) follows a power law, for long waiting times. Based on 25 years of soft X-ray flares observed by Geostationary Operational Environmental Satellite (GOES) instruments it is shown that 1. the waiting-time distribution of flares is consistent with a time-dependent Poisson process, and 2. the fraction of time the Sun spends with different flaring rates approximately follows an exponential distribution. The second result is a new phenomenological law for flares. It is shown analytically how the observed power-law behavior of the waiting times originates in the exponential distribution of flaring rates. These results are argued to be consistent with a non-stationary avalanche model for flares.