The origin of the solar flare waiting-time distribution

It was recently pointed out that the distribution of times between solar fl ares (the flare waiting-time distribution) follows a power law for long wai ting times. Based on 25 years of soft X-ray flares observed by Geostationar y Operational Environmental Satellite instruments, it is shown that (1) the waiting-time distribution of flares is consistent with a time-dependent Po isson process and (2) the fraction of time the Sun spends with different fl aring rates approximately follows an exponential distribution. The second r esult is a new phenomenological law for flares. It is shown analytically ho w the observed power-law behavior of the waiting times originates in the ex ponential distribution of flaring rates. These results are argued to be con sistent with a nonstationary avalanche model for flares.