Waiting-time distributions in lattice models of solar flares

It has recently been argued that the distribution of waiting times between successive solar flares is incompatible with the prediction of lattice mode ls, which interpret flares as avalanches of magnetic reconnection events wi thin a stressed magnetic structure driven to a state of self-organized crit icality by stochastic motions of the photospheric magnetic footpoints. Insp ired by a suggestion recently made by Wheatland, we construct modified latt ice models driven by a nonstationary random process. The resulting models h ave frequency distributions of waiting times that include a power-law tail at long waiting times, in agreement with observations. One model, based on a random walk modulation of an otherwise stationary driver, yields an expon ent for the power-law tail equal to 2.51 +/- 0.16, in reasonable agreement with observational inferences. This power-law tail survives in the presence of noise and a detection threshold. These findings lend further support to the avalanche model for solar flares.