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 models, which interpret flares as avalanches of magnetic reconnection events within a stressed magnetic structure driven to a state of self-organized criticality by stochastic motions of the photospheric magnetic footpoints. Inspired by a suggestion recently made by Wheatland, we construct modified lattice models driven by a nonstationary random process. The resulting models have 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 exponent 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.