A Statistical Search for a Uniform Trigger Threshold in Solar Flares from Individual Active Regions

Solar flares result from the sudden release of energy deposited by sub-photospheric motions into the magnetic field of the corona. The deposited energy accumulates secularly between events. One may interpret the observed event statistics as resulting from a state-dependent Poisson process, in which the instantaneous flare rate is a function of the stress in the system, and a flare becomes certain as the stress approaches a threshold set by the micro-physics of the flare trigger. If the system is driven fast, and if the threshold is static and uniform globally, a cross-correlation is predicted between the size of a flare and the forward waiting time to the next flare. This cross-correlation is broadly absent from the Geostationary Operational Environmental Satellite (GOES) soft X-ray flare database. One also predicts higher cross-correlations in active regions where the shapes of the waiting time and size distributions match. Again there is no evidence for such an association in the GOES data. The data imply at least one of the following: i) the threshold at which a flare is triggered varies in time; ii) the rate at which energy is driven into active regions varies in time; iii) historical flare catalogs are incomplete; or iv) the description of solar flares as resulting from a build-up and release of energy, once a threshold is reached, is incomplete.