Including flare sympathy in a model for solar flare statistics

There is a variety of observational evidence for solar flare sympathy, i.e., the triggering of a flare in one active region by a flare in another region. Models for solar flare statistics, however, usually ignore sympathy by assuming that flares occur as independent events. In this paper, we argue that statistical flare models should be robust to the effects of sympathetic flaring. Further, we investigate the consequences of flare sympathy for a specific model of flare statistics, the M. S. Wheatland and I. J. D. Craig (Astrophys. J. 595, 458, 2003) model. The original treatment describes an assembly of reconnecting structures (labelled separators) that flare independently according to simple rules consistent with magnetohydrodynamic flare models. This description is modified by allowing a flare at one separator to increase the probability of flaring at all other separators for a period of time following the flare, by an amount proportional to the energy of the flare. Simulations illustrate the transition of the model from weak to strong sympathy. In the limit of weak sympathy, the model reproduces observed flare frequency-energy and waiting-time distributions.