Toward a reconnection model for solar flare statistics

A model to account for observed solar flare statistics in terms of a superposition of independent random flaring elements (assumed to be sites of magnetic reconnection in the coronal magnetic field and hence termed “separators”) is described. A separator of length is assumed to flare as a Poisson process in time, with a rate v(l) inversely proportional to the Alfvén transit time for the structure. It is shown that a relationship ξ∞lk between the mean energy of events ξ at a separator and the separator length implies a relationship E∞Tk between individual waiting times τ and energies E of events at the separator. The most plausible K=2 model is found to be compatible with simple pictures for magnetohydrodynamic energy storage prior to magnetic reconnection in a current sheet with anomalous (turbulent) resistivity. Formal inversion of the observed flare frequency-energy distribution is shown to imply a distribution P(l) ∞l-1 of the separator lengths in active regions. A simulation confirms the basic results of the model. It is also demonstrated that a model comprising time-dependent separator numbers N=N(t) can reproduce an observed power-law tail in the flare waiting-time distribution, for large waiting times