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 l is assumed to flare as a Poisson process in time, with a rate ðlÞ inversely proportional to the Alfvén transit time for the structure. It is shown that a relationship E / l between the mean energy of events E at a separator and the separator length implies a relationship E / between individual waiting times and energies E of events at the separator. The most plausible 1⁄4 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 PðlÞ / 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 1⁄4 NðtÞ can reproduce an observed power-law tail in the flare waitingtime distribution, for large waiting times. Subject headings: MHD — Sun: activity — Sun: corona — Sun: flares — Sun: magnetic fields