A Model of Solar Flares and Their Homologous Behavior

A model describing physical processes of solar flares and their homologous behavior is presented based on resistive MHD simulations of magnetic arcade evolution subject to continuous shear-increasing footpoint motions. It is proposed in our model that the individual flaring process encompasses magnetic reconnection of arcade field lines, generation of magnetic islands in the magnetic arcade, and coalescence of magnetic islands. When a magnetic arcade is sheared, a current sheet is formed and magnetic reconnection can take place to form a magnetic island. A continuing increase of magnetic shear can trigger a new reconnection process and create another island in the underlying arcade below the original magnetic island. The newborn island rises faster than the preceding island and merges with it to form one island. Before completing the merging process, the newborn island exhibits two different phases of rising motion: the first phase with a slower rising speed and the second phase with a faster rising speed. This is consistent with the Yohkoh observation by Ohyama & Shibata (1998) of X-ray plasma ejecta motion. The first phase, in which reconnection of line-tied field in the underlying arcade is important, can be regarded as being related with the preflare phase. In the second phase, the island coalescence takes place, which creates an elongated current sheet below and enhances the reconnection rate of the line-tied arcade field. This phase is interpreted as the impulsive phase or the flash phase of flares. The obtained reconnection electric field is large enough to accelerate electrons to an energy level higher than 10 keV, which is necessary for observed X-ray emissions. After merging of the islands is completed, magnetic reconnection continues in the current sheet under the integrated island for rather a long period, which can be considered as the main phase of flares. The sequence of all these processes is repeated with some time interval while a shear-increasing motion continues. We propose that a series of these flaring processes constitutes a set of homologous flares. The time interval between successive flaring events depends on the energy input rate into the system, which is governed by the nature of the footpoint motion and the flux reconnecting rate. We also have investigated the destruction of a magnetic island in a system undergoing a decrease of magnetic shear. The result suggests that there is a critical value of magnetic shear for existence of a magnetic island in an arcade-like field configuration.