The correlation between expansion speed and magnetic field in solar flare ribbons

In this paper, we study the correlation between the expansion speed of two-ribbon flares and the magnetic field measured in the ribbon location, and compare such correlation for two events with different magnetic configurations. These two events are: an M1.0 flare in the quiet sun on September 12, 2000 and an X2.3 flare in Active Region NOAA 9415 on April 10, 2001. The magnetic configuration of the M1.0 flare is simple, while that of X2.3 event is complex. We have derived a power-law correlation between the ribbon expansion speed (V-r) and the longitudinal magnetic field (B-z) with an empirical relationship V-r = A x B-z(-delta), where A is a constant and delta is the index of the power-law correlation. We have found that 6 for the M1.0 flare in the simple magnetic configuration is larger than that for the X2.3 flare in the complex magnetic configuration.