Evolution of Spatial Complexity in Flare Ribbon Substructure and Its Relationship to Magnetic Reconnection Dynamics

Abstract Recent three-dimensional flare models suggest that flare ribbon substructure is linked to the fragmentation of the reconnecting current sheet in the corona. Flare ribbon substructure can therefore potentially serve as a unique diagnostic tool for physical processes in the flare current sheet. In this paper, we describe a new method to quantify the evolution of ribbon substructure that first extracts the ribbon’s bright leading edge and then quantifies its morphology using the box-counting dimension and correlation dimension mapping (CDM). We first test our method using synthetic observations. We then apply it to an M6.5-class solar flare on 2015 June 22 observed by the Interface Region Imaging Spectrograph (IRIS) 1330 Å slit-jaw imager. We find that when the flare ribbon boundary has more multiple-spatial-scale features (a higher box-counting dimension), hard X-ray emission and magnetic reconnection rates are the strongest. We also find that the flare ribbon complexity characterized by CDM has a moderate correlation with the IRIS Si IV 1402.77 Å nonthermal velocity (in the negative polarity ribbon) and reconnection flux rates (in ribbons of both magnetic polarities). We conclude that the buildup of the spatial complexity of the ribbons at multiple spatial scales can serve as an observational proxy for current-sheet fragmentation in the corona.