Electric current evolution at the footpoints of solar eruptions

Electric currents play a critical role in the triggering and dynamics of solar eruptions. Characterizing their location and evolution can contribute in fine-tuning the standard flare model in 3D, in deriving the acceleration of coronal mass ejections, and in addressing the long-standing debate between the circuit and MHD approach of flare physics. Using a constrained selection of X-class eruptive flares as observed by SDO, complemented by a generic MHD simulation, we analyse the time-evolution of photospheric currents at the footpoints of erupting flux ropes. The latter are believed to be located within the area surrounded by the hook of current and/or EUV flare ribbons. We focus on footpoints of field lines that remain within the erupting flux-rope during the main phase of the events considered, so as to discard flare-related reconnecting loops from the analysis. In the observations, for each case where a flux-rope fooptoint is identifiable and the currents can be measured with HMI, we identify that both the mean electric-current density and the total current are dominated by direct-currents, and that they are strongly diminishing in the early phases of the flare. We also find the same trend in the MHD simulation. There we show that the current decreases at the line-tied photospheric boundary is caused by the lengthening of coronal field lines, in which the twist per unit-length also diminishes. The coupled analysis between the model and the observations leads to several conclusions. Firstly, the photospheric electric current should neither be considered as a physical source nor as a boundary condition in solar eruption models. Secondly during eruptions these surface currents evolve as a response to the coronal dynamics, in line with the MHD paradigm. Thirdly, measuring their time-evolution may offer a new window for measuring the rate of expansion of coronal flux rope in the early stages of solar eruptions, in the region where they are typically difficult to observe far above the limb yet below the edge of the coronograph.