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| - III. Slip-running reconnection properties
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| - The standard flare model in three dimensions
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| - Context. A standard model for eruptive flares aims at describing observational 3D features of the reconnecting coronal magnetic field. Extensions to the 2D model require the physical understanding of 3D reconnection processes at the origin of the magnetic configuration evolution. However, the properties of 3D reconnection without null point and separatrices still need to be analyzed. Aims. We focus on magnetic reconnection associated with the growth and evolution of a flux rope and associated flare loops during an eruptive flare. We aim at understanding the intrinsic characteristics of 3D reconnection in the presence of quasi-separatrix layers (QSLs), how QSL properties are related to the slip-running reconnection mode in general, and how this applies to eruptive flares in particular. Methods. We studied the slip-running reconnection of field lines in a magnetohydrodynamic simulation of an eruptive flare associated with a torus-unstable flux rope. The squashing degree and the mapping norm are two parameters related to the QSLs. We computed them to investigate their relation with the slip-running reconnection speed of selected field lines. Results. Field lines associated with the flux rope and the flare loops undergo a continuous series of magnetic reconnection, which results in their super-Alfvénic slipping motion. The time profile of their slippage speed and the space distribution of the mapping norm are shown to be strongly correlated. We find that the motion speed is proportional to the mapping norm. Moreover, this slip-running motion becomes faster as the flux rope expands, since the 3D current layer evolves toward a current sheet, and QSLs to separatrices. Conclusions. The present analysis extends our understanding of the 3D slip-running reconnection regime. We identified a controlling parameter of the apparent velocity of field lines while they slip-reconnect, enabling the interpretation of the evolution of post flare loops. This work completes the standard model for flares and eruptions by giving its 3D properties.
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