Evidence for solar tether-cutting magnetic reconnection from coronal field extrapolations

Magnetic reconnection is one of the primary mechanisms for triggering solar eruptive events, but direct observation of this rapid process has been a challenge. In this Letter, using a nonlinear force-free field (NLFFF) extrapolation technique, we present a visualization of field line connectivity changes resulting from tether-cutting reconnection over about 30 minutes during the 2011 February 13 M6.6 flare in NOAA AR 11158. Evidence for the tether-cutting reconnection was first collected through multiwavelength observations and then by analysis of the field lines traced from positions of four conspicuous flare 1700 Å footpoints observed at the event onset. Right before the flare, the four footpoints are located very close to the regions of local maxima of the magnetic twist index. In particular, the field lines from the inner two footpoints form two strongly twisted flux bundles (up to ∼1.2 turns), which shear past each other and reach out close to the outer two footpoints, respectively. Immediately after the flare, the twist index of regions around the footpoints diminishes greatly and the above field lines become low-lying and less twisted (≲0.6 turns), overarched by loops linking the two flare ribbons formed later. About 10% of the flux (∼3 × 10¹⁹ Mx) from the inner footpoints undergoes a footpoint exchange. This portion of flux originates from the edge regions of the inner footpoints that are brightened first. These rapid changes of magnetic field connectivity inferred from the NLFFF extrapolation are consistent with the tether-cutting magnetic reconnection model.