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The theoretical concept that braided magnetic field lines in the solar coronamay dissipate a sufficient amount of energy to account for the brighteningobserved in the active-region corona, has been substantiated by high-resolutionobservations only recently. From the analysis of coronal images obtained withthe High Resolution Coronal Imager, first observational evidence of thebraiding of magnetic field lines was reported by Cirtain et al. 2013 (hereafterCG13). We present nonlinear force-free reconstructions of the associatedcoronal magnetic field based on vector SDO/HMI magnetograms. We deliverestimates of the free magnetic energy associated to a braided coronalstructure. Our model results suggest (~100 times) more free energy at thebraiding site than analytically estimated by CG13, strengthening thepossibility of the active-region corona being heated by field line braiding. Wewere able to assess the coronal free energy appropriately by using vector fieldmeasurements and attribute the lower energy estimate of CG13 to theunderestimated (by a factor of 10) azimuthal field strength. We also quantifythe increase of the overall twist of a flare-related flux rope which had beenclaimed by CG13. From our models we find that the overall twist of the fluxrope increased by about half a turn within twelve minutes. Unlike anothermethod, to which we compare our results to, we evaluate the winding of the fluxrope's constituent field lines around each other purely based on their modeledcoronal 3D field line geometry -- to our knowledge for the first time.

Force-free field modeling of twist and braiding-induced magnetic energy in an active-region corona