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

The theoretical concept that braided magnetic field lines in the solar corona may dissipate a sufficient amount of energy to account for the brightening observed in the active-region corona, has been substantiated by high-resolution observations only recently. From the analysis of coronal images obtained with the High Resolution Coronal Imager, first observational evidence of the braiding of magnetic field lines was reported by Cirtain et al. 2013 (hereafter CG13). We present nonlinear force-free reconstructions of the associated coronal magnetic field based on vector SDO/HMI magnetograms. We deliver estimates of the free magnetic energy associated to a braided coronal structure. Our model results suggest (~100 times) more free energy at the braiding site than analytically estimated by CG13, strengthening the possibility of the active-region corona being heated by field line braiding. We were able to assess the coronal free energy appropriately by using vector field measurements and attribute the lower energy estimate of CG13 to the underestimated (by a factor of 10) azimuthal field strength. We also quantify the increase of the overall twist of a flare-related flux rope which had been claimed by CG13. From our models we find that the overall twist of the flux rope increased by about half a turn within twelve minutes. Unlike another method, to which we compare our results to, we evaluate the winding of the flux rope's constituent field lines around each other purely based on their modeled coronal 3D field line geometry -- to our knowledge for the first time.