Evidence for partial Taylor relaxation from changes in magnetic geometry and energy during a solar flare

Context. Solar flares are powered by energy stored in the coronal magnetic field, a portion of which is released when the field reconfigures into a lower energy state. Investigation of sunspot magnetic field topology during flare activity is useful to improve our understanding of flaring processes. Aims. Here we investigate the deviation of the non-linear field configuration from that of the linear and potential configurations, and study the free energy available leading up to and after a flare. Methods. The evolution of the magnetic field in NOAA region 10953 was examined using data from Hinode/SOT-SP, over a period of 12 h leading up to and after a GOES B1.0 flare. Previous work on this region found pre- and post-flare changes in photospheric vector magnetic field parameters of flux elements outside the primary sunspot. 3D geometry was thus investigated using potential, linear force-free, and non-linear force-free field extrapolations in order to fully understand the evolution of the field lines. Results. Traced field line geometrical and footpoint orientation differences show that the field does not completely relax to a fully potential or linear force-free state after the flare. Magnetic and free magnetic energies increase significantly ~6.5–2.5 h before the flare by ~1031 erg. After the flare, the non-linear force-free magnetic energy and free magnetic energies decrease but do not return to pre-flare “quiet” values. Conclusions. The post-flare non-linear force-free field configuration is closer (but not equal) to that of the linear force-free field configuration than a potential one. However, the small degree of similarity suggests that partial Taylor relaxation has occurred over a time scale of ~3–4 h.