Evolution of the flaring active region NOAA 10540 as a sequence of nonlinear force-free field extrapolations

Context. The solar corona is structured by magnetic fields. As direct measurements of the coronal magnetic field are not routinely available, it is extrapolated from photospheric vector magnetograms. When magnetic flux emerges from below the solar surface and expands into the corona, the coronal magnetic field is destabilized, leading to explosive phenomena like flares or coronal mass ejections. Aims. We study the temporal evolution of the flaring active region NOAA 10540 and are in particular interested in the free magnetic energy available to power the flares associated with it. Methods. We extrapolated photospheric vector magnetograms measured with the Solar Flare Telescope, located in Tokyo, into the corona with the help of a nonlinear force-free field model. This coronal magnetic field model is based on a well-tested multigrid-like optimization code with which we were able to estimate the energy content of the 3D coronal field, as well as an upper limit for its free magnetic energy. Furthermore, the evolution of the energy density with height and time was studied. Results. The coronal magnetic field energy in active region 10540 increases slowly during the three days before an M6.1 flare and drops significantly after it. We estimated the energy that was set free during this event as proportional to 10(25) J. A sequence of nonlinear force-free extrapolations of the coronal magnetic field shows a build up of magnetic energy before a flare and release of energy during the flare. The drop in magnetic energy of the active region is sufficient to power an M6.1 flare.