Nonlinear force-free field extrapolation of the coronal magnetic field using the data obtained by the Hinode satellite

The Hinode satellite can obtain high‐quality photospheric vector magnetograms of solar active regions and the simultaneous coronal loop images in soft X‐ray and extreme ultraviolet (EUV) bands. In this paper, we continue the work of He and Wang (2008) and apply the newly developed upward boundary integration computational scheme for the nonlinear force‐free field (NLFFF) extrapolation of the coronal magnetic field to the photospheric vector magnetograms acquired by the Spectro‐Polarimeter of the Solar Optical Telescope aboard Hinode. Three time series vector magnetograms of the same solar active region, NOAA 10930, are selected for the NLFFF extrapolations, which were observed within the time interval of 26 h during 10–11 December 2006 when the active region crossed the central area of the Sun's disk. Parallel computation of the NLFFF extrapolation code was realized through OpenMP multithreaded, shared memory parallelism and Fortran 95 programming language for the extrapolation calculations. The comparison between the extrapolated field lines and the coronal loop images obtained by the X‐Ray Telescope and the EUV Imaging Spectrometer of Hinode shows that, in the central area of the active region, the field line configurations generally agree with the coronal images, and the orientations of the field lines basically coincide with the coronal loop observations for all three successive magnetograms. This result supports the NLFFF model being used for tracing the time series evolution of the 3‐D coronal magnetic structures as the responses of the quasi‐equilibrium solar atmosphere to the vector magnetic field changes in the photosphere.