Accuracy analysis and application of extrapolation of force-free fields in solar active and quiet regions

Liu Suo, lius@nao.cas.cn, National Astronomical Observatory, Chinese Academy of Sciences, Beijing, China
Zhang Hongqi, hzhang@nao.cas.cn, National Astronomical Observatory, Chinese Academy of Sciences, Beijing, China
Su Jiangtao, sjt@nao.cas.cn, National Astronomical Observatory, Chinese Academy of Sciences, Beijing, China
Song Mutao, Purple Mountain Observatory, Chinese Academy of Sciences, Nanjing, China

Abstract
The force free approximation is an important tool to understanding the possible distribution of magnetic field in solar atmosphere. The availability, applicability and deviation of nonlinear force-free (NLFF) fields extrapolated by Approximate Vertical Integration (AVI), Direct Boundary Integral Equation (DBIE) and Optimization (Opt.) methods are studied based on the comparison with two semi-analytical fields (Low & Lou 1990). It is found that the correlation coefficients between the first semi-analytical field (SAF1) and extrapolated field by DBIE and AVI are greater than 90% in the low solar atmosphere. While for the second semi-analytical field (SAF2), the correlation coefficients are greater than 80%. The mean values of relative standard deviations (RSD) of a along field lines have been estimated for NLFF field extrapolated by AVI, DBIE and Opt. methods. More over these numerical NLFF extrapolations based on the observational vector magnetograms are used to study the spatial magnetic field in the quiet Sun. It is found that the strength differences between the extrapolated NLFF and potential fields exist in the low layers. These differences tend to disappear as the height increases. The analysis shows that the reconstructed NLFF fields deviate significantly from the potential field and the azimuths are different among three NLFF fields.