Comparison of Nonlinear Force-free Field and Potential Field in the Quiet Sun

In this paper, a potential field extrapolation and three nonlinear force-free (NLFF) field extrapolations (optimization, direct boundary integral (DBIE) and approximate vertical integration (AVI) methods) are used to study the spatial configuration of magnetic field in the quiet Sun. It is found that the strength differences between the three NLFF and potential fields exist in the low layers. However, they tend to disappear as the height increases, which are of the order of 0.1 G when the height exceeds $\sim$ 2000 km above the photosphere. The absolute azimuth difference between one NLFF field and the potential field is as follows: for the optimization field, it decreases evidently as the height increases; for the DBIE field, it almost keeps constant and shows no significant change as the height increases; for the AVI field, it increases slowly as the height increases. The analysis shows that the reconstructed NLFF fields deviate significantly from the potential field in the quiet Sun.