Chromospheric Magnetic Field: A Comparison of He I 10830 A Observations with Nonlinear Force-free Field Extrapolation

The nonlinear force-free field (NLFFF) modeling has been extensively used to infer the three-dimensional magnetic field in the solar corona. One of the assumptions in the NLFFF extrapolation is that the plasma beta is low, but this condition is considered to be incorrect in the photosphere. We examine direct measurements of the chromospheric magnetic field in two active regions through spectropolarimetric observations at He i 10830 Å, which are compared with the potential fields and NLFFFs extrapolated from the photosphere. The comparisons allow quantitative estimation of the uncertainty in the NLFFF extrapolation from the photosphere. Our analysis shows that observed chromospheric magnetic field may have larger nonpotentiality compared to the photospheric magnetic field. Moreover, the large nonpotentiality in the chromospheric height may not be reproduced by the NLFFF extrapolation from the photospheric magnetic field. The magnitude of the underestimation of the nonpotentiality at chromospheric heights may reach 30°-40° in shear signed angle in some locations. This deviation may be caused by the non-force-freeness in the photosphere. Our study suggests the importance of the inclusion of measured chromospheric magnetic fields in the NLFFF modeling for the improvement of the coronal extrapolation.