Interpretation of vector magnetograph data including magneto-optic effects. I - Azimuth angle of the transverse field

In this paper, the presence of Faraday rotation in measurements of the orientation of a sunspot's transverse magnetic field is investigated. Using observations obtained with the Marshall Space Flight Center's (MSFC) vector magnetograph, the derived vector magnetic field of a simple, symmetric sunspot is used to calculate the degree of Faraday rotation in the azimuth of the transverse field as a function of wavelength from analytical expressions for the Stokes parameters. These results are then compared with the observed rotation of the field's azimuth which is derived from observations at different wavelengths within the Fe I 5250 A spectral line. From these comparisons, it is found: the observed rotation of the azimuth is simulated to a reasonable degree by the theoretical formulations if the line-formation parameter is varied over the sunspot; these variations are substantiated by the line-intensity data; for the MSFC system, Faraday rotation can be neglected for field strengths less than 1800 G and field inclinations greater than 45 deg; to minimize the effects of Faraday rotation in sunspot umbrae, MSFC magnetograph measurements must be made in the far wings of the Zeeman-sensitive spectral line.