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Spectral Lines for Polarization Measurements of the Coronal Magnetic Field. V. Information Content of Magnetic Dipole Lines

Stokes profiles of typical magnetic dipole coronal emission lines contain information on the embedded magnetic fields, but the interpretation of the lines is subject to ambiguities. The present study illuminates the information content of coronal emission line measurements that include all four Stokes parameters. The simplest case of localized emission along the line of sight, such as that from a single bright loop, is scrutinized. Knowledge of the "atomic alignment" is central to the diagnosis of magnetic fields beyond determining the field's azimuth projected on the plane of the sky. For localized emission, a method to determine the atomic alignment is presented, combining Stokes I, Q, and U observations and statistical equilibrium calculations, related to work by Querfeld. The method yields the sign of the alignment under conditions that might exist 25% of the time, thereby reducing the Van Vleck ambiguity from one of 90° to 180°. Even then, the magnitude of the alignment is sometimes ambiguous. With measurements of Stokes V, unambiguous knowledge of the alignment also yields the vector field B with just an ambiguity of 180° in the plane of the sky. In other, more general cases, neither the sign nor the magnitude of the atomic alignment can be uniquely determined. Suggestions are made as to how these more serious ambiguities might be ameliorated by assuming continuity of magnetic fields underlying the polarization maps, an idea first expressed by House in 1972. Some conclusions are offered concerning the relative merits of formal inversions, diagnosis of magnetic properties from a localized region, tomography using solar rotation, and forward modeling.