Using Multi-line Spectropolarimetric Observations of Forbidden Emission Lines to Measure Single-point Coronal Magnetic Fields
Polarized magnetic dipole (M1) emission lines provide important diagnostics for the magnetic field dominating the evolution of the solar corona. This paper advances a multi-line technique using specific combinations of M1 lines to infer the full vector magnetic field for regions of optically thin emission that can be localized along a given line of sight. Our analytical formalism is a generalization of the "single-point inversion" approach introduced by Plowman. We show that combinations of M1 transitions for which each is either a $J=1\to 0$ transition or has equal Landé g-factors for the upper and lower levels contain degenerate spectropolarimetric information that prohibits the application of the single-point inversion technique. This may include the pair of Fe xiii lines discussed by Plowman. We identify the Fe xiii 10747 Å and Si x 14301 Å lines as one alternative combination for implementing this technique. Our sensitivity analysis, based on coronal loop properties, suggests that for photon noise levels around 10−4 of the line intensity, which will be achievable with the National Science Foundation's Daniel K. Inouye Solar Telescope, magnetic fields with sufficient strength (∼10 G) and not severely inclined to the line of sight (≲35°) can be recovered with this method. Degenerate solutions exist, though we discuss how added constraints may help resolve them or reduce their number.