Using multi-line spectropolarimetric observations of forbidden emission lines to measure single-point coronal magnetic fields
Abstract
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→0 transition or has equal Land\'e 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 infrared Fe XIII lines discussed by Plowman. We identify the Fe XIII 1074.7 nm and Si X 1430.1 nm 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.