Magnetic Diagnostics of Prominence Eruptions through the Hanle Effect of the He <sc>i</sc> 1083 nm Line

The magnetic field vector of the solar corona is not regularly and comprehensively being measured because of the complexity and degeneracy inherently present in the types of observations currently available. To address some of the current limitations of coronal polarimetry, we present computations that demonstrate the possibility of magnetometry using the unsaturated Hanle effect of the He i 1083 nm line. The main purpose of this investigation is to show how the linear polarization of this line can be used to routinely diagnose the orientation of the field in erupting prominences, thus providing an important constraint on the B z determination at 1 AU. For this work, we adopted a simplified magnetic model of a flux rope, consisting of a toroidal helical structure embedded in a hydrostatically stratified corona. Our results demonstrate the possibility to discern different orientations of the magnetic field vector in such structures under rather general and practicable viewing conditions. In particular, observations from the Sun-Earth Lagrange points are found to provide excellent locations for the deployment of synoptic instruments aiming at the estimation of the magnetic field of Earth-directed coronal mass ejections. We complete our demonstration by showing how a small (similar to 5 cm) space-borne coronagraph can achieve sufficient signal-to-noise ratios to make the coronal magnetometry goal outlined above feasible.