Vector magnetic field measurements along a cooled stereo-imaged coronal loop

The variation of the vector magnetic field along structures in the solar corona remains unmeasured. Using a unique combination of spectropolarimetry and stereoscopy, we infer and compare the vector magnetic field structure and three-dimensional morphology of an individuated coronal loop structure undergoing a thermal instability. We analyze spectropolarimetric data of the He I 10830 {\AA} triplet ($1s2s{\ }^{3}S_{1} - 1s2p{\ }^{3}P_{2,1,0}$) obtained at the Dunn Solar Telescope with the Facility Infrared Spectropolarimeter on 19 September 2011. Cool coronal loops are identified by their prominent drainage signatures in the He I data (redshifts up to 185 km sec$^{-1}$). Extinction of EUV background radiation along these loops is observed by both the Atmospheric Imaging Assembly onboard the Solar Dynamics Observatory and the Extreme Ultraviolet Imager onboard spacecraft A of the Solar Terrestrial Relations Observatory, and is used to stereoscopically triangulate the loop geometry up to heights of 70 Mm ($0.1$ $R_{sun}$) above the solar surface. The He I polarized spectra along this loop exhibit signatures indicative of atomic-level polarization as well as magnetic signatures through the Hanle and Zeeman effects. Spectropolarimetric inversions indicate that the magnetic field is generally oriented along the coronal loop axis, and provide the height dependence of the magnetic field intensity. The technique we demonstrate is a powerful one that may help better understand the thermodynamics of coronal fine structure magnetism.