Determining the 3D Structure of the Corona Using Vertical Height Constraints on Observed Active Region Loops

The corona associated with an active region is structured by high-temperature, magnetically dominated closed and open loops. The projected 2D geometry of these loops is captured in EUV filtergrams. In this study using SDO/AIA 171 Å filtergrams, we expand our previous method to derive the 3D structure of these loops, independent of heliostereoscopy. We employ an automated loop recognition scheme (Occult-2) and fit the extracted loops with 2D cubic Bézier splines. Utilizing SDO/HMI magnetograms, we extrapolate the magnetic field to obtain simple field models within a rectangular cuboid. Using these models, we minimize the misalignment angle with respect to Bézier control points to extend the splines to 3D (Gary, Hu, and Lee 2014). The derived Bézier control points give the 3D structure of the fitted loops. We demonstrate the process by deriving the position of 3D coronal loops in three active regions (AR 11117, AR 11158, and AR 11283). The numerical minimization process converges and produces 3D curves which are consistent with the height of the loop structures when the active region is seen on the limb. From this we conclude that the method can be important in both determining estimates of the 3D magnetic field structure and determining the best magnetic model among competing advanced magnetohydrodynamics or force-free magnetic-field computer simulations.