3D Reconstruction of Coronal Loops by the Principal Component Analysis

Knowing the three dimensional structure of plasma filaments in the uppermost part of the solar atmosphere, known as coronal loops, and especially their length, is an important parameter in the wave-based diagnostics of this part of the Sun. The combination of observations of the Sun from different points of observations in space, thanks to the most recent missions, including the Solar Dynamics Observatory (SDO) and the Solar TErrestrial RElations Observatory (STEREO), allows us to infer information about the geometrical shape of coronal loops in 3D space. Here, we propose a new method to reconstruct the loop shape starting from stereoscopically determined 3D points, which sample the loop length, by principal component analysis. This method is shown to retrieve in an easy way the main parameters that define the loop, e. g., the minor and major axes, the loop plane, the azimuthal and inclination angles, for the special case of a coplanar loop.