The cross-sectional shape and height expansion of coronal loops: High-resolution Coronal Imager (Hi-C) analysis of AR 12712

Coronal loop observations have existed for many decades yet the precise shape of these fundamental coronal structures is still widely debated since the discovery that they appear to undergo negligible expansion between their footpoints and apex. In this work a selection of eight EUV loops and their twenty-two sub-element strands are studied from the second successful flight of NASA's High resolution Coronal Imager (Hi-C 2.1). Four of the loops correspond to open fan structures with the other four considered to be magnetically closed loops. Width analysis is performed on the loops and their sub-resolution strands using our method of fitting multiple Gaussian profiles to cross-sectional intensity slices. It is found that whilst the magnetically closed loops and their sub-element strands do not expand along their observable length, open fan structures may expand an additional 150% of their initial width. Following recent work, the Pearson correlation coefficient between peak intensity and loop/strand width are found to be predominantly positively correlated for the loops (~88%) and their sub-element strands (~80%). These results align with the hypothesis of Klimchuk & DeForest that loops and - for the first time - their sub-element strands have approximately circular cross-sectional profiles.