On Anisotropy in Expansion of Magnetic Flux Tubes in the Solar Corona

Most one-dimensional hydrodynamic models of plasma confined to magnetic flux tubes assume circular tube cross sections. We use potential field models to show that flux tubes in circumstances relevant to the solar corona do not, in general, maintain the same cross-sectional shape through their length and therefore the assumption of a circular cross section is rarely true. We support our hypothesis with mathematical reasoning and numerical experiments. We demonstrate that lifting this assumption in favor of realistic, non-circular loops makes the apparent expansion of magnetic flux tubes consistent with that of observed coronal loops. We propose that in a bundle of ribbon-like loops, those that are viewed along the wide direction would stand out against those that are viewed across the wide direction due to the difference in their column depths. That result would impose a bias toward selecting loops that appear not to be expanding, seen projected in the plane of sky. An implication of this selection bias is that the preferentially selected non-circular loops would appear to have increased pressure scale heights even if they are resolved by current instruments.