A New Method to Constrain the Iron Abundance from Cooling Delays in Coronal Loops

Recent observations with the Transition Region and Coronal Explorer reveal that the time delay between the appearance of a cooling loop in different EUV temperature filters is proportional to the loop length, Δt12 ∝ L. We model this cooling delay in terms of radiative loss and confirm this linear relationship theoretically. We derive an expression that can be used to constrain the coronal iron enhancement αFe = A/A relative to the photospheric value as function of the cooling delay Δt12, flux F2, loop width w, and filling factor qw ≤ 1. With this relation, we find upper limits on the iron abundance enhancement of αFe ≤ 4.8 ± 1.7 for 10 small-scale nanoflare loops, and αFe ≤ 1.4 ± 0.4 for five large-scale loops, in the temperature range of T ≈ 1.0-1.4 MK. This result supports the previous finding that low first ionization potential elements, including Fe, are enhanced in the corona. The same relation constitutes also a lower limit for the filling factor, which is qw ≥ 0.2 ± 0.1 and qw ≥ 0.8 ± 0.2 for the two groups of coronal loops.