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

Recent observations with TRACE reveal that the time delay between the appearance of a cooling loop in different EUV temperature filters is proportional to the loop length, ∆t12 ∝ 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 = Acor Fe /A Ph Fe relative to the photospheric value as function of the cooling delay ∆t12, 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 5 large-scale loops, in the temperature range of T ≈ 1.0 − 1.4 MK. This result supports the previous finding that low-FIP 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. Subject headings: Sun: Corona — Sun: UV radiation