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, dt_12 ~ 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 alpha_Fe=A_Fe^cor/A_Fe^Ph relative to the photospheric value as function of the cooling delay dt_12, flux F_2, loop width w, and filling factor q_w < 1. With this relation we find upper limits on the iron abundance enhancement of alpha_Fe < 4.8+/-1.7 for 10 small-scale nanoflare loops, and alpha_Fe < 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 q_w > 0.2+/-0.1 and q_w > 0.8+/-0.2 for the two groups of coronal loops.