The Width Distribution of Loops and Strands in the Solar Corona -- Are we Hitting Rock Bottom ?

Abstract

In this study we analyze {\sl Atmospheric Imaging Assembly (AIA)} and Hi-C images in order to investigate absolute limits for the finest loop strands. We develop a model of the occurrence-size distribution function of coronal loop widths, characterized by a lower limit of widths $w_{min}$, a peak width $w_p$, a peak occurrence number $n_p$, and a power law slope $a$. Our data analysis includes automated tracing of curvi-linear features with the OCCULT-2 code, automated sampling of the cross-sectional widths of coronal loops, and fitting of the theoretical size distribution to the observed distribution. With Monte-Carlo simulations and variable pixel sizes $\Delta x$ we derive a first diagnostic criterion to discriminate whether the loop widths are unresolved $(w_p/\Delta x \approx 2.5\pm0.2)$, or fully resolved (if $w_p/\Delta x > 2.7$). For images with resolved loop widths we can apply a second diagnostic criterion that predicts the lower limit of loop widths, $w_{min} \approx 3 (\Delta x_{crit}-0.37")$ as a function of the critical resolution $\Delta x_{crit}$. We find that the loop widths are marginally resolved in AIA images, but are fully resolved in Hi-C images, where our model predicts a lower limit of loop widths at $w_{min} \approx 100$ km and a most frequent (peak) value at $w_p \approx 300$ km, in agreement with recent results of Brooks et al. This result agrees with the statistics of photospheric granulation sizes and thus supports coronal heating mechanisms operating on the macroscopic scale of photospheric magneto-convection, rather than nanoflare heating models with unresolved microscopic scales.