A Statistical Approach to Study Spatial Characteristics of EUV Emission in Active Regions

Heating of the solar corona is one of the major problems in solar physics, and spatial dimension and structuring of the processes involved in heating are yet to be understood. Observations of the numerous thin coronal loops above active regions (ARs) suggest that coronal heating itself is highly variable on small scales, heating plasma in collections of thin flux tubes. It has recently been theorized, based on simulations, that emitting plasma in ARs can also be structured in larger flux tubes with irregular boundaries. The emission of these large flux tubes can appear like emission of loop bundles, with variations of the column depth at their boundaries causing an impression of individual loops. This "coronal veil" theory was argued to be a more general scenario, which better explains AR emission properties than previous models. If confirmed observationally, it will have a large impact on coronal heating studies, suggesting that existing measurements of temperature and density in coronal loops may need to be reevaluated. The observational validation of this hypothesis is as important as it is difficult. For a given coronal loop, it is difficult to tell whether it is a compact feature or a projection artifact. In this talk, we propose a new statistical approach to address this problem. Instead of trying to analyze each loop individually, we focus on scaling relationship between a number of loops in a given AR and the AR's total brightness in a given wavelength. We argue that these two quantities are related by a power law. We demonstrate in theoretical calculations how the power law coefficients will differ depending on whether the emission is structured into (a) compact features, (b) large features with irregular boundaries, or (c) extended and thin veil-like features. We demonstrate that these power laws exist in observations and discuss numerical experiments which may help us to determine which of these scenarios, if any, best describes observations.