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The bulk of solar coronal radiative loss consists of soft X-ray emission from quasi-static loops at the cores of Active Regions. In order to develop diagnostics for determining the heating mechanism of these loops from observations by coronal imaging instruments, I have developed analytical solutions for the temperature structure and scaling laws of loop strands for a wide range of heating functions, including footpoint heating, uniform heating, and heating concentrated at the loop apex. Key results are that the temperature profile depends only weakly on the heating distribution -not sufficiently to be of significant diagnostic value -and that the scaling laws survive for this wide range of heating distributions, but with the constant of proportionality in the RTV scaling law (P 0 L ∼ T 3 max ) depending on the specific heating function. Furthermore, quasi-static analytical solutions do not exist for an excessive concentration of heating near the loop footpoints, a result in agreement with recent numerical simulations. It is demonstrated that a generalization of the solutions to the case of a strand with a variable diameter leads to only relatively small correction factors in the scaling laws and temperature profiles for constant diameter loop strands. A quintet of leading theoretical coronal heating mechanisms is shown to be captured by the formalism of this paper, and the differences in thermal structure between them may be verified through observations. Preliminary results from full numerical simulations demonstrate that, despite the simplifying assumptions, the analytical solutions from this paper are stable and accurate.

We analyze the determination of coronal line-of-sight temperatures with the technique of narrowband filter ratios that is currently employed for data obtained with the Transition Region and Coronal Explorer and the EUV Imaging Telescope on board the Solar and Heliospheric Observatory. We demonstrate that the simple fact that the observed differential emission measure curves in coronal loops have a broad plateau everywhere along the length of the loop leads to the finding of isothermal loops with different temperatures for each pair of filters. We show that none of the temperatures thus obtained correctly describe the state of the loop plasma, which instead must be characterized by the full differential emission measure per pixel. We conclude that the recent discovery of a new class of isothermal loops is probably a mere artifact of the narrowband filter ratio method and show that the shift in the location of the plateau in the differential emission measure along the loop indicates significant heating near the loop tops.

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