Scaling Laws and Temperature Profiles for Solar and Stellar Coronal Loops with Non-uniform Heating - AstrophysicsReport as inadecuate

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Abstract: The bulk of solar coronal radiative loss consists of soft X-ray emission fromquasi-static loops at the cores of Active Regions. In order to developdiagnostics for determining the heating mechanism of these loops fromobservations by coronal imaging instruments, I have developed analyticalsolutions for the temperature structure and scaling laws of loop strands for awide range of heating functions, including footpoint heating, uniform heating,and heating concentrated at the loop apex. Key results are that the temperatureprofile depends only weakly on the heating distribution - not sufficiently tobe of significant diagnostic value - and that the scaling laws survive forthis wide range of heating distributions, but with the constant ofproportionality in the RTV scaling law $P {0}L \thicksim T {max}^3$ dependingon the specific heating function. Furthermore, quasi-static analyticalsolutions do not exist for an excessive concentration of heating near the loopfootpoints, a result in agreement with recent numerical simulations. It isdemonstrated that a generalization of the solutions to the case of a strandwith a variable diameter leads to only relatively small correction factors inthe scaling laws and temperature profiles for constant diameter loop strands. Aquintet of leading theoretical coronal heating mechanisms is shown to becaptured by the formalism of this paper, and the differences in thermalstructure between them may be verified through observations. Preliminaryresults from full numerical simulations demonstrate that, despite thesimplifying assumptions, the analytical solutions from this paper are stableand accurate.

Author: P.C.H. Martens



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