Reconstructing the thermal and spatial form of a solar flare from scaling laws and soft X-ray measurements

The thermal and spatial structure of individual solar flares can be modeled from full-disk soft X-ray measurements by invoking scaling laws that provide a theoretical relationship between certain thermal properties of the flare, its X-ray light curve, and its size and shape. The well-known scaling law, often called RTV after the authors Rosner, Tucker, & Vaiana, relates the hare loop length L, the maximum (loop-top) temperature T-m, and the internal pressure p. In the present analysis GOES soft X-ray data (two channels) are used to derive two diagnostic parameters, T-a and epsilon, which can then be used to compute T-m and p. T-a is the temperature obtained from the observed integrated X-ray flux; epsilon is the emission measure. The operation to compute T-m and p has a unique solution only when a representative value of the loop length, L, is available. Another scaling law by Hawley and coworkers and Metcalf & Fisher relates L to the flare rise and decay times, tau(r) and tau(d). This law, calibrated against measured loops from Yohkoh SXT imagery, can provide an initial estimate of the loop length. We demonstrate that the character of individual flares can be inferred from nonimaged, full-disk soft X-ray measurements in combination with scaling laws: the X-ray light curve is used to; estimate the length dimension from the rise and decay times, and discrete X-ray measurements are used to compute the macro thermal and spatial structure at any selected time during the decay.