The direct relation between the duration of magnetic reconnection and the evolution of GOES light curves in solar flares

Abstract: GOES soft X-ray light curves are used to measure the timing and duration of solar flare emission. The timing and duration of the magnetic reconnection and subsequent energy release which drives solar flares are unknown, though the light curves are presumably related. It is therefore critical to understand the physics which connects the two: how does the time scale of reconnection produce an observed GOES light curve? In this work, we model the formation and expansion of an arcade of loops with a hydrodynamic model, which we then use to synthesize GOES light curves. We calculate the FWHM and the e-folding decay time of the light curves and compare them to the separation of the centroids of the two ribbons which the arcade spans, which is representative of the size scale of the loops. We reproduce a linear relation between the two, as found observationally in previous work. We show that this demonstrates a direct connection between the duration of energy release and the evolution of these light curves. We also show that the cooling processes of individual loops comprising the flare arcade directly affect the measured time scales. From the clear consistency between the observed and modeled linearity, we conclude that the primary factors that control the flare time scales are the duration of reconnection and the loop lengths.