  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.
