In this paper, the cooling of 72 M- and X-class flares is examined using GOES/XRS and SDO/EVE. The observed cooling rates are quantified and the observed total cooling times are compared with the predictions of an analytical zero-dimensional hydrodynamic model. We find that the model does not fit the observations well, but does provide a well-defined lower limit on a flare's total cooling time. The discrepancy between observations and the model is then assumed to be primarily due to heating during the decay phase. The decay-phase heating necessary to account for the discrepancy is quantified and found be ~50% of the total thermally radiated energy, as calculated with GOES. This decay-phase heating is found to scale with the observed peak thermal energy. It is predicted that approximating the total thermal energy from the peak is minimally affected by the decay-phase heating in small flares. However, in the most energetic flares the decay-phase heating inferred from the model can be several times greater than the peak thermal energy....
Ryan, D. F., Chamberlin, P. C., Milligan, R. O., & Gallagher, P. T. (2013). Decay-phase Cooling and Inferred Heating of M- and X-class Solar Flares. The Astrophysical Journal, 778, 68-80. https://doi.org/10.1088/0004-637X/778/1/68