Decay Phase Cooling and Inferred Heating of M- and X-class Solar Flares

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 to the predictions of an analytical 0-D hydrodynamic model. It is found 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.