Global Energetics of Solar Flares. XI. Flare Magnitude Predictions of the GOES-Class

Abstract

In this study we determine scaling relationships of observed solar flares that can be used to predict upper limits of the GOES-class magnitude of solar flares. The flare prediction scheme is based on the scaling of the slowly-varying potential energy $E_p(t)$, which is extrapolated in time over an interval of $\Delta t \le$ 24 hrs. The observed scaling of the dissipated energy $E_{diss}$ scales with the potential field energy as $E_{diss} \propto E_p^{1.32}$. In addition, the observed scaling relationship of the flare volume, $V \propto E_{diss}^{1.17}$, the multi-thermal energy, $E_{th} \propto V^{0.76}$, the flare emission measure $EM \propto E_{th}^{0.79}$, the EM-weighted temperature $T_{w}$, and the GOES flux, $F_8(t) \propto E_p(t)^{0.92}$, allows us then to predict an upper limit of the GOES-class flare magnitude in the extrapolated time window. We find a good correlation (CCC$\approx 0.7$) between the observed and predicted GOES-class flare magnitudes (in 172 X and M-class events). This is the first algorithm that employs observed scaling laws of physical flare parameters to predict GOES flux upper limits, an important capability that complements previous flare prediction methods based on machine-learning algorithms used in space weather forecasting.