Energetic Relations between the Disappearing Solar Filaments and the Associated Flare Arcades

Abstract

Abstract We present the temporal and statistical relations between the mechanical energies of disappearing solar filaments and the thermal energies of the associated flare arcades in soft X-rays. Measuring the 3-D velocity fields of 10 eruptive filaments, we calculated their mechanical energy gain rate, $\epsilon_{\rm mc}$, per unit volume and compared it to the thermal energy release rate per unit volume, $\epsilon_{\rm th}$, derived with Yohkoh/SXT data. For the statistical relation, we found a relation that can be approximated as $\epsilon_{\rm th} \propto \epsilon_{\rm mc}^{1.9}$. This relation can be explained by interpreting the energy input to an arcade via the Poynting flux in the magnetic reconnection process and the acceleration of a filament by the Lorentz force. This explanation is also supported by the strong dependence of the observed increase rates of both the thermal and mechanical energy densities on the mean magnetic field strength of the source region. We also investigated their temporal variations, and found that the start time of increase in the mechanical energy of a filament preceded that of the thermal energy of the coronal arcade in some cases. These relations imply that the basic mechanisms that accelerate a filament and create a hot plasma are different, and both energy increase rates are determined primary by the magnetic field strengths.