On the time evolution of brightness, volume and height of a coronal source in an M-class flare

We study brightness, volume and heights of the X-ray thermal emission components for an M-class solar flare on 17 May 2012. Based on the RHESSI data availability, we present the results for 01:42–01:58 UT over the late-flare phase. It is observed that the spatial evolution of the thermal emission components 6–12 and 12–18 keV are well associated with the hottest plasma in the corona. Results show that the ascending height (\({\sim} 1.35 \times 10^{4}~\mbox{km}\)) and speed (\({\sim} 14.0~\mbox{km}\,\mbox{s}^{-1}\)) of coronal source component 6–12 keV is slightly smaller than the ascending height (\({\sim} 1.45 \times 10^{4}~\mbox{km}\)) and speed (\({\sim}15.1~\mbox{km}\,\mathrm{s}^{-1}\)) of the coronal source component 12–18 keV. Mean flux intensity (\(I_{\mathit{mean}}\)) of the 6–12 keV maintained a good fit (\(\chi^{2} = 0.41\)) with the corresponding volume (\(V\)) following strongly the power law [\(I_{\mathit{mean}} = (15.8\pm 0.21) V^{-1.28\pm 0.03}\)]. In contrast, the 12–18 keV maintained a weak fit (\(\chi^{2} = 2.37\)) following still the power law [\(I_{\mathit{mean}} = (0.19\pm 0.01)V^{-1.88\pm 0.16}\)]. The power law indices (\(-1.28 \pm 0.03; -1.88\pm 0.16\)) obtained by the observational analysis slightly differ from the power law index (−1.67) obtained by a theoretical model. The observations are consistent with adiabatic expansion of the coronal source component.