Thermal and Magnetic Parameters in Solar Flares Derived from GOES X-Ray Light Curves

Abstract

Abstract The purpose of this study is to reproduce the GOES X-ray (1–8 ${Å}$) light curves of the impulsive phase of 20 solar flares and to estimate the thermal and magnetic parameters in flare loops. The expected X-ray light curves are calculated from the values of the coronal field strength and inflow velocity under some assumptions. We used the magnetic reconnection heating model of Shibata and Yokoyama (2002, ApJ, 577, 422), photospheric vector magnetic field data, and a simple 1-D flare loop model. It is found the maximum inflow velocities are $\sim $10$^{7} $cm s$^{-1}$, and that the maximum magnetic reconnection rates are 0.006–0.9, and further that the characteristic coronal field strengths are 6–100 G. Using the thermal and magnetic parameters derived, we found that geometrically our calculated flare loops are higher than the potential fields that model the postflare loops, and are also higher than the preflare loops containing magnetic free energy that is large enough to provide the thermal energy of a flare. Hence, we conclude that the plasma $\beta $ value would be near unity in the flare loops we studied, and the magnetic field lines shrunk during the decay phase. The downward velocities of the field-line shrinkage are estimated to be 10$^{6}$–10$^{7} $cm s$^{-1}$ except one event. The height of the reconnection point was roughly estimated to be from 10$^{10} $cm to 4 $\times$ 10$^{10} $cm. We propose a new interpretation of the Neupert effect, and also discuss a temporal relationship between the X-ray flux and the flare loop heating.