Magnetohydrodynamic Simulation of a Solar Flare with Chromospheric Evaporation Effect Based on the Magnetic Reconnection Model

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Abstract
Two-dimensional magnetohydrodynamic (MHD) simulation of a solar flare including the effect of anisotropic heat conduction and chromospheric evaporation based on the magnetic reconnection model is performed. In the simulation model, the coronal magnetic energy is converted to the thermal energy of plasma by magnetic reconnection. This energy is transported to the chromosphere by heat conduction along magnetic field lines and causes an increase in temperature and pressure of the chromospheric plasma. The pressure gradient force drives upward motion of the plasma toward the corona, i.e., chromospheric evaporation. This enhances the density of the coronal reconnected flare loops, and such evaporated plasma is considered to be the source of the observed soft X-ray emission of a flare. The results show that the temperature distribution is similar to the cusp-shaped structure of long-duration-event (LDE) flares observed by the soft X-ray telescope aboard the Yohkoh satellite. The simulation results are understood by a simple scaling law for the flare temperature described as where Ttop, B, ρ, and κ0 are the temperature at the flare loop top, coronal magnetic field strength, coronal density, and heat conduction coefficient, respectively. This formula is confirmed by the extensive parameter survey about B, κ0, and L in the simulation. The energy release rate is found to be described as a linearly increasing function of time: |dEm/dt| ≈ B2/(4π)VinCAt ≈ B2/(4π)0.1Ct, where Em is the magnetic energy, Vin is the inflow velocity, and CA is the Alfvén velocity. Thus, the second time derivative is found to be |d2Em/dt2| ∝ B4. We also find that the major feature of the reconnection inflow region is the expansion wave propagating outward from the magnetic neutral point. This expanded plasma has very low emission measure, which is 4 orders of magnitude smaller than that of the brightest feature in a flare. This explains the dimming phenomena associated with flares.