Numerical MHD Simulations of Reconnection in Solar Flares: Effects of the Magnetic-Field Strength in the Current Sheet

We simulate the evolution of reconnection in solar flares to study the influence of magnetic-field strength and thermal conduction on the dynamics of the magnetic-reconnection and energy-conversion processes. For this, we solve the 2.5D resistive magnetohydrodynamics (MHD) equations with thermal conduction on a domain that contains the chromosphere–corona interface. The flare is triggered at a null point where a Gaussian resistivity distribution is maximum, and further evolution is tracked. The parameter space considers magnetic-field strength [B0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$B_{0}$\end{document}] between 22 G and 50 G, and thermal conductivity [κ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\kappa $\end{document}] in the range from zero to 10−11\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$10^{-11}$\end{document} W m−1K−7/2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$^{-7/2}$\end{document}. In this parameter space, we find that the magnetic field determines the reconnection rate, which can change by a 100% in the range of B0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$B_{0}$\end{document}, whereas thermal conduction can induce a rate change of at most 10%. We also measure the evolution of magnetic, internal, and kinetic energies in a region just above the reconnection point and measure their interplay. For all simulations, magnetic energy dominates initially and relaxes on a time scale of about 20 seconds. In this interval, the magnetic energy drops by ≈50%\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\approx 50\%$\end{document}, whereas the internal energy grows by ≈100%\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\approx 100\%$\end{document}. During the process, part of the energy becomes kinetic, which pushes the reconnection jet upwards and is bigger for the bigger B0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$B_{0}$\end{document} and smaller κ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\kappa $\end{document}.