A Lagrangian scheme for time-dependent ionization in simulations of astrophysical plasmas

Time-dependent ionization is important in astrophysical environments where the thermodynamical time scale is shorter than the ionization or recombination time scales. In this work, we report a FORTRAN program that performs fast non-equilibrium ionization calculations in post-processing based on hydrodynamics(HD) or magnetohydrodynamics(MHD) simulation results. Using HD or MHD simulation results, we track the movement of plasma in a Lagrangian framework, and obtain the evolutionary history of temperature and electron density. The time-dependent ionization equations are then solved by the Eigenvalue method. For any complex temperature and electron density histories, we introduce an adaptive time-step strategy to improve the computational efficiency. Our tests show that this program has advantages of high numerical stability and high accuracy. In addition, it is also easy to extend this solver to other HD and MHD simulations. This code is freely available for download from the Web.