Time-dependent MHD shocks and line intensity ratios in the HH 30 jet: a focus on cooling function and numerical resolution

Context. The coupling between time-dependent, multidimensional MHD numerical codes and radiative line emission is of utmost importance in the studies of the interplay between dynamical and radiative processes in many astrophysical environments, with particular interest for problems involving radiative shocks. There is a widespread consensus that line emitting knots observed in Herbig-Haro jets can be interpreted as radiative shocks. Velocity perturbations at the jet base steepen into shocks to emit the observed spectra. To derive the observable characteristics of the emitted spectra, such as line intensity ratios, one has to study physical processes that involve the solution of the MHD equations coupled with radiative cooling in non-equilibrium conditions. Aims. In this paper we address two different aspects relevant to the time-dependent calculations of the line intensity ratios of forbidden transitions, resulting from the excitation by planar, time-dependent radiative shocks traveling in a stratified medium. The first one concerns the impact of the radiation and ionization processes included in the cooling model, and the second one the effects of the numerical grid resolution. Methods. Dealing with both dynamical and radiative processes in the same numerical scheme means to treat phenomena characterized by different time and length scales. This may be especially arduous and computationally expensive when discontinuities are involved, such as in the case of shocks. Adaptive mesh refinement (AMR) methods have been introduced in order to alleviate these difficulties. In this paper we apply the AMR methodology to the treatment of radiating shocks and show how this method is able to vastly reduce the integration time. Results. The technique is applied to the knots of the HH 30 jet to obtain the observed line intensity ratios and derive the physical parameters, such as density, temperature and ionization fraction. We consider the impact of two different cooling functions and different grid resolutions on the results. Conclusions. We conclude that the use of different cooling routines has effects on results whose weight depends upon the line ratio considered. Moreover, we find the minimum numerical resolution of the simulation grid behind the shock to achieve convergence in the results. This is crucial for the forthcoming 2D calculations of radiative shocks.