Numerical simulations of protostellar jets with nonequilibrium cooling. I. Method and two-dimensional results

In a series of three papers, multidimensional time-dependent numerical simulations of the propagation of protostellar jets into both uniform and plane stratified ambient media are presented. For the first time these simulations combine a nonequilibrium treatment of optically thin radiative cooling with time-dependent hydrodynamics. Both two- and three-dimensional models are presented; synthetic emission maps and position velocity diagrams are constructed in the latter case for direct comparison to observations. This first paper concentrates on a description of the numerical algorithms needed to solve the coupled time-dependent hydrodynamics and nonequilibrium rate equation. A test problem based on the overstability of radiative shocks is detailed. Two-dimensional models of protostellar jets computed with both time-dependent nonequilibrium cooling and time-independent cooling using the assumption of complete ionization are compared. Substantial differences in the morphology of the jets in these two cases are noted and are attributable to differences in the effective cooling rates between the two formalisms for the same model parameters. The general characteristics of previous studies of nonadiabatic jets are recovered including the dependence of the degree of collimation of the jet and the size of its cocoon on the cooling strength, and the formation and fragmentation of a thin dense shell at the head of the jet. Two- and three-dimensional models of pulsed protostellar jets are presented in Paper II of this series, while Paper III focuses on three-dimensional simulations of steady jets.