The stability of radiatively cooling jets .1. Linear analysis

The results of a spatial stability analysis of a two-dimensional slab jet, in which optically thin radiative cooling is dynamically important, are presented. We study both magnetized and unmagnetized jets at external Mach numbers of 5 and 20. We model the cooling rate by using two different cooling curves: one appropriate to interstellar gas, and the other to photoionized gas of reduced metallicity. Thus, our results will be applicable to both protostellar (Herbig-Haro) jets and optical jets from active galactic nuclei. We present analytical solutions to the dispersion relations in useful limits and solve the dispersion relations numerically over a broad range of perturbation frequencies. We find that the growth rates and wavelengths of the unstable Kelvin-Helmholtz (K-H) modes are significantly different from the adiabatic limit, and that the form of the cooling function strongly affects the results. In particular, if the cooling curve is a steep function of temperature in the neighborhood of the equilibrium state, then the growth of K-H modes is reduced relative to the adiabatic jet. On the other hand, if the cooling curve is a shallow function of temperature, then the growth of K-H modes can be enhanced relative to the adiabatic jet by the increase in cooling relative to heating in overdense regions. Inclusion of a dynamically important magnetic field does not strongly modify the important differences between an adiabatic jet and a cooling jet, provided the jet is highly supermagnetosonic and not magnetic pressure-dominated. In the latter case, the unstable modes behave more like the transmagnetosonic magnetic pressure-dominated adiabatic limit. We also plot fluid displacement surfaces associated with the various waves in a cooling jet in order to predict the structures that might arise in the nonlinear regime. This analysis predicts that low-frequency surface waves and the lowest order body modes will be the most effective at producing observable features in the jet.