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 importan t, are presented. We study both magnetized and unmagnetized jets at ex ternal Mach numbers of 5 and 20. We model the cooling rate by using tw o different cooling curves: one appropriate to interstellar gas, and t he other to photoionized gas of reduced metallicity. Thus, our results will be applicable to both protostellar (Herbig-Haro) jets and optica l jets from active galactic nuclei. We present analytical solutions to the dispersion relations in useful limits and solve the dispersion re lations numerically over a broad range of perturbation frequencies. We find that the growth rates and wavelengths of the unstable Kelvin-Hel mholtz (K-H) modes are significantly different from the adiabatic limi t, and that the form of the cooling function strongly affects the resu lts. In particular, if the cooling curve is a steep function of temper ature 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 t he increase in cooling relative to heating in overdense regions. Inclu sion of a dynamically important magnetic held does not strongly modify the important differences between an adiabatic jet and a cooling jet, provided the jet is highly supermagnetosonic and not magnetic pressur e-dominated. In the latter case, the unstable modes behave more like t he transmagnetosonic magnetic pressure-dominated adiabatic limit. We a lso 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 sur face waves and the lowest order body modes will be the most effective at producing observable features in the jet.