Instabilities in Astrophysical Jets. I. Linear Analysis of Body and Surface Waves

In this paper, we investigate the instabilities of astrophysical jets in a new and more generalized way than in previous studies. We solve the dispersion equations for a thermally confined slab jet in a complex (k,ω domain. We find a number of singularities related to certain wave modes in this system. We show that the internal jet flow in the system is characterized by two internal sound waves, propagating against and with the flow, respectively. These two body waves grow in amplitude. The one propagating against the flow is condensed, which is crucial to disruption of jets. The other, propagating with the flow, is rarefied and less important in jet disruption. In addition, there are a number of surface waves existing in the interface between the jet flow and the ambient medium. Two of them are identified to couple to their relevant acoustic body waves. They also grow in amplitude. Our study in this paper suggests that the growing internal body waves and abundant growing surface waves can potentially explain the wealth of observed phenomena in astrophysical jets, such as quasi-periodic wiggles, jet disruption, limb- brightened features, and surface filaments. It also is a great help in understanding the plentiful features observed in numerical simulations. The predictions made in this paper will be directly compared with two- dimensional nonlinear numerical simulations in Paper II.