Instability of Supersonic Cold Streams Feeding Galaxies I: Linear Kelvin-Helmholtz Instability with Body Modes

Massive galaxies at high redshift are predicted to be fed from the cosmic web by narrow, dense, cold streams. These streams penetrate supersonically through the hot medium encompassed by a stable shock near the virial radius of the dark-matter halo. Our long-term goal is to explore the heating and dissipation rate of the streams and their fragmentation and possible breakup, in order to understand how galaxies are fed, and how this affects their star-formation rate and morphology. We present here the first step, where we analyze the linear Kelvin-Helmholtz instability (KHI) of a cold, dense slab or cylinder flowing through a hot, dilute medium in the transonic regime. The current analysis is limited to the adiabatic case with no gravity and assuming equal pressure in the stream and the medium. By analytically solving the linear dispersion relation, we find a transition from a dominance of the familiar rapidly growing surface modes in the subsonic regime to more slowly growing body modes in the supersonic regime. The system is parameterized by three parameters: the density contrast between the stream and the medium, the Mach number of stream velocity with respect to the medium, and the stream width with respect to the halo virial radius. We find that a realistic choice for these parameters places the streams near the mode transition, with the KHI exponential-growth time in the range 0.01-10 virial crossing times for a perturbation wavelength comparable to the stream width. We confirm our analytic predictions with idealized hydrodynamical simulations. Our linear-KHI estimates thus indicate that KHI may in principle be effective in the evolution of streams by the time they reach the galaxy. More definite conclusions await the extension of the analysis to the nonlinear regime and the inclusion of cooling, thermal conduction, the halo potential well, self-gravity and magnetic fields.