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.
