The Cosmic Ray Staircase: the Outcome of the Cosmic Ray Acoustic
  Instability
  Recently, cosmic rays (CRs) have emerged as a leading candidate for driving
galactic winds. Small-scale processes can dramatically affect global wind
properties. We run two-moment simulations of CR streaming to study how sound
waves are driven unstable by phase-shifted CR forces and CR heating. We verify
linear theory growth rates. As the sound waves grow non-linear, they steepen
into a quasi-periodic series of propagating shocks; the density jumps at shocks
create CR bottlenecks. The depth of a propagating bottleneck depends on both
the density jump and its velocity; {\Delta}P_c is smaller for rapidly moving
bottlenecks. A series of bottlenecks creates a CR staircase structure, which
can be understood from a convex hull construction. The system reaches a steady
state between growth of new perturbations, and stair mergers. CRs are decoupled
at plateaus, but exert intense forces and heating at stair jumps. The absence
of CR heating at plateaus leads to cooling, strong gas pressure gradients and
further shocks. If bottlenecks are stationary, they can drastically modify
global flows; if their propagation times are comparable to dynamical times,
their effects on global momentum and energy transfer are modest. The CR
acoustic instability is likely relevant in thermal interfaces between cold and
hot gas, as well as galactic winds. Similar to increased opacity in radiative
flows, the build-up of CR pressure due to bottlenecks can significantly
increase mass outflow rates, by up to an order of magnitude. It seeds unusual
forms of thermal instability, and the shocks could have distinct observational
signatures.
