On the Decelerating Shock Instability of Plane-Parallel Slab with Finite Thickness

Dynamical stability of the shock compressed layer with finite thickness is investigated. It is characterized by self-gravity, structure, and shock condition at the surfaces of the compressed layer. At one side of the shocked layer, its surface condition is determined via the ram pressure, while at the other side the thermal pressure supports its structure. When the ram pressure dominates the thermal pressure, we expect deceleration of the shocked layer. Especially, in this paper, we examine how the stratification of the decelerating layer has an effect on its dynamical stability. Performing the linear perturbation analysis, a more general dispersion relation than the previous one obtained by one of the authors is derived. It gives us an interesting information about the stability of the decelerating layer; When the deceleration of the layer dominates the self-gravity, the so-called DSI (Decelerating Shock Instability) is efficient, while the gravitational instability occurs when the self-gravity works better than the deceleration. The length-scales of the two instabilities are the order of the width of the decelerating layer. Their growth time-scales are the order of the free-fall time in the density of the shocked slab. Importantly, they are always incompatible. We also consider the evolution effect of the shocked layer. In the early stages of its evolution, only DSI occurs. On the contrary, in the late stages, it is possible for the shocked layer to be unstable for the DSI (in smaller scale) and the gravitational instability (in larger scale), ordinary. The onset-time of the gravitational instability is the order of the free-fall time of the external medium. After onset, as shown above, growth time-scale becomes the free-fall time of the dense slab, which is much shorter than the free-fall time of the external – 2 – medium. Furthermore, we find there is a stable range of wavenumbers against both the DSI and the gravitational instability between respective unstable wavenumber ranges. These stable modes suggest the ineffectiveness of DSI for the fragmentation of the decelerating slab. Thus, in various cases, the structure of the shocked layer should be determined when its stability is discussed. Subject headings: hydrodynamics — instabilities — shock waves — stars:formation