The structure of nearly isothermal, adiabatic shock waves

ABSTRACT An explosively generated shock wave with time-dependent radius R(t) is characterized by a phase in which the shocked gas becomes radiative with an effective adiabatic index γ ≃ 1. Using the result that the post-shock gas is compressed into a shell of width ΔR/R ≃ δ, where δ = γ − 1, we show that a choice of self-similar variable that exploits this compressive behaviour in the limit that γ → 1 naturally leads to a series expansion of the post-shock fluid density, pressure, and velocity in the small quantity δ. We demonstrate that the leading-order (in δ) solutions, which are increasingly accurate as γ → 1, can be written in simple, closed forms when the fluid is still approximated to be in the energy-conserving regime (i.e. the Sedov–Taylor limit), and that the density declines exponentially rapidly with distance behind the shock. We also analyse the solutions for the bubble surrounding a stellar or galactic wind that interacts with its surroundings, and derive expressions for the location of the contact discontinuity that separates the shocked ambient gas from the shocked wind. We discuss the implications of our findings in the context of the dynamical stability of nearly isothermal shocks.

The isothermal evolution of a shock-filament interaction

ABSTRACT Studies of filamentary structures that are prevalent throughout the interstellar medium are of great significance to a number of astrophysical fields. Here, we present 3D hydrodynamic simulations of shock-filament interactions where the equation of state has been softened to become almost isothermal. We investigate the effect of such an isothermal regime on the interaction (where both the shock and filament are isothermal), and we examine how the nature of the interaction changes when the orientation of the filament, the shock Mach number, and the filament density contrast are varied. We find that only sideways-oriented filaments with a density contrast of 102 form a three-rolled structure, dissimilar to the results of a previous study. Moreover, the angle of orientation of the filament plays a large role in the evolution of the filament morphology: the greater the angle of orientation, the longer and less turbulent the wake. Turbulent stripping of filament material leading to fragmentation of the core occurs in most filaments; however, filaments orientated at an angle of 85° to the shock front do not fragment and are longer lived. In addition, values of the drag time are influenced by the filament length, with longer filaments being accelerated faster than shorter ones. Furthermore, filaments in an isothermal regime exhibit faster acceleration than those struck by an adiabatic shock. Finally, we find that the drag and mixing times of the filament increase as the angle of orientation of the filament is increased.

Turbulent adiabatic shock waves and diffusive particle acceleration

We investigate the properties of turbulent adiabatic shock waves resulting from the self-consistent inclusion of finite Alfvén-wave pressure in the shock balance equations. We demonstrate (i) the absence of a switch-on shock; (ii) the existence of two separated domains where the Mach number is greater than unity that have gas compression, and an associated domain where the gas compression ratio is less than unity (i.e. a rarefaction domain); (iii) the difference between the scattering-centre compression ratio and the gas compression ratio for all upstream wave cross-helicity values except for the isolated case of zero helicity; (iv) the presence of anomalous domains where the cosmic-ray particle spectral index can be negative. All of these results are brought about by including the upstream and downstream turbulent wave energies in the shock balance structure. Without the waves, none of the effects persists.