Internal Shocks Hydrodynamics: the Collision of Two Cold Shells in Detail

TL;DR

This paper models the hydrodynamics of internal shocks from collisions of two cold shells in astrophysical transients, revealing differences in shock behavior and energy transfer mechanisms relevant to phenomena like GRBs and supernovae.

Contribution

It provides a detailed planar hydrodynamic analysis of shell collisions, highlighting the asymmetry between forward and reverse shocks and their impact on energy dissipation.

Findings

Reverse shock often dominates energy production.

Rarefaction waves can limit shock energy dissipation.

Energy transfer across contact discontinuity is significant.

Abstract

Emission in many astrophysical transients originates from a shocked fluid. A central engine typically produces an outflow with varying speeds, leading to internal collisions within the outflow at finite distances from the source. Each such collision produces a pair of forward and reverse shocks with the two shocked regions separated by a contact discontinuity (CD). As a useful approximation, we consider the head-on collision between two cold and uniform shells (a slower leading shell and a faster trailing shell) of finite radial width, and study the dynamics of shock propagation in planar geometry. We find significant differences between the forward and reverse shocks, in terms of their strength, internal energy production efficiency, and the time it takes for the shocks to sweep through the respective shells. We consider the subsequent propagation of rarefaction waves in the shocked regions and explore the cases where these waves can catch up with the shock fronts and thereby limit the internal energy dissipation. We demonstrate the importance of energy transfer from the trailing to leading shell through $pdV$ work across the CD. We outline the parameter space regions relevant for models of different transients,e.g., Gamma-ray burst (GRB) internal shock model, fast radio burst (FRB) blastwave model, Giant flare due to magnetars, and superluminous supernovae (SLSN) ejecta. We find that the reverse shock likely dominates the internal energy production for many astrophysical transients.