Stability of Cosmic Ray Modified Shocks: Two-Fluid Approach

TL;DR

This study uses numerical simulations to analyze the stability of cosmic ray modified shocks, revealing that certain solutions are stable while others are unstable, which impacts the understanding of cosmic ray acceleration efficiency.

Contribution

It demonstrates the stability characteristics of multiple solutions in a two-fluid model of CRMS, highlighting the robustness of the bistable nature across parameters.

Findings

Efficient and inefficient solutions are stable under perturbations.

Intermediate solutions are unstable and evolve into inefficient states.

CR production efficiency at supernova shocks may be lower than previously thought.

Abstract

The stability of the cosmic ray modified shock (CRMS) is studied by means of numerical simulations. Owing to the nonlinear feedback of cosmic-ray (CR) acceleration, a downstream state of the modified shock can no longer be uniquely determined for given upstream parameters. It is known that up to three distinct solutions exist, which are characterized by the CR production efficiency as "efficient", "intermediate" and "inefficient" branches. The stability of these solutions is investigated by performing direct time-dependent simulations of a two-fluid model. It is found that both the efficient and inefficient branches are stable even against a large-amplitude perturbation, while the intermediate one is always unstable and evolves into the inefficient state as a result of nonlinear time development. This bistable feature is robust in a wide range of parameters and does not depend on the injection model. Fully nonlinear time evolution of a hydrodynamic shock with injection results in the least efficient state in terms of the CR production, consistent with the bistable feature. This suggests that the CR production efficiency at supernova remnant shocks may be lower than previously discussed in the framework of the nonlinear shock acceleration theory considering the efficient solution of the CRMS.