A hydrodynamical analysis of the steady-state shock model

TL;DR

This paper critically examines the steady-state shock model in hydrodynamics, revealing its limitations and questioning its applicability in astrophysical contexts, and advocates for time-dependent models as more accurate alternatives.

Contribution

The paper provides a detailed review of the hydrodynamical limitations of the steady-state shock model and discusses when its use is appropriate or should be replaced.

Findings

Steady-state assumption often cannot be satisfied in practical contexts.

Without boundary conditions, the model lacks physical relevance.

Time-dependent models better describe post-shock structures.

Abstract

In this article some of the hydrodynamical (HD) aspects of steady shocks as described by the steady-state shock model are reviewed and discussed. It is found that, at least in some of the contexts in which the steady-state model is used, the steady-state assumption cannot be satisfied. Moreover, the main result of the present work is that even if the assumptions on steadiness and on the geometry are fully satisfied, serious limitations in the application of the model are found: (i) in the absence of down-stream boundary conditions the model is not related to the physical process(es) that originate the shock, (ii) matter shocked during the presumed phase of steadiness of the shock is not hydrodynamically interacting with previously shocked matter, and (iii) the steady-state model assumes that the flow is stable against perturbations. Furthermore, even if boundary conditions were assumed, the link between the steady model and the astrophysical context would not be strictly speaking the correct HD link. Time-dependent HD computations in different astrophysical contexts (e.g. SNRs and molecular shocks) show that the steady-state approximation is inadequate to describe these post-shock structures. Based on the HD limitations of the steady-state model, it is advised that the model be used to describe post-shock structures only in those astrophysical contexts where full time-dependent HD models have already positively tested the steadiness of the flow. Alternatively, it is suggested to replace the steady-state model either with time-dependent HD models, or with less problematic approximations.