2019/01/14 by Eric R. Coughlin, Stephen Ro, Eliot Quataert · 15 citations
Physics and Astronomy · #Astrophysics and Cosmic Phenomena #Formalism (music) #Gamma-ray bursts and supernovae #Gravitation #Gravitational field #Laser-Plasma Interactions and Diagnostics #Perturbation (astronomy) #Radial velocity #Shock (circulatory) #Shock wave #Stability (learning theory) #astro-ph.HE
paper · pdf · doi:10.3847/1538-4357/ab09ec
published in The Astrophysical Journal 874(1), 58 (IOP Publishing) · ApJ Submitted
arxiv created 2019/01/14 · openalex created_date 2019/01/25 · openalex publication_date 2019/03/20 · arxiv updated 2019/04/03 · openalex updated_date 2026/08/05
Abstract Coughlin et al. derived and analyzed a new regime of self-similarity that describes weak shocks (Mach number of order unity) in the gravitational field of a point mass. These solutions are relevant to low-energy explosions, including failed supernovae. In this paper, we develop a formalism for analyzing the stability of shocks to radial perturbations, and we demonstrate that the self-similar solutions of Paper I are extremely weakly unstable to such radial perturbations. Specifically, we show that perturbations to the shock velocity and post-shock fluid quantities (the velocity, density, and pressure) grow with time as t α ; interestingly, we find that α ≲ 0.12, implying that the 10-folding timescale of such perturbations is roughly 10 orders of magnitude in time. We confirm these predictions by performing high-resolution, time-dependent numerical simulations. Using the same formalism, we also show that the Sedov–Taylor blast wave is trivially stable to radial perturbations provided that the self-similar, Sedov–Taylor solutions extend to the origin, and we derive simple expressions for the perturbations to the post-shock velocity, density, and pressure. Finally, we show that there is a third, self-similar solution (in addition to the solutions in Paper I and the Sedov–Taylor solution) to the fluid equations that describes a rarefaction wave, i.e., an outward-propagating sound wave. We interpret the stability of shock propagation in light of these three distinct self-similar solutions.