2006/06/30 by T. Foglizzo, P. Galletti, L. Scheck +3 · 4 citations
Physics and Astronomy · #Accretion (finance) #Advection #Astrophysical Phenomena and Observations #Astrophysics #Astrophysics and Star Formation Studies #Gamma-ray bursts and supernovae #Instability #Limit cycle #Mechanics #Nonlinear system #Oscillation (cell signaling) #Physics #RADIUS #Shock (circulatory) #Thermodynamics #WKB approximation #astro-ph
paper · pdf · doi:10.1086/509612
published as Astrophys.J.654:1006-1021,2007 · 29 pages, 18 figures, to appear in ApJ (1 new Section, 2 new Figures)
arxiv created 2006/09/21 · openalex publication_date 2007/01/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We analyze the linear stability of a stalled accretion shock in a perfect gas with a parameterized cooling function ∝ ρ β-α P α . The instability is dominated by the l = 1 mode if the shock radius exceeds 2-3 times the accretor radius, depending on the parameters of the cooling function. The growth rate and oscillation period are comparable to those observed in the numerical simulations of Blondin & Mezzacappa. The instability mechanism is analyzed by separately measuring the efficiencies of the purely acoustic cycle and the advective-acoustic cycle. These efficiencies are estimated directly from the eigenspectrum and also through a WKB analysis in the high-frequency limit. Both methods prove that the advective-acoustic cycle is unstable and that the purely acoustic cycle is stable. Extrapolating these results to low frequency leads us to interpret the dominant mode as an advective-acoustic instability, different from the purely acoustic interpretation of Blondin & Mezzacappa. A simplified characterization of the instability is proposed, based on an advective-acoustic cycle between the shock and the radius r ∇ where the velocity gradients of the stationary flow are strongest. The importance of the coupling region in this mechanism calls for a better understanding of the conditions for an efficient advective-acoustic coupling in a decelerated, nonadiabatic flow, in order to extend these results to core-collapse supernovae.