The linear stability of isothermal Bondi accretion with a shock is studiedanalytically in the asymptotic limit of high incident Mach number M_1. The flowis unstable with respect to radial perturbations as expected by Nakayama(1993), due to post-shock acceleration. Its growth time scales like theadvection time from the shock r_sh to the sonic point r_son. The growth rate ofnon-radial perturbations l=1 is higher by a factor M_1^{2/3}, and is thereforeintermediate between the advection and acoustic frequencies. Besides theseinstabilities based on post-shock acceleration, our study revealed anothergeneric mechanism based on the cycle of acoustic and vortical perturbationsbetween the shock and the sonic radius, independently of the sign of post-shockacceleration. The vortical-acoustic instability is fundamentally non-radial. Itis fed by the efficient excitation of vorticity waves by the isothermal shockperturbed by acoustic waves. The growth rate exceeds the advection rate by afactor log M_1. Unstable modes cover a wide range of frequencies from thefundamental acoustic frequency ~c/r_sh up to a cut-off ~c/r_son associated withthe sonic radius. The highest growth rate is reached for l=1 modes near thecut-off. The additional cycle of acoustic waves between the shock and the sonicradius is responsible for variations of the growth rate by a factor up to 3depending on its phase relative to the vortical-acoustic cycle. The instabilityalso exists, with a similar growth rate, below the fundamental acousticfrequency down to the advection frequency, as vorticity waves are efficientlycoupled to the region of pseudosound. These results open new perspectives toaddress the stability of shocked accretion flows.
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