Non-radial instabilities of isothermal Bondi accretion with a shock: Vortical-acoustic cycle vs. post-shock acceleration

The linear stability of isothermal Bondi accretion with a shock is studied analytically in the asymptotic limit of high incident Mach number M-1. The flow is unstable with respect to radial perturbations as expected by Nakayama (1993), due to post-shock acceleration. Its growth-time scales like the advection time from the shock r(sh) to the sonic point r(son). The growth rate of non-radial perturbations l = 1 is higher by a factor M-1(2/3), and is therefore intermediate between the advection and acoustic frequencies. Besides these instabilities based on post-shock acceleration, our study revealed another generic mechanism based on the cycle of acoustic and vortical perturbations between the shock and the sonic radius, independently of the sign of post-shock acceleration. The vortical-acoustic instability is fundamentally non-radial. It is fed by the efficient excitation of vorticity waves by the isothermal shock perturbed by acoustic waves. The growth rate exceeds the advection frequency by a factor log M-1. Unstable modes cover a wide range of frequencies from the fundamental acoustic frequency similar toc/r(sh) up to a cut-off similar toc/r(son) associated with the sonic radius. The highest growth rate is reached for l = 1 modes near the cut-off. The additional cycle of acoustic waves between the shock and the sonic radius is responsible for variations of the growth rate by a factor up to 3 depending on its phase relative to the vortical-acoustic cycle. The instability also exists, with a similar growth rate, below the fundamental acoustic frequency down to the advection frequency, as vorticity waves are efficiently coupled to the region of pseudosound. These results open new perspectives to address the stability of shocked accretion flows.