Jets from active galactic nuclei in the centers of galaxy clusters inflate cavities of low density relativistic plasma and drive shock and sound waves into the intracluster medium. When these waves overrun previously inflated cavities, they form a differentially rotating vortex through the Richtmyer-Meshkov instability. The dissipation of energy captured in the vortex can contribute to the feedback of energy into the atmospheres of cool core clusters. Using a series of hydrodynamic simulations we investigate the efficiency of this process: we calculate the kinetic energy in the vortex by decomposing the velocity field into its irrotational and solenoidal parts. Compared to the two-dimensional case, the 3-dimensional Richtmyer-Meshkov instability is about a factor of 2 more efficient. The energy in the vortex field for weak shocks is E_vortex ~ rho_ICM v_shock^2 V_bubble (with dependence on the geometry, density contrast, and shock width). For strong shocks, the vortex becomes dynamically unstable, quickly dissipating its energy via a turbulent cascade. We derive a number of diagnostics for observations and laboratory experiments of shock-bubble interactions, like the shock-vortex standoff distance, which can be used to derive lower limits on the Mach number. The differential rotation of the vortex field leads to viscous dissipation, which is sufficiently efficient to react to cluster cooling and to dissipate the vortex energy within the cooling radius of the cluster for a reasonable range of vortex parameters. For sufficiently large filling factors (of order a few percent or larger), this process could thus contribute significantly to AGN feedback in galaxy clusters.
We use a new non-parametric Bayesian approach to obtain the most probable mass distributions and circular velocity curves along with their confidence ranges, given deprojected density and temperature profiles of the hot gas surrounding X-ray bright elliptical galaxies. For a sample of six X-ray bright ellipticals, we find that all circular velocity curves are rising in the outer parts due to a combination of a rising temperature profile and a logarithmic pressure gradient that increases in magnitude. Comparing the circular velocity curves we obtain from X-rays to those obtained from dynamical models, we find that the former are often lower in the central ~10 kpc. This is probably due to a combination of: i) Non-thermal contributions of up to ~35% in the pressure (with stronger effects in NGC 4486), ii) multiple-temperature components in the hot gas, iii) incomplete kinematic spatial coverage in the dynamical models, and iv) mass profiles that are insufficiently general in the dynamical modelling. Complementing the total mass information from the X-rays with photometry and stellar population models to infer the dark matter content, we find evidence for massive dark matter haloes with dark matter mass fractions of ~35-80% at 2Re, rising to a maximum of 80-90% at the outermost radii. We also find that the six galaxies follow a Tully-Fisher relation with slope ~4 and that their circular velocities at 1Re correlate strongly with the velocity dispersion of the local environment. As a result, the galaxy luminosity at 1Re also correlates with the velocity dispersion of the environment. These relations suggest a close link between the properties of central X-ray bright elliptical galaxies and their environments (abridged).
