The stability of buoyant bubbles in the atmospheres of galaxy clusters

The buoyant rise of hot plasma bubbles inflated by active galactic nuclei outflows in galaxy clusters can heat the cluster gas and thereby compensate radiative energy losses of this material. Numerical simulations of this effect often show the complete disruption of the bubbles followed by the mixing of the bubble material with the surrounding cluster gas due to fluid instabilities on the bubble surface. This prediction is inconsistent with the observations of apparently coherent bubble structures in clusters. We derive a general description in the linear regime of the growth of instabilities on the surface between two fluids under the influence of a gravitational field, viscosity, surface tension provided by a magnetic field and relative motion of the two fluids with respect to each other. We demonstrate that Kelvin–Helmholtz instabilities are always suppressed, if the fluids are viscous. They are also suppressed in the inviscid case for fluids of very different mass densities. We show that the effects of shear viscosity as well as a magnetic field in the cluster gas can prevent the growth of Rayleigh–Taylor instabilities on relevant scalelengths. Rayleigh–Taylor instabilities on parsec scales are suppressed even if the kinematic viscosity of the cluster gas is reduced by two orders of magnitude compared to the value given by Spitzer for a fully ionized, unmagnetized gas. Similarly, magnetic fields exceeding a few ?G result in an effective surface tension preventing the disruption of bubbles. For more massive clusters, instabilities on the bubble surface grow faster. This may explain the absence of thermal gas in the north-west bubble observed in the Perseus cluster compared to the apparently more disrupted bubbles in the Virgo cluster

Stochastic heating of cooling flows

It is generally accepted that the heating of gas in clusters of galaxies by active galactic nuclei (AGN) is a form of feedback. Feedback is required to ensure a long term, sustainable balance between heating and cooling. This work investigates the impact of proportional stochastic feedback on the energy balance in the intracluster medium. Using a generalised analytical model for a cluster atmosphere, it is shown that an energy equilibrium can be reached exponentially quickly. Applying the tools of stochastic calculus it is demonstrated that the result is robust with regard to the model parameters, even though they affect the amount of variability in the system.Comment: 7 pages, 6 figures, accepted by MNRAS, http://www.astro.soton.ac.uk/~gbp/pub/pavlovski_stochh.pd

Hydrodynamical simulations of the decay of high-speed molecular turbulence. I. Dense molecular regions

We present the results from three dimensional hydrodynamical simulations of decaying high-speed turbulence in dense molecular clouds. We compare our results, which include a detailed cooling function, molecular hydrogen chemistry and a limited C and O chemistry, to those previously obtained for decaying isothermal turbulence. After an initial phase of shock formation, power-law decay regimes are uncovered, as in the isothermal case. We find that the turbulence decays faster than in the isothermal case because the average Mach number remains higher, due to the radiative cooling. The total thermal energy, initially raised by the introduction of turbulence, decays only a little slower than the kinetic energy. We discover that molecule reformation, as the fast turbulence decays, is several times faster than that predicted for a non-turbulent medium. This is caused by moderate speed shocks which sweep through a large fraction of the volume, compressing the gas and dust. Through reformation, the molecular density and molecular column appear as complex patterns of filaments, clumps and some diffuse structure. In contrast, the molecular fraction has a wider distribution of highly distorted clumps and copious diffuse structure, so that density and molecular density are almost identically distributed during the reformation phase. We conclude that molecules form in swept-up clumps but effectively mix throughout via subsequent expansions and compressions.Comment: 12 pages, 12 figures; For a version of the article with higher resolution figures, see http://star.arm.ac.uk/preprints/381.p

Mass transport by buoyant bubbles in galaxy clusters

We investigate the effect of three important processes by which AGN-blown bubbles transport material: drift, wake transport and entrainment. The first of these, drift, occurs because a buoyant bubble pushes aside the adjacent material, giving rise to a net upward displacement of the fluid behind the bubble. For a spherical bubble, the mass of upwardly displaced material is roughly equal to half the mass displaced by the bubble, and should be ~ 10^{7-9} solar masses depending on the local ICM and bubble parameters. We show that in classical cool core clusters, the upward displacement by drift may be a key process in explaining the presence of filaments behind bubbles. A bubble also carries a parcel of material in a region at its rear, known as the wake. The mass of the wake is comparable to the drift mass and increases the average density of the bubble, trapping it closer to the cluster centre and reducing the amount of heating it can do during its ascent. Moreover, material dropping out of the wake will also contribute to the trailing filaments. Mass transport by the bubble wake can effectively prevent the build-up of cool material in the central galaxy, even if AGN heating does not balance ICM cooling. Finally, we consider entrainment, the process by which ambient material is incorporated into the bubble. AbridgedComment: Accepted for publication in MNRAS. 17 pages, 4 figures, 2 tables. Formatted for letter paper and adjusted author affiliations

The effect of thermal conduction on the Virgo cluster

Thermal conduction has been suggested as a possible mechanism by which sufficient energy is supplied to the central regions of galaxy clusters to balance the effect of radiative cooling. Recent high resolution observations of the nearby Virgo cluster make it an ideal subject for an attempt to reproduce the properties of the cluster by numerical simulations, since most of the defining parameters are comparatively well known. Here we present the results of a simulated high-resolution, 3-d Virgo cluster for different values of thermal conductivity (1, 1/10, 1/100, 0 times the full Spitzer value). Starting from an initially isothermal cluster atmosphere we allow the cluster to evolve freely over time scales of roughly 1.3-4.7×109 yrs. Our results show that thermal conductivity at the Spitzer value can increase the central ICM radiative cooling time by a factor of roughly 3.6. In addition, for larger values of thermal conductvity the simulated temperature and density profiles match the observations significantly better than for the lower values. However, no physically meaningful value of thermal conductivity was able to postpone the cooling catastrophe (characterised by a rapid increase in the central density) for longer than a fraction of the Hubble time nor explain the absence of a strong cooling flow in the Virgo cluster today. We also calculate the effective adiabatic index of the cluster gas for both simulation and observational data and compare the values with theoretical expectations. Using this method it appears that the Virgo cluster is being heated in the cluster centre by a mechanism other than thermal conductivity. Based on this and our simulations it is also likely that the thermal conductivity is suppressed by a factor of at least 10 and probably more. Thus, we suggest that thermal conductivity, if present at all, has the effect of slowing down the evolution of the ICM, by radiative cooling, but only by a factor of a few

Morphology of flows and buoyant bubbles in the Virgo cluster

There is growing evidence that the active galactic nuclei (AGN) associated with the central elliptical galaxy in clusters of galaxies are playing an important role in the evolution of the intracluster medium (ICM) and clusters themselves.We use high-resolution three-dimensional simulations to study the interaction of the cavities created by AGN outflows (bubbles) with the ambient ICM. The gravitational potential of the cluster is modelled using the observed temperature and density profiles of the Virgo cluster. We demonstrate the importance of thehydrodynamical Kutta–Zhukovsky forces associated with the vortex ring structure of the bubbles, and discuss possible effects of diffusive processes on their evolution