Edward C. D. Pope

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.

The effects of thermal conduction on the intracluster medium of 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. 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 timescales of roughly

Heating rate profiles in galaxy clusters

1.3-4.7 \times 10^{9}

Morphology of flows and buoyant bubbles in the Virgo cluster

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 conductvity is suppressed by a factor of at least 10 and probably more. Thus, we suggest that thermal conductvity, 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.

Cold gas in the intracluster medium: implications for flow dynamics and powering optical nebulae

In recent years evidence has accumulated suggesting that the gas in galaxy clusters is heated by non-gravitational processes. Here we calculate the heating rates required to maintain a physically motived mass flow rate, in a sample of seven galaxy clusters. We employ the spectroscopic mass deposition rates as an observational input along with temperature and density data for each cluster. On energetic grounds we find that thermal conduction could provide the necessary heating for A2199, Perseus, A1795 and A478. However, the suppression factor, of the clasical Spitzer value, is a different function of radius for each cluster. Based on the observations of plasma bubbles we also calculate the duty cycles for each AGN, in the absence of thermal conduction, which can provide the required energy input. With the exception of Hydra-A it appears that each of the other AGNs in our sample require duty cycles of roughly 106 ? 107 yrs to provide their steady-state heating requirements. If these duty cycles are unrealistic, this may imply that many galaxy clusters must be heated by very powerful Hydra-A type events interspersed between more frequent smaller-scale outbursts. The suppression factors for the thermal conductivity required for combined heating by AGN and thermal conduction are generally acceptable. However, these suppression factors still require ‘fine-tuning‘ of the thermal conductivity as a function of radius. As a consequence of this work we present the AGN duty cycle as a cooling flow diagnostic.

The generation of optical emission-line filaments in galaxy clusters

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 the hydrodynamical KuttaZhukovsky forces associated with the vortex ring structure of the bubbles, and discuss possible effects of diffusive processes on their evolution.

Investigating the properties of active galactic nucleus feedback in hot atmospheres triggered by cooling-induced gravitational collapse: AGN triggered by gravitational collapse

We show that the mechanical energy-injection rate generated as the intracluster medium (ICM) flows around cold clouds may be sufficient to power the optical and near-infrared emission of nebulae observed in the central regions of a sample of seven galaxy clusters. The energy-injection rate is extremely sensitive to the velocity difference between the ICM and cold clouds, which may help to explain why optical and infrared luminosity is often larger than expected in systems containing active galactic nuclei. We also find that mass recycling is likely to be important for the dynamics of the ICM. This effect will be strongest in the central regions of clusters where there is more than enough cold gas for its evaporation to contribute significantly to the density of the hot phase.

Buoyant Bubbles in the Virgo Cluster

Recent data support the idea that the filaments observed in Ha emission near the centres of some galaxy clusters were shaped by bulk flows within their intracluster medium (ICM). We present numerical simulations of evaporated clump material interacting with impinging winds to investigate this possibility. In each simulation, a clump falls due to gravity while the drag of a wind retards the fall of evaporated material leading to elongation of the tail. However, we find that long filaments can only form if the outflowing wind velocity is sufficiently large, ∼10 8 cm s -1 . Otherwise, the tail material sinks almost as quickly as the cloud. For reasonable values of parameters, the morphological structure of a tail is qualitatively similar to those observed in clusters. Under certain conditions, the kinematics of the tail resemble those reported in Hatch et al. A comparison of the observations with the numerical results indicates that the filaments are likely to be a few tens of Myr old. We also present arguments which suggest that the momentum transfer, from an outflowing wind, in the formation of these filaments is probably significant. As a result, tail formation could play a role in dissipating some of the energy injected by a central active galactic nuclei (AGN) close to the cluster centre where it is needed most. The trapping of energy by the cold gas may provide an additional feedback mechanism that helps to regulate the heating of the central regions of galaxy clusters and couple the AGN to the ICM.

γ‐ray emission associated with cluster‐scale AGN outbursts

Radiative cooling may plausibly cause hot gas in the centre of a massive galaxy, or galaxy cluster, to become gravitationally unstable. The subsequent collapse of this gas on a dynamical time-scale can provide an abundant source of fuel for active galactic nucleus (AGN) heating and star formation. Thus, this mechanism provides a way to link the AGN accretion rate to the global properties of an ambient cooling flow, but without the implicit assumption that the accreted material must have flowed on to the black hole from tens of kpc away. It is shown that a fuelling mechanism of this sort naturally leads to a close balance between AGN heating and the radiative cooling rate of the hot, X-ray-emitting halo. Furthermore, AGN powered by cooling-induced gravitational instability would exhibit characteristic duty cycles (δ) which are redolent of recent observational findings: δ∝ LX/σ3*, where LX is the X-ray luminosity of the hot atmosphere and σ* is the central stellar velocity dispersion of the host galaxy. Combining this result with well-known scaling relations, we deduce a duty cycle for radio AGNs in elliptical galaxies that is approximately ∝ M1.5BH, where MBH is the central black hole mass. Outburst durations and Eddington ratios are also given. Based on the results of this study, we conclude that gravitational instability could provide an important mechanism for supplying fuel to AGNs in massive galaxies and clusters, and warrants further investigation.

Dynamics of buoyant bubbles in clusters of galaxies

In this study we have constructed and tested 3D numerical model of the Virgo cluster, the core of which is thermally supported by the bubbles produced by the active galactic nucleus of the central galaxy. The physical properties of the plasma (intracluster medium, ICM) are not precisely known. Usually the ICM models use the values of thermal diffusivity and kinematic viscosity calculated in the classical work of Spitzer [10] (see also review by M. Ruszkowski in this volume). It is accepted, however, that magnetic fields decrease the diffusivity, since they suppress movements of charged particles across the field lines. The same is believed to be true for the value of the viscosity as well. Usually a fraction of the Spitzer value is used to approximate thermal diffusivity of the ICM [3, 6], which assumes chaotic orientation of magnetic field lines (i.e., magnetic field lines are bent on scales smaller than the mean free path of an electron in the plasma).