Georgi Pavlovski

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

Mass transport by buoyant bubbles in galaxy clusters

1.3-4.7 \times 10^{9}

Heating rate profiles in galaxy clusters

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.

Morphology of flows and buoyant bubbles in the Virgo cluster

We investigate the effect of three important processes by which active galactic nuclei (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 M ⊙ depending on the local intracluster medium (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 buildup 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. Studies of observed bubbles show that they subtend an opening angle much larger than predicted by simple adiabatic expansion. We show that bubbles that entrain ambient material as they rise will expand faster than the adiabatic prediction; however, the entrainment rate required to explain the observed opening angle is large enough that the density contrast between the bubble and its surroundings would disappear rapidly. We therefore conclude that entrainment is unlikely to be a dominant mass transport process. Additionally, this also suggests that the bubble surface is much more stable against instabilities that promote entrainment than expect for pure hydrodynamic bubbles.

Hydrodynamical simulations of the decay of high-speed molecular turbulence - II. Divergence from isothermality

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.

A relativistic mixing-layer model for jets in low-luminosity radio galaxies

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.

Stochastic heating of cooling flows

A roughly constant temperature over a wide range of densities is maintained in molecular clouds through radiative heating and cooling. An isothermal equation of state is therefore frequently employed in molecular cloud simulations. However, the dynamical processes in molecular clouds include shock waves, expansion waves, cooling induced collapse and baroclinic vorticity, all incompatible with the assumption of a purely isothermal flow. Here, we incorporate an energy equation including all the important heating and cooling rates and a simple chemical network into simulations of 3D, hydrodynamic, decaying turbulence. This allows us to test the accuracy of the isothermal assumption by directly comparing a model run with the modified energy equation to an isothermal model. We compute an extreme case in which the initial turbulence is sufficiently strong to dissociate much of the gas and alter the specific heat ratio. The molecules then reform as the turbulence weakens. We track the true specific heat ratio as well as its effective value. We analyse power spectra, vorticity and shock structures, and discuss scaling laws for decaying turbulence. We derive some limitations to the isothermal approximation for simulations of the interstellar medium using simple projection techniques. Overall, even given the extreme conditions, we find that an isothermal flow provides an adequate physical and observational description of many properties. The main exceptions revealed here concern behaviour directly related to the high-temperature zones behind the shock waves.

Buoyant Bubbles in the Virgo Cluster

We present an analytical model for jets in Fanaroff & Riley Class I (FR I) radio galaxies, in which an initially laminar, relativistic flow is surrounded by a shear layer. We apply the appropriate conservation laws to constrain the jet parameters, starting the model where the radio emission is observed to brighten abruptly. We assume that the laminar flow fills the jet there and that pressure balance with the surroundings is maintained from that point outwards. Entrainment continuously injects new material into the jet and forms a shear layer, which contains material from both the environment and the laminar core. The shear layer expands rapidly with distance until finally the core disappears, and all of the material is mixed into the shear layer. Beyond this point, the shear layer expands in a cone and decelerates smoothly. We apply our model to the well-observed FR I source 3C 31 and show that there is a self-consistent solution. We derive the jet power, together with the variations of mass flux and entrainment rate with distance from the nucleus. The predicted variation of bulk velocity with distance in the outer parts of the jets is in good agreement with model fits to Very Large Array observations. Our prediction for the shape of the laminar core can be tested with higher-resolution imaging.

The entrainment-limited evolution of FR II sources: maximum sizes and a possible connection to FR Is

It is generally accepted that the heating of gas in clusters of galaxies by active galactic nuclei 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 generalized 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.