arXiv subjects

Edward C. D. Pope

Publications and source records attributed to Edward C. D. Pope.

12 recordsLinked to original sources

arXiv2012

Why and when is internally-driven AGN feedback energetically favoured?

AGN outflows are the heat given up when gas in a galaxy evolves towards thermodynamic equilibrium. Indeed, while AGN feedback regulates the growth of massive galaxies, its origins can be understood as the spontaneous thermodynamic process which ensures that the (Gibbs) free energy of the system always decreases, enabling the galaxy to reach a more energetically favourable state. In particular, it is shown that feedback heating processes will be favoured whenever the hot atmosphere of a galaxy would effectively gain energy as a result of cooling. For example, as the hot atmosphere of a galaxy cools and contracts, the work done by gravity will be thermalised, with a fraction of the gas also being captured by stars and the supermassive black hole at the centre of the galaxy. If this gain of energy exceeds the loss of energy that occurs when cooling gas drops out of the atmosphere, the Gibbs free energy of the system would increase overall. Since this is energetically unfavourable, feedback heating is initiated which acts to reduce the net cooling rate of the atmosphere, thereby preventing any build-up of energy. The Gibbs free energy can also decrease in the absence of feedback heating, but only if the loss of energy due to mass dropping out of the atmosphere exceeds the gains of energy described above. Therefore, to ensure that the Gibbs free energy always decreases, a galaxy will necessarily flip between these two states, experiencing episodes of heating and cooling. Due to the close long-term balance between heating and cooling, the gas in a galaxy will evolve quasi-statically towards thermodynamic equilibrium, which has the observable appearance of galaxy growth being regulated by AGN feedback. The same mechanism also provides an explanation for why strong AGN feedback occurs more frequently in cool-core galaxy clusters than in non cool-core clusters.

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arXiv2011

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

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 timescale can provide an abundant source of fuel for 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 onto the black hole from 10s of kiloparsecs 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 (delta) which are redolent of recent observational findings: delta is proportional to L_X/sigma_{*}^{3}, where L_X is the X-ray luminosity of the hot atmosphere, and sigma_{*} 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 AGN in elliptical galaxies that is approximately proportional to M_{BH}^{1.5}, where M_{BH} 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 AGN in massive galaxies and clusters, and warrants further investigation.

astro-ph.CO↗

arXiv2011

Investigating a model of optimised AGN feedback

Feedback heating from AGN in massive galaxies and galaxy clusters can be thought of as a naturally occurring control system which plays a significant role in regulating both star formation rates and the X-ray luminosity of the surrounding hot gas. In the simplest case, negative feedback can be viewed as a system response that is `optimised' to minimise deviations from equilibrium, such that the system rapidly evolves towards a steady state. However, a general solution of this form appears to be incompatible with radio observations which indicate intermittent AGN outbursts. Here, we explore an energetically favourable scenario in which feedback is required to both balance X-ray gas cooling, and minimise the sum of the energy radiated by the gas and the energy injected by the AGN. This specification is equivalent to ensuring that AGN heating balances the X-ray gas cooling with minimum black hole growth. It is shown that minimum energy heating occurs in discrete events, and not at a continuous, constant level. Furthermore, systems with stronger feedback experience proportionally more powerful heating events, but correspondingly smaller duty cycles. Interpreting observations from this perspective would imply that stronger feedback occurs in less massive objects - elliptical galaxies, rather than galaxy clusters. One direct consequence of this effect would be that AGN heating events are sufficiently powerful to expel hot gas from the gravitational potential of a galaxy, but not a galaxy cluster, which is consistent with theoretical explanations for the steepening of the L_X-T relation at temperatures below 1-2 keV.

astro-ph.CO↗

arXiv2010

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. Abridged

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arXiv2010

On the exclusion of intra-cluster plasma from AGN-blown bubbles

Simple arguments suggest that magnetic fields should be aligned tangentially to the surface of an AGN-blown bubble. If this is the case, charged particles from the fully ionised intra-cluster medium (ICM) will be prevented, ordinarily, from crossing the boundary by the Lorentz force. However, recent observations indicate that thermal material may occupy up to 50% of the volume of some bubbles. Given the effect of the Lorentz force, the thermal content must then be attributed to one, or a combination, of the following processes: i) the entrainment of thermal gas into the AGN outflow that inflated the bubble; ii) rapid diffusion across the magnetic field lines at the ICM/bubble interface; iii) magnetic reconnection events which transfer thermal material across the ICM/bubble boundary. Unless the AGN outflow behaves as a magnetic tower jet, entrainment may be significant and could explain the observed thermal content of bubbles. Alternatively, the cross-field diffusion coefficient required for the ICM to fill a typical bubble is roughly 10^16 cm^2 s^-1, which is anomalously high compared to predictions from turbulent diffusion models. Finally, the mass transfer rate due to magnetic reconnection is uncertain, but significant for plausible reconnection rates. We conclude that entrainment into the outflow and mass transfer due to magnetic reconnection events are probably the most significant sources of thermal content in AGN-blown bubbles.

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arXiv2009

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.

astro-ph.CO↗

arXiv2009

Observable consequences of kinetic and thermal AGN feedback in elliptical galaxies and galaxy clusters

We have constructed an analytical model of AGN feedback and studied its implications for elliptical galaxies and galaxy clusters. The results show that momentum injection above a critical value will eject material from low mass elliptical galaxies, and leads to an X-ray luminosity, $L_{\rm X}$, that is $\propto$ $σ^{8-10}$, depending on the AGN fuelling mechanism, where $σ$ is the velocity dispersion of the hot gas. This result agrees well with both observations and semi-analytic models. In more massive ellipticals and clusters, AGN outflows quickly become buoyancy-dominated. This necessarily means that heating by a central cluster AGN redistributes the intracluster medium (ICM) such that the mass of hot gas, within the cooling radius, should be $ \propto L_{\rm X}(<r_{\rm cool})/[g(r_{\rm cool})σ]$, where $g(r_{\rm cool})$ is the gravitational acceleration at the cooling radius. This prediction is confirmed using observations of seven clusters. The same mechanism also defines a critical ICM cooling time of $\sim 0.5$ Gyr, which is in reasonable agreement with recent observations showing that star formation and AGN activity are triggered below a universal cooling time threshold.

astro-ph.GA↗

arXiv2007

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

astro-ph↗

arXiv2007

Dynamics of buoyant bubbles in clusters of galaxies

We present a phenomenological model of the dynamics of buoyant bubbles in the atmosphere of a cluster of galaxies. The derived equations describe velocity, size, mass, temperature and density of the buoyant bubbles as functions of time based on several simple approximations. The constructed model is then used to interpret results of a numerical experiment of heating of the cluster core with buoyant bubbles in a hydrodynamical approximation (i.e. in the absence of magnetic fields, viscosity, and thermal diffusion). Based on the model parameters we discuss possible limitations of the numerical treatment of the problem, and highlight the main physical processes that govern the dynamics of bubbles in the intracluster medium.

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arXiv2007

Rapidly varying accretion and AGN feedback

Accretion rates onto AGN are likely to be extremely variable on short timescales; much shorter than the typical cooling time of X-ray emitting gas in elliptical galaxies and galaxy clusters. Using the Langevin approach it is shown that, for a simple feedback system, this can induce variability in the AGN power output that is of much larger amplitude, and persists for longer timescales, than the initial fluctuations. An implication of this is that rich galaxy clusters are expected to show the largest and longest-lived fluctuations. Stochastic variations in the accretion rate also mean that the AGN injects energy across a wide range of timescales. This allows the AGN to maintain a much closer balance with its surroundings than if it was periodically activated. The possible non-linear correlation between Bondi accretion rate and jet power, found by Allen et al 2006, can be explained if the instantaneous accretion rate, scaled by jet power, varies log-normally. This explanation also implies that the duty cycle of AGN activity increases with the radiative losses of the surroundings, in qualitative agreement with Best et al 2005.

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arXiv2006

Heating Rate Profiles in Galaxy Clusters

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 $10^{6}-10^{7}$ 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.

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arXiv2005

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. 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 $ 1.3-4.7 \times 10^{9} $ 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.

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