Mass transport by buoyant bubbles in galaxy clusters

Edward C. D. Pope 2 Aaron Dotter 2 Arif Babul 2 Georgi Pavlovski 1 Richard G. Bower 0 0 Institute for Computational Cosmology, Department of Physics, Durham University , South Road, Durham DH1 3LE 1 School of Physics and Astronomy, University of Southampton , Southampton SO17 1BJ 2 Department of Physics and Astronomy, University of Victoria , Victoria, BC , V8P 1A1, Canada A B S T R A C T 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 107-9 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. - The hot, gaseous atmospheres of galaxy clusters often show depressions in the X-ray surface brightness (see e.g. McNamara 2002; Brzan et al. 2004; Dunn, Fabian & Taylor 2005; Rafferty et al. 2006). These depressions are indicative of empty cavities, or bubbles, embedded in the hot gas (e.g. McNamara & Nulsen 2007). The presence of bubbles is generally taken to be a signature of active galactic nuclei (AGN) feedback. In this model, a fraction of the material cooling from the gaseous atmosphere is accreted by a supermassive black hole located in the central galaxy. This releases vast amounts of energy often in the form of outflows which couple to the hot atmosphere (e.g. Churazov et al. 2002b; Benson & Babul 2009). AGN feedback is widely considered to have important consequences for the evolution of single galaxies, as well as galaxy groups and clusters. For example, feedback is thought to be key in determining the upper mass cut-off of the galaxy mass function (Benson et al. 2003; Bower et al. 2006; Croton et al. 2006), balancing the radiative losses in cool-core galaxy clusters, as well as providing the non-gravitational pre-heating that may be important for non cool-core clusters (e.g. Babul et al. 2002; McCarthy et al. 2004, 2008). Feedback also seems to play a role in determining the relationship between the temperature and X-ray luminosity of hot atmospheres across a range of halo masses (Babul et al. 2002; McCarthy et al. 2004; Bower, McCarthy & Benson 2008; Dave, Oppenheimer & Sivanandam 2008; Puchwein, Sijacki & Springel 2008; Pope 2009). As a direct consequence, feedback also regulates supermassive black hole growth (e.g. Silk & Rees 1998; Churazov et al. 2005) and, therefore, its relation to the properties of the host galaxy. Considerable effort has been invested in understanding the impact of supermassive black holes. One of the key challenges is understanding how the energy from the AGN affects and couples to the broader environment. Most studies that have sought to describe this relationship have focused on bulk motion, shock waves and pressure/gravity waves induced by AGN outbursts and the subsequent dissipation of the associated energy (see McNamara & Nulsen 2007, for a review). In this article, we focus on the transport of material out of the cluster centre by AGN-blown bubbles. As an example, the filaments of cool material observed behind AGN-blown bubbles (e.g. Conselice, Gallagher & Wyse 2001; Crawford, Sanders & Fabian 2005; Hatch et al. 2006) are a strong indication of bubbleinduced mass transport within several tens of kiloparsecs of the cluster centre. The most obvious example is the Perseus cluster in which the filaments contain some 108 solar masses of cool material (e.g. Salome et al. 2006, 2008). More generally, some of the transport mechanisms we discuss in this paper may carry matter out to 100 kpc from the cluster centre. Mass transport by bubbles not only reduces the amount of material available for forming new stars in the central galaxy, allowing the normally adopted stringent requirement that AGN heating perfectly balances cooling to be some relaxed, but also affects the bubble dynamics and energetics. Hence, a better understanding of the main mass transport mechanisms is essential for describing the energy balance in the intracluster medium (ICM). Here, we focus on three important processes by which bubbles can transport material: drift, wake transport and the entrainment of ambient material into the bubble. The aim of this article is to quantitatively describe these three main mechanisms and also the corresponding implications. The discussion is largely analytical, intended to facilitate a better understanding of the underappreciated aspects of these mechanisms and aid in the interpretation of both observations and numerical simulations. This article is arranged in the following way. Section 2 outlines the basic bubble model that serves as a backdrop for subsequent discussions. Sections 3, 4 and 5 focus on each of the three mechanisms drift, wake transport and entrainment. In each section, we discuss a process as well as associated, potentially observable consequences, like trailing optical filaments. In Section 6, we consider how mass transport modifies the ongoing debate about whether or not AGN heating needs balance cooling precisely. We summarize our key findings in Section 7. 2 B U B B L E M O D E L The magnitude and spatial extent of mass transport associated with buoyant bubbles depend heavily on the dynamics and the energetics (...truncated)