Recent years have seen a growing realization that the cores of rich galaxy clusters are complex and dynamic environments. In particular, it is becoming clear that the radio-loud active galactic nuclei (AGN) often hosted by the cD galaxies in rich clusters can have a major influence on the hydrodynamics and thermodynamics of the core regions of the intracluster medium (ICM). As we discuss below, the rich datasets coming from the Chandra X-ray Observatory and XMM-Newton now demand theoretical models that go beyond the simple picture of jet-blown ``bubbles'' rising in a static ICM described by ideal hydrodynamics. Bulk ICM motions (including turbulence), magnetohydrodynamics (MHD), thermal conductivity, and viscosity may all be relevant to data that are currently being taken.
Even before the launches of Chandra and XMM-Newton, Einstein and ROSAT studies revealed prominent radio-galaxy/cluster interactions in three clusters; Perseus-A (Böhringer et al. 1993; Heinz, Reynolds & Begelman 1998), Virgo-A (Feigelson et al. 1987; Böringer et al. 1995) and Cygnus-A (Carilli, Perley & Harris 1994; Harris, Carilli & Perley 1994). ROSAT showed Perseus-A and Cygnus-A to possess intracluster medium (ICM) cavities coincident with the prominent radio-lobes in these two sources, suggesting supersonic inflation of a bubble in the ICM by the jetted AGN (Clarke, Harris & Carilli 1997). Virgo-A, on the other hand, showed a cooler (and soft X-ray brighter) region of ICM associated with the outer eastern ``ear'' seen in low-frequency radio maps of Virgo-A (Owen, Eilek & Kassim 2000). It was first suggested by Böhringer et al. (1995) that this phenomenon might be caused by lower entropy gas from the cluster center being dragged upwards in the ICM atmosphere by a buoyantly rising radio-lobe.
More recent observations by Chandra and XMM-Newton show
that radio-galaxy induced ICM substructure is surprisingly ubiquitous
and complex. The basic results described above, i.e., the existence
of ICM cavities associated with active radio-lobes and the presence of
cool material that appears to lie in the wake of old, buoyantly rising
radio-lobes, have been confirmed in numerous systems (e.g., Hydra-A;
McNamara et al. 2000, Abell 2052; Blanton et al. 2001, Virgo-A; Young,
Wilson & Mundell 2002, Perseus-A; Fabian et al. 2000, 2003a).
However, these new data have raised several mysteries and are
increasingly at odds with simple models for radio-galaxy/ICM
interactions. Firstly, in any ideal hydrodynamic model, the cavities
must be inflated supersonically or else they would be destroyed by
Rayleigh-Taylor (RT) instabilities faster than they are inflated.
Curiously, the strong and hot ICM shocks that one expects to find
around the active cavities are notably absent; instead, many ICM
cavities are surrounded by ICM shells that are cooler than the
ambient ICM. We shall refer to this as the ``shock problem''.
Secondly, ICM cavities that are not associated with any obvious
radio-lobe (``ghost cavities'') have been discovered. Examples are
found in the Perseus cluster (Fabian et al. 2003a), Abell 2597
(McNamara et al. 2001), and Abell 4059 (Heinz et al. 2002, Choi et al.
2004). In some cases, ghost cavities are coincident with regions of
low-frequency (74MHz) radio emission supporting the hypothesis that
they correspond to old radio-lobes from previous and now extinct AGN
outbursts (Fabian et al. 2002a). Interestingly, as we will explicitly
demonstrate in this paper, ideal hydrodynamic models fail to reproduce
the observed morphology of at least some ghost cavities. Finally,
most clusters have been found to possess a ``temperature-floor'' in
the sense that the radiative cooling of the ICM appears not to proceed
below temperatures of 
(Tamura et al. 2001; Peterson
et al. 2001). Again, no clear explanation for this fact is provided
by an ideal hydrodynamic model. Brüggen & Kaiser (2002) suggest
that stirring of the ICM core by a central radio galaxy may be
responsible for the temperature floor; however, such a scenario only
postpones rather than prevents radiative cooling, and is hard to
reconcile with the strong metallicity gradients observed in the cores
of some clusters (David et al. 2001, Matsushita et al. 2002; Sanders
& Fabian 2002). This has led several authors (Narayan & Medvedev
2001; Fabian et al. 2002b; Voigt et al. 2002; Kim & Narayan 2003) to
resurrect the notion that thermal conduction may be important in
determining the thermodynamics of ICM cores.
Faced with the multiple failures of simple hydrodynamic models for cluster cores, we must carefully examine the other physical processes that might be relevant. Both the dynamical and thermodynamical effects of magnetic fields are largely unexplored and are the subject of on-going large-scale simulations. However, the qualitative success of models including thermal conduction in solving the temperature floor problem begs a study of other transport processes and, in particular, the effects of shear viscosity on the dynamics of a radio-galaxy/ICM interaction.
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Perseus-A and the core of the Perseus cluster continues to be one of
the best studied examples of a rich cluster core and a complex
radio-galaxy/cluster interaction. The most detailed X-ray
investigation to date, based on a deep (200ks) observation by Chandra/ACIS-S, has been presented by Fabian et al. (2003a). These
authors report the discovery of wave-like disturbances in the ICM on
spatial scales of 
, approximately twice the spatial
scales of the most obvious ghost cavity to the north-west of
Perseus-A. They discuss a scenario in which viscous dissipation of
these disturbances may act as a significant heat source for the ICM
core. It is shown that, provided viscosity operates reasonably close
to its ideal unmagnetized value, it is possible for viscous
dissipation of radio-galaxy induced disturbances to balance radiative
cooling of the ICM. This suggestion has been supported by recent
simulation work by Ruszkowski, Brüggen & Begelman (2003).
Circumstantial evidence for the presence of significant ICM viscosity
is also provided by an examination of the morphology of H
filaments. Several of the filaments appear to trace well-defined arcs
in the region below the ghost cavity (Fig. 1; also see
Fabian 2003b). This argues against the presence of strong turbulence
in the ICM core, possibly resulting from the action of viscosity. If
we make the stronger presumption that the H filaments follow
streamlines in the ICM, the morphology of the filaments suggests the
existence of a vortex ring within the ICM just below the NW ghost
cavity.
With this background and motivation, this paper presents hydrodynamic simulations of the buoyant evolution of an AGN-blown cavity in a viscous ICM. In order to bring clarity to the discussion of such a complex system, this paper deals with the focused question of how ICM viscosity effects the observed morphology and associated flow patterns of old (ghost) cavities. Detailed investigations of the effects of viscosity on the growth of active cavities and the thermodynamic state of the ICM will be addresses in future work. Section 2 reviews the importance of viscosity in typical clusters, and touches upon the robustness of viscosity in the presence of magnetic fields. Section 3 describes the basic set-up of our simulations, as well as our results on the morphology and flow patterns. Section 4 discusses some of the limitations of this work, and possible implications of ICM viscosity. Finally, conclusions are presented in Section 5.