The Models Where to Go Next

The important question in the context of this meeting is, how much energy does a "typical" central AGN deposit in the cooling core plasma? To answer this, we must determine the mean jet power, Pj, averaged over the lifetime of a typical CCRG, and how effectively that power is deposited in the local plasma. We emphasize that we have no direct measure of Pj. The radio power of the CCRG is a poor tracer of the jet power [5]. The best we can do directly from observations is to use minimum-pressure arguments, which are possible if the jet is resolved (e.g. M87 [17]). This gives us a lower bound on Pj. To go further, we must choose a dynamical model for the RG and its interaction with the local ICM. This sounds simple, but the devil is in the details.

4.1 Calorimetry

The simplest cases are cooling cores which have clear X-ray cavities that coincide with an extended RG. In these the mean jet power can be found from the energy within the cavity and the age of the source. This is a simple, attractive appproach, which has been applied by various authors (e.g., [1,4]). However, it has complications. One is that measuring the energy content of the cavity is not straightforward, because it is hard to know the extent to which the radio and X-ray plasmas have mixed in most of these clusters. A second concern is how to estimate the age of the source. Most authors currently assume the radio source is passive, having been previously inflated by an AGN which has since turned off. If this holds, the source age is its size divided by the bouyant speed, vb. But what is vb? The sound speed is no more than an optimistic upper limit, because vb is quite subsonic for small structures. In addition, magnetic tension from even a very small intracluster field can exceed hydrodynamic drag, and reduce vb even more [12].

A more serious concern, however, is the evidence from our work that every CCRG is currently being driven by jets from an active AGN, and that large-scale radio haloes have mixed with the ICM. It follows that very few CCRGs are well described as isolated, passive, buoyant bubbles (although buoyancy surely plays some role in the evolution of the RG). New models are needed.

4.2 Possible Dynamical Models

As a first step towards such new models, we suggest that CCRG evolution can be broken into two stages. We envision an early stage in which young, driven sources interact with and expand into the ICM, and a later stage in which the RGs have grown into extended mini-haloes mixed with the ICM. If AGN activity is cyclic, an older mini-halo could coexist with a younger, restarted inner core. We note that our ideas here are no more than toy models; they need to be developed and tested against real, well-observed CCRGs.

Because the observations show that the AGN in every CCRG is "alive", and because CCRGs are often amorphous, we suggest that small, young sources are being driven by a quasi-isotropic energy flux (as from an unstable jet). Such evolution can be approximated by a self-similar analysis [8]. However, because the edges of the X-ray cavities are not strong shocks (e.g., [9]), we know the expansion is slow; this suggests the expansion proceeds at approxiate pressure balance [17]. Such a model predicts the source size R(t) a: (Pjt)x, where x depends on the ambient pressure gradient. We emphasize that Pj and t cannot be determined separately in this model; the best we can do is the limit R < cs, which gives an upper limit to Pj.

Because the data also show the radio and X-ray plasmas are well mixed for larger RGs, we further suggest that CCRGs eventually fragment and mix with the ICM. The fragmentation may occur via MHD surface effects (such as the tearing-mode instability) which create magnetic filaments or flux ropes. Alternatively, the small-scale flux ropes which we know exist in MHD turbulence may retain coherence and diffuse into the extended ICM in late stages of CCRG evolution. (The ubiquity of filaments in well-imaged RGs suggests such structures are common in general; why should CCRGs be different?) We expect the flux ropes to rise slowly under buoyancy, and to retain their identity for awhile, after which they probably dissipate and merge with the local ICM. In principle, Pj could be estimated for such a source from the energy content of the radio plasma and its buoyant rise time, but uncertainties in filling factors and flux rope sizes limit the quantitative usefulness of this approach.

4.3 The Large Radio Haloes

Some of our radio haloes are large enough to raise the question, where does "CCRG" end and "cluster halo" begin? That is, on what scale is the physics of the full cluster more important than the influence of the AGN? The synchrotron size is one criterion: how large can the radio halo be without needing in situ energization? We are skeptical of simple synchrotron-aging estimates, because magnetic fields in the radio source and the ICM are almost certainly inhomogeneous. One can, however, derive a useful limit. The lowest loss rate for the radio-loud electrons is that of inverse Compton losses on the cosmic microwave background. If the electrons spend most of their time in sub-^G magnetic fields, and occasionally migrate into high-field regions (probably a few yU,G) where they become radio-loud, we can find an upper limit to their synchrotron life.

This cartoon predicts the radio plasma in a buoyant flux rope can reach ~ 100 kpc before it fades away. Radio sources larger than this must be undergoing extended, in situ re-energization. It follows that some driver other than the AGN must exist on large scales. Ongoing minor mergers are thought to support radio haloes in large, non-CC clusters. They may be important in CC clusters as well (e.g., [16]), and may be driving the larger haloes. But then, if we admit the need for non-AGN heating of CC clusters on large scales, can we be sure that the cooling core itself is heated only by the AGN?

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