Two major pieces of evidence point to mechanical heating by AGN as an important energy source in the ICM. First, there is the absence of `cooling flows'. Radiative cooling timescales in the central regions of clusters are often much shorter than the Hubble time. Initially, this led to suggestions that the intracluster medium (ICM) is flowing into the cluster center at rates of up to 1000 M / yr. However, XMM Newton and Chandra observations suggest that the actual inflow rates are much smaller than expected, indicating that some mechanism compensates for the cooling (e.g., Fabian et al. 2000, 2002; McNamara et al. 2000; Blanton et al. 2001; Churazov et al. 2002). The possibility that active galaxies provide the heating is supported by observations that ~ 70% of cD galaxies show evidence for active radio sources (Burns 1990), and that the ensemble-averaged power from radio galaxies may be adequate to offset the mean level of cooling (; Böhringer et al. 2002). An advantage of the AGN heating model over other models (e.g., thermal conduction from large radii) is that the heating is supplied near the cluster center where the cooling flow problem is most acute. AGN heating may explain why the gas temperature, while declining towards cluster centers, does not drop by more than a factor ~ 2 - 3 between the cooling radius and the cluster center (Allen et al. 2001; Fabian et al. 2001; Peterson et al. 2001, 2003).
The second piece of evidence is the excess entropy found in clusters. Cluster X-ray luminosities and gas masses increase with temperature more steeply than predicted by hierarchical merging models (Markevitch 1998; Nevalainen et al. 2000). In other words, the atmospheres in less massive clusters and groups are hotter than they should be, given the gravitational interactions that assembled them. These correlations apply to regions of clusters well outside the cooling radius, as well as to clusters without cooling cores. They can be interpreted as evidence for an entropy `floor' (Lloyd-Davies et al. 2000) or a systematic excess of entropy (Ponman et al. 2003); the most plausible explanation appears to be AGN heating before or during cluster assembly (e.g., Valageas & Silk 1999; Nath & Roychowdhury 2002; McCarthy et al. 2002, and references therein).
Both pieces of evidence suggest that the heating, whatever its cause, must be both widely distributed and gentle. Radiatively cooling gas in clusters is prone to thermal instability, since the cooling rate increases rapidly with density. To avoid a `cooling catastrophe', heat must be spread evenly though the ICM, and especially targeted at regions with large density gradients. Measurements of excess entropy also show that the heat must be spread over a range of radii, extending out to half the cluster virial radius. That the central heat source is relatively gentle in cooling flow clusters is suggested by the absence of X-ray emitting shocks bounding radio lobes (Fabian et al. 2000) and the fact that cluster cores appear to have positive radial entropy gradients, i.e., they are convectively stable (David et al. 2001; Böhringer et al. 2002).
Can a centrally located AGN provide mechanical heating that is gentle, yet spreads widely through the cluster? At first glance it seems unlikely. Powerful radio galaxies, like Cygnus A, produce overpressured cocoons that expand supersonically into their surroundings. After a transient phase dominated by the momentum flux in the jets, cocoons resemble spherical, supersonic stellar wind bubbles (Begelman & Cioffi 1989). The evolution of the bubble can be described approximately by a self-similar model in which the internal and kinetic energy are comparable, and share the integrated energy output of the wind. The speed of expansion is
where Lj is the power of the jets, is the ambient density, and R is the radius of the shock. The supersonic expansion phase ends when the expansion speed drops below the sound speed in the ambient medium. This occurs at a radius
where <L43> is the time-averaged jet power in units of 1043 erg s-1, n is the ambient particle density in units of cm-3, and TkeV is the ambient temperature in units of keV. Thereafter the evolution is dominated by buoyancy (Gull & Northover 1973). We have chosen fiducial parameters that are fairly typical of conditions at the centers of rich clusters - note how small Rsonic is, compared to a typical cluster core radius, or even the core radius of the host galaxy. Cygnus A, which has been expanding for several million years, is hundreds of kpc across, and is still overpressured by a factor ~ 2 - 3 with respect to the ambient medium, is the exception rather than the rule. It is a very powerful source expanding into a relatively tenuous ambient medium (Smith et al. 2002). During most of the evolution of clusters we can expect the energy injection to be in the buoyant regime, and the heating therefore relatively gentle.
A clue to the widespread distribution of the heat comes from the apparent immiscibility of the hot (possibly relativistic) plasma injected by the jets and the thermal gas of the ICM. It has been known since the time of ROSAT (Böhringer et al. 1993) that the plasma in radio lobes can displace cooler thermal gas, creating holes in the X-ray emission. More sensitive Chandra images have shown not only how common such holes are, but also how long they can persist. In particular, numerous examples of `ghost cavities' have been found (e.g., McNamara et al. 2001; Johnstone et al. 2002; Mazzotta et al. 2002), where the X-ray deficit persists but the compensating radio emission is either absent or too weak to detect. These are presumably buoyant bubbles left over from earlier epochs of activity.
The persistence of highly buoyant bubbles implies that energy can be transported to large radii, despite the convective stability of the ICM. The Schwarzschild criterion refers to heat transport by marginally buoyant fluid elements, not the highly buoyant bubbles that appear to be present. We therefore obtain the following description of how the ICM can be heated by a central AGN:
Pockets of very buoyant gas rise subsonically through the ICM pressure gradient. A large density contrast is maintained between the buoyant gas and its surroundings, i.e., there is little mixing.
The buoyant gas does pdV work on the ICM as it rises and expands. This work goes initially into a combination of kinetic energy, internal energy, and gravitational potential energy (e.g., sound waves, g-modes, and internal waves).
The energy transferred to the ICM energy is converted to heat by damping and/or mixing.
We call this process effervescent heating (Begelman 2001; Ruszkowski & Begelman 2002).