Several groups have addressed this question already many years ago. David et al. (1991) proposed the first models taking into account the effects of galactic winds on the ICM enrichment. They found that the results depend sensitively on their input parameters: the initial mass function, the adopted supernova rate and the primordial mass fraction of the ICM.
The first 3D simulations calculating the full gas dynamics and the effects of winds on cluster scales were performed by Metzler & Evrard (1994, 1997). They concluded that winds can account for the observed metal abundances in the ICM, but they found strong metallicity gradients (almost a factor of ten between cluster centre and virial radius) which are not in agreement with observations. Gnedin (1998) took into account not only galactic winds, but also galaxy-galaxy interactions and concluded that most of the metals are ejected by galaxy mergers. In contrast to this result Aguirre et al. (2001) found that galaxy-galaxy interactions and ram-pressure stripping are of minor importance while galactic winds dominate the metal enrichment of the ICM.
That these early results disagree so much is probably due to the large range of scales that is involved. On the one hand the whole cluster with its infall region has to be simulated, on the other hand processes within galaxies or even within the active core of a galaxy are important. It is not possible to calculate all of this accurately in one type of simulation and therefore new methods have been developed.
Recently several simulations for the enrichment have been performed. They calculate the exact composition and evolution of the ISM by varying the initial mass function and the yields of supernova explosions (see Borgani et al. 2008 - Chapter 18, this volume), but it is not distinguished by which process the enriched gas is transported into the ICM. Specially for the transport processes a new simulation method has been developed, in which N-body/hydrodynamic simulations with mesh refinement including a semi-analytical method have been combined with separate descriptions of the various enrichment processes, which can be switched on and off individually (Schindler et al. 2005).
The results obtained with this method show an inhomogeneous distribution of the metals independent of the enrichment processes (Schindler et al. 2005, Domainko et al. 2006, Kapferer et al. 2006, Moll et al. 2007, see Fig. 7). These results are in very good agreement with the observed metallicity maps (see Werner et al. 2008 - Chapter 16, this volume). The gas lost by the galaxies is obviously not mixed immediately with the ICM. There are usually several maxima visible in the metallicity distribution, which are not necessarily associated with the cluster centre. The maxima are typically at places where galaxies just have lost a lot of gas to ICM of low density, mostly due to star bursts. The metallicities vary locally between 0 and 4 times Solar.
Figure 7. Simulated metallicity map, i.e. an X-ray emission weighted, projected metal distribution. The high metallicity region at the top is caused by a group of galaxies with recent starburst. Overlaid contours indicate the origin of the metals: ram-pressure stripping (white) and galactic winds (black) (adopted from Kapferer et al. 2007a).
A detailed comparison between the two enrichment mechanisms - winds and ram-pressure stripping - revealed that these two processes yield different metal distributions (see Fig. 7) and a different time dependence of the enrichment (Kapferer et al. 2007a, Rasia et al. 2007). The ram-pressure stripped gas is more centrally concentrated. The reason for this is that the ICM density as well as the galaxies velocities are larger in the cluster centre, so that ram-pressure stripping is very efficient there. Galactic winds, however, can be suppressed by the high pressure of the ICM in the centre (Kapferer et al. 2006), so that in massive clusters galactic winds do hardly contribute to the central enrichment. The resulting radial metal profiles are correspondingly relatively flat for galactic winds and steep for ram-pressure stripping. When both processes are taken into account they are in good agreement with the observed profiles (see also Borgani et al. 2008 - Chapter 18, this volume).
The time scales for the enrichment are also different for the two processes (Kapferer et al. 2007a). The mass loss of galaxies due to winds is larger at high redshifts. Between redshifts 2 and 1 ram-pressure stripping becomes more important for the mass loss and it is by far more efficient at low redshift (see Fig. 8). The reason is that on the one hand galactic winds become weaker because the star formation rate decreases and on the other hand ram-pressure stripping becomes stronger because clusters with ICM have formed/are forming, which is interacting with the galaxies. In total the mass loss due to ram-pressure stripping is usually larger than the mass loss due to winds, in some cases up to a factor of three.
Figure 8. Mass loss of the galaxies in a simulation taking into account mass loss due to galactic winds (dashed line) and mass loss due to ram-pressure stripping (solid line) at different redshifts (adopted from Kapferer et al. 2007a).
Generally it is very hard to provide numbers for the relative efficiencies of the various processes as the efficiencies depend strongly on the properties of the clusters. In a massive or in a merger cluster, for example, ram-pressure stripping is very efficient.
The simulated metallicities can be converted to artificial X-ray metallicities, metallicity profiles, metallicity maps and metallicity evolution. There is in general a good agreement between these quantities derived from simulation and observation (Kapferer et al. 2007b). The metallicity values are in the right range and the spatial distribution and the evolution are in good agreement with the observations. Also the evolution of the metallicity since z = 1 found in observations (Balestra et al. 2007, Maughan et al. 2008) can be reproduced by the simulations. Of course there is a large scatter in all these quantities, because they vary very much from cluster to cluster both in simulations and observations.
Summarising, from the comparison of observations with simulations it seems clear that several processes are involved in the metal enrichment and none of them can be ruled out immediately as being not efficient enough. The processes can also influence each other (e.g. AGN outflows can enhance an existing galactic wind or one process can suppress another one). Obviously the interaction between galaxies and the ICM is a very complex issue. In order to know what is really going on at the transition between galaxies and ICM many more observations and simulations are needed.
Acknowledgements The authors thank ISSI (Bern) for support of the team "Non-virialized X-ray components in clusters of galaxies". We thank Wolfgang Kapferer und Thomas Kronberger for useful discussions. The authors acknowledge financial support by the Austrian Science Foundation (FWF) through grants P18523-N16 and P19300-N16, by the Tiroler Wissenschaftsfonds and through the UniInfrastrukturprogramm 2005/06 by the BMWF. Partial support from the PRIN2006 grant "Costituenti fondamentali dell'Universo" of the Italian Ministry of University and Scientific Research and from the INFN grant PD51 is also gratefully acknowledged.