2 Dwarf galaxies in clusters

2.1 Theoretical background on the evolution of dwarf galaxies in clusters

In their review about dwarf elliptical galaxies, Ferguson & Binggeli (1994) summarized the formation and evolutionary scenarios that are predicted by theoretical models. It is generally accepted that galaxy formation started from gaseous conditions in the early universe followed by the collapse of primordial density fluctuations, cooling of the gas and subsequent star formation (e.g. White & Frenk 1991; Blanchard et al. 1992; Cole et al. 1994; Kauffmann et al. 1993; Lacey et al. 1993). In cold dark matter (CDM) dominated models the formation of low-mass galaxies is favored, because for dwarf galaxy halos collapsing at $z \simeq 3-10$ the cooling time is short compared to the free-fall time, thus cooling should be very efficient, and accordingly many dwarfs will be formed. A steep slope, $\alpha = -2$, of the initial mass function (N(M)d$M \propto M^\alpha$) is predicted (e.g. Blanchard et al. 1992). In contrast, the faint end slope of the observed luminosity functions in nearby clusters are around $\alpha \simeq -1.3\pm0.4$ (see Ferguson & Binggeli 1994). This contradiction is the so-called "overcooling problem'' (e.g. Cole 1991). If the CDM model prediction is correct, there must have been active some mechanisms that either counteracted the cooling during the collapse of dwarfs or destroyed the numerous dwarfs after their formation. Plausible mechanisms that involve internal as well as external agents are summarized in the review by Ferguson & Binggeli (1994).

In the following, we focus our attention on the possibility that many dwarf galaxies have merged with the central galaxy. For a CDM power spectrum in an $\Omega = 1$ cosmology the epoch of dwarf galaxy formation is believed to be also the epoch of rapid merging. Kauffmann et al. (1994) included the merging of satellite galaxies in their CDM models and found that most of the observational data can be reproduced when adopting a merging timescale that is a tenth of the tidal friction timescale, and when star formation is suppressed in low-circular-velocity halos until they are accreted into larger systems. Further, efficient merging at all epochs results in a decrease of the faint end slope of the LF compared to the initial predicted value of $\alpha = -2$.

2.2 Dwarf galaxies and cD halo

Several authors have suggested that tidal disruption (total dissolution of the galaxy light) of galaxies in cluster centers as well as tidal stripping (only outer parts are affected, a remnant survives) might be related to the formation of cD halos (see references below). The time of formation is being discussed. Most authors assume that the stripping processes take place after the cluster collapse (e.g. Gallagher & Ostriker 1972; Richstone 1976; Ostriker & Hausman 1977; Richstone & Malumuth 1983). In contrast, Merritt (1984) explained the general appearence of cD halos as the result of dynamical processes during the cluster collapse. In his scenario the accumulation of slowly-moving galaxies in the cluster core via dynamical friction only plays an important role for groups or clusters with small velocity dispersion $\sigma_v \leq 500$ km s^-1 (Fornax: $\sigma_v \simeq 360$ km s^-1). White (1987) argued that, in the case of tidal disruption and stripping, the distribution of stripped and disrupted material (diffuse light, dark matter, GCs) should be more concentrated to the center than the relaxed galaxy distribution, because galaxies closer to the center are more affected by disruption processes than galaxies outside. In the case of Merritt's model, galaxies formed before the collapse, stripping occured during the collapse, and finally the stripped material is distributed in the same way as the galaxies through collective relaxation.

Furthermore, it is interesting to note that also a large amount of the intracluster gas (seen as X-ray halo) might have had its origin in dwarf galaxies, which could have expelled their gas by supernova-driven winds, or stripped off their gas (Trentham 1994; Nath & Chiba 1995). In the Virgo cluster, for example, Okazaki et al. (1993) estimated that the amount of gas expelled from the E and S0 galaxies is not adequate to account for the total gas mass in the cluster. Mac Low & Ferrara (1999) calculated that low mass dwarf galaxies can easily blow away metals from supernovae which might enrich the halo gas.