8 Constraints and estimations for the dwarf galaxy infall scenario in the Fornax cluster

8.1 Why the present day dwarf galaxy population supports the hypothesis of early infall

In a scenario where a sufficient number of dwarfs has been dissolved into a cD halo, one would expect a flat faint end slope of the LF compared to the initial value. López-Cruz et al. (1997) found in a sample of 45 clusters that clusters with a pronounced cD galaxy indeed tend to have a flat LF faint end slope. This is what we also find for the Fornax cluster.

Furthermore, the surface density slope of dE and dS0 galaxies within the core radius of the cluster ($r_{\rm c}=0\hbox{$.\!\!^\circ$}7$)is flatter than the slope of all possibly dissolved and/or stripped material: cD halo stars, GCs, and perhaps rest gas. This is consistent with White's (1987) argument that disrupted material is more concentrated than the relaxed galaxy distribution.

Moreover, like in other evolved clusters, the gas-rich late-type Fornax galaxies are found at the outskirts of the cluster, whereas the early-type (possibly stripped) dwarfs are more concentrated towards the center (Ferguson 1989).

One also expects that the LF of compact dwarfs is steeper than the LF of less compact dwarfs (since they are more easily disrupted). Indeed, in the Fornax cluster the LF of the non-nucleated dE/dS0s is flatter than the LF of the (on the average) more luminous nucleated dE/dS0s.

Furthermore, if the stripping of gas and stars was more effective in the inner regions, one would expect to find a larger number of fainter remnants in the center than outside. This is indeed seen for the non-nucleated dE/dS0s. The fainter dwarfs are more concentrated to the center than the brighter ones (Ferguson & Sandage 1988).

Finally, two probable candidates for survived nuclei of dissolved dwarfs have been found (see Papers 1 and 2), which would indicate that also dwarfs from the brighter nucleated dE/dS0 population have been dissolved.

8.2 Constraints from the metallicity distribution

Constraints on the metallicity have to be considered, if one assumes that the metallicity distribution of the GCs is bimodal rather than equally distributed over the range of possible GCs metallicities, $-2.0 < {\rm [Fe/H]} <$ 0.0 dex. Primordial gas, expelled and stripped from low mass dwarfs, is normally believed to be a contributor to the metal-poor GC subpopulation (${\rm [Fe/H]}<-1.1$ dex), if transformed into GCs. However, this may not always be the case. Mac Low & Ferrara (1999) calculated that galaxies less massive than about $10^8\ M_{\hbox{$\odot$}}$ can eject metals from supernovae into the intergalactic medium easier than their interstellar gas. Thus, the expelled gas might also be enriched from the supernovae ejecta and more metal-rich GCs could have been formed as well. The capture of GCs of early-type dwarf galaxies can only have contributed to the metal-poor GCs, since all observed GCs in such dwarfs seem to be more metal-poor than ${\rm [Fe/H]} = -1.2$ dex (e.g. Minniti et al. 1996). Côté et al. (1998) have shown via Monte Carlo simulations that the capture of dwarf galaxies can indeed reproduce the bimodal color distribution around M 49 and M 87 under the assumption that the red globular cluster population is the intrinsic GCS of the galaxies. The mean metallicity of the captured GCs peaks around $\overline{{\rm [Fe/H]}} = -1.3$ dex for a steep initial LF slope in their simulations. However, they do not include dwarf galaxies fainter than M_V = -13 mag. As shown in Sect. 6, the inclusion of these galaxies and an extrapolation of the metallicity-luminosity relation for their GCs, can push the mean metallicity of the captured GCs to a lower value.

Since the metallicity of the accreted stellar population of dwarfs itself is between -2.0 to -0.6 (taking the values of Local Group dwarfs, e.g. Grebel 1997), one should also see a low metallicity in the cD halo light. Unfortunately, the metallicity determination of the cD halo is quite difficult due to the low surface brightness, and in the center the light of the bulge of NGC 1399 would dominate a metal-poor halo component. On the other hand, the metallicity of the halo is probably a mixture of different metallicities, if one assumes that not only metal-poor dwarfs have been dissolved, but also stellar populations of more massive galaxies had been stripped and new stars from infalling gas of higher metallicities might have formed.

To explain by the accretion scenario the majority of the red metal-rich GC subpopulation (${\rm [Fe/H]} \simeq -0.6$ dex), either already existing GCs of this metallicity had to be captured, or GCs had to be newly formed from enriched infalling gas. This is possible, if one allows that the gas-rich dwarfs first had time to enrich their interstellar matter to at least -0.8 dex, before the stripping of the gas became important and/or before new cluster formation in these dwarfs has been triggered by interaction processes. In the LMC, for example, no clusters were formed between about 3 to 10 Gyr ago. Whereas the few old clusters have a metallicity of about -1.8 dex, the younger clusters have metallicities around -0.4 dex (e.g. Olszewski et al. 1991; Hilker et al. 1995). Concerning the time scale for metal enrichment in spirals, e.g. Möller et al. (1997) estimated that 2-3 Gyr is enough time to enrich the iron abundance of the interstellar medium from -1.5 dex to about -0.6 dex for early-type spirals (Sa, Sb), whereas at least 7 Gyr are needed for late-type spirals (Sc, Sd). Similarly, Fritze-v. Alvensleben & Gerhard (1994) calculated the metallicity of a secondary GC population in a early-type spiral-spiral merger to be about ${\rm [Fe/H]} =$ -0.6 dex after about 2 Gyr of their life time, and after about 8 Gyr in a late-type spiral-spiral merger.

Assuming that the metal-rich GC population in Fornax was formed by the infall of all types of gas-rich galaxies, one therefore should expect a range of ages among them in order to account for a metallicity peak around -0.6 dex. First, the metal-rich GCs should be at least 2 Gyr younger than the metal-poor GCs with ${\rm [Fe/H]} =$ -1.3 dex. Second, their age spread should be in the order of 2-6 Gyr. It would be interesting to know whether this prediction can be proved or disproved in further investigations.

We note that a large number of metal-rich GCs also might have been accumulated by stripping from more massive early-type galaxies. According to the metallicity-luminosity relation by Côté et al. (1998), the mean metallicity, ${\rm [Fe/H]} = -0.6$ dex, of the red GC population around NGC 1399 corresponds to a luminosity of the former parent galaxies of about M_V = -20 mag. This value is typical for the low-luminosity ellipticals in Fornax, as for example NGC 1374, NGC 1379, and NGC 1427.

8.3 Constraints from the spatial distribution of globular clusters

A further point that has to be explained is why the red GC population is more concentrated than the blue one (Forbes et al. 1997). The answer might be that star formation from infalling gas is more concentrated to the inner part of the dense cluster core, as it is also expected for a merging scenario (Ashman & Zepf 1992). Another possibility is that most of the red GCs have nothing to do with a secondary formation or accretion process, but rather belong to the original GC population of the bulge of NGC 1399. However, as we show in the next section, not more than about 1300 GCs can belong to the bulge light, if one assumes reasonable values of the initial GC specific frequency. This comprises only about half of the red GC subpopulation.