9 The correct mix of accreted and newly formed GCs

Let us imagine that the infall of dwarf galaxies and gas was really the dominating process for the building-up of the cD halo and the GCS. How many dwarfs and their transformed gas would then have contributed to the cD halo light and how many GCs might belong to the cD halo?

  

Table 7: Possible mixtures of different processes of GC accretion, formation, and stripping that can explain the observed cD halo properties. In each line, the contribution of each process can be added to the following properties of the cD halo: $M_{V,{\rm cD}} =$ -21.65 mag, $N_{\rm *tot,cD} = 4500$, and S_N = 10. See text for more details

NGC 1399 possesses about 5800 globular clusters (see Sect. 3.2). About 1300 of them would belong to the bulge, $M_{V,{\rm gal}} = -21.5$ mag (see Sect. 3.3.1), if one assumes an initial specific frequency of S_N = 3.2, which is the mean value for the other ellipticals in the Fornax cluster, except NGC 1404 and NGC 1380. That means that 4500 GCs would belong to the cD halo and its specific frequency would be about $S_N = 10\pm1$. Note that half of the total GCS (= 2900 GCs) are assigned to the metal-poor peak around [Fe/H] $\simeq$ -1.3 dex, and therefore at least 1600 metal-rich GCs ([Fe/H] $\simeq$ -0.6 dex) have to be explained by the infall scenario, if one assumes that all 1300 remaining bulge GCs belong to the metal-rich sub-population.

How can dwarf galaxies account for such a high S_N?

As presented in Sect. 5, there are mainly three scenarios possible. Firstly, accreted gas-poor dwarfs possessed high GC frequencies themselves. In this case, the average S_N of all accreted dwarfs and GCs can have values between 4 and 22 depending on the initial conditions (see Table 5). Secondly, the infalling gas of previously gas-rich dwarfs was effectively converted into globular clusters. Regarding the starburst as an isolated entity its resulting systems of stars and clusters can have S_N values between 40 and 90 (see Table 6). Finally, the stripping of GCs from dwarf galaxies was more effective than the stripping of their field population. That this is in principal possible is indicated by the fact that the S_N value of the outer parts of galaxies that are primarily affected by stripping can be in the order of 30 (see Sect. 5.1, case 1b).

Among these 3 possibilities the stripping of GCs from dwarf galaxies most probably plays a minor role. Even if all 50 dE/dS0s within the core radius of the galaxy distribution are remnants, whose outer GCs have been stripped off, we calculate that maximally some hundred GCs have been captured by this process, assuming an initial S_N = 5.5, S_N = 30 for the stripped stars and GCs, and a final S_N = 3.0 for the remnant (similar to the values for NGC 4472, McLaughlin et al. 1994). In the following, we consider the case that at most 500 GCs have been stripped.

What is the correct mixture of the two other processes that fulfil the following assumptions?

(1) The cD halo has been formed only by accreted and newly formed matter, and its total luminosity is $M_{V,{\rm cD}} = -21.65$ mag.

(2) The specific frequency of the accreted and newly formed GCs with respect to the halo luminosity is S_N = 10, (= 4500 GCs).

(3) The 4500 GCs in the cD halo consist of 2500 metal-poor (blue) and 2000 metal-rich (red) GCs (this implies that the GCS of the bulge has 400 metal-poor and 900 metal-rich GCs).

(4) GCs captured by accretion and stripping of dwarfs can only be metal-poor.

In Table 7 we present the possible mixtures of the 3 processes, starting with cases for which GC accretion is dominant and ending with cases in which most GCs have been formed from infalling gas.

In the first five cases we assumed that all metal-poor GCs were captured or stripped. Assuming a high S_N value for the accretion process (S_N = 9, cases 1 and 2), the cluster formation efficiency (CFE) does not need to be as high as estimated for merger and starburst situations (see Table 6). However, as discussed in Sect. 6, a high S_N requires a high accretion rate of dwarf galaxies, a steep initial slope of the faint end of the galaxy LF, and also very faint dwarf galaxies should have possessed at least one GC. The faintest dwarf galaxies with a GCS observed so far are the Local Group dSphs Fornax and Sagittarius ($M_V \simeq -12.5$ mag).

The other way around, if starbursts from stripped gas can produce a high S_N value (40 < S_N < 80, cases 3-5) and have formed 2000 metal-rich GCs, the S_N for the accreted metal-poor GCs is in the order 5-6. Such values can easily be achieved by the accretion scenario presented in Sect. 6 under various reasonable initial conditions (see Table 5).

In the cases 6 to 8 we assumed that the majority of the GCs had their origin from infalling gas with a low value of the estimated starburst CFEs (20 < S_N < 40). The specific frequency for the remaining 1500 accreted GCs then can be very low (3 < S_N < 5), very faint dwarfs do not need to possess GCs, and the numbers of dissolved dwarfs can be of the order of 250-500. However, one then has to assume that GCs formed from metal-rich as well as metal-poor gas and that most of the original dwarf galaxies have been very gas-rich.