6 Enhancement of S_N by accretion of gas-free dwarf galaxies

The possibility that the accretion of gas-poor dwarfs can increase S_N of the central GCS requires that the S_N value of a large number of accreted dwarfs themselves is very high. Only few examples of dwarf galaxies with very high GC frequencies are known. In the Local Group the Fornax and Sagittarius dwarf spheroidals have extraordinarily high S_N values: $29\pm6$ and $25\pm9$ respectively (Durrell et al. 1996). Their absolute luminosities are about M_V =-13 mag. Durrell et al. (1996) found in the Virgo cluster two dE,Ns fainter than M_V = -15.5 mag that have GC specific frequencies in the order of $S_N = 14\pm8$.Recently Miller et al. (1998) found that exclusively dE,Ns can possess high S_N GCSs, whereas dEs have "normal'' values. In this respect, it is worthwhile noting that the nuclei of dE,Ns could be merged globular clusters, and thus the S_N of these galaxies might have been even higher in the past. It seems that all of the high S_N dwarf galaxies belong to the faint luminosity end of the dwarf galaxy population. Thus, their total numbers of GCs are very small, $4 < N_{\rm tot} < 20$ and it might reflect the stochastic effect, where a low mass dwarf is able to produce no, 1, 2, or several clusters.

  

Figure 3: The dotted and dashed lines are initial Schechter-type luminosity functions with different slopes as indicated. The hatched area represents the present day luminosity function for dE and dS0 galaxies in Fornax. Note that for MB > -12.0 mag the galaxy counts in Fornax are incomplete

We tested with Monte Carlo (MC) simulations the possibility that 2500 GCs were captured by gas-poor dwarf galaxy accretion in the center of the Fornax cluster. The number 2500 comprises about the blue GC subpopulation. We assumed that galaxies with absolute luminosities in the range -18.0 < M_B < -8.5 mag have been accreted. Each galaxy contains GCs according to its luminosity. For galaxies with -18.0 < M_B < -15.5 we adopted a mean GC specific frequency of S_N = 4.5 (Durrell et al. 1996). In the fainter magnitude bins, the number of GCs was chosen randomly in such a way that the ranges of observed S_N (Miller et al. 1998) were reproduced. In Table 4 the initial conditions for the dwarf GCSs are summarized. We simulated 3 cases, a very optimistic one (simulation run 1, very faint dwarfs can also possess GCs), a pessimistic case (run 3), where no dwarf fainter than M_B = -12.5 can possess GCs (as it seems to be the case for the Local Group dSphs), and a medium case (run 2, dwarfs fainter then M_B = -10.5 can not possess any GC). However, if faint dEs are already stripped dwarf galaxies, the simulation run 1 or 2 seems more reasonable.

  

Table 5: Results of MC simulations for the disruption of gas-poor dwarfs in the center of the Fornax cluster. In simulation run 1 all dwarfs down to M_B = -8.5 mag can possess GCs (see also Table 4), whereas in run 2 and 3 only dwarfs brighter than M_B = -10.5 and -12.5 mag can possess GCs, respectively. $\alpha$ and M^* are the parameters for the initial LF, $N_{\rm tot}$ is the number of galaxies that has been disrupted to account for 2500 GCs, $S_{N,{\rm dw}}$ is the specific frequency of captured GCs compared to the disrupted galaxy light, $\Delta L = L_{\rm dw}/L_{\rm cD}$ is the ratio of disrupted galaxy light $M_{B,{\rm t}}$ and the present day cD halo light, and $\overline{{\rm [Fe/H]}}$ is the mean metallicity of the accreted GCs

We started our simulations with an initial Schechter-type LF with a given characteristic luminosity M^* and faint end slope $\alpha$.Then we "disrupted'' galaxies of randomly chosen luminosities as long as 2500 GCs have been accumulated, considering the condition that the final LF resembles the present one of the Fornax cluster. We have chosen the following initial faint end slopes: $\alpha = -1.1$ (the present day faint end slope of dE/dS0s), $\alpha = -1.4$, and $\alpha = -1.8$. We varied the characteristic luminosity between M^* = -15.3 (present day), M^* = -16.3, and M^* = -17.3. The brighter M^* the higher is the fraction of disrupted dwarf galaxies at the bright end of the LF. Figure 3 shows the initial LFs with different slopes compared to the present day LF (hatched area). For each simulation we calculated the total number of disrupted dwarfs $N_{\rm tot}$, their total luminosity $M_{B,{\rm tot}}$, the fraction of their light compared to the cD halo light $\Delta L = L_{\rm dw}/L_{\rm cD}$, and the specific frequency of GCs compared to the disrupted stellar light $S_{N,{\rm dw}}$.In addition, we estimated the mean metallicity of the accreted GCs. For galaxies brighter than M_V = -13 mag, we adopted the metallicity-luminosity relation given by Côté et al. (1998), $\overline{{\rm [Fe/H]}} = 2.31 + 0.638\cdot M_V + 0.0247\cdot M_V^2$. For the fainter dwarfs, a metallicity-luminosity relation was derived from a linear regression to the Côté et al. data with M_V < -13 mag, $\overline{{\rm [Fe/H]}} = -0.10\cdot M_V -3.13$. With this relation, the GCs of the faintest dwarfs in our simulations, M_B = -8.5 mag, have a mean metallicity of about $\overline{{\rm [Fe/H]}} = -2.3$ dex. Table 5 summarizes the results of our simulations.

The MC simulations show that high S_N values around 10 can only be achieved under the assumption that dwarf galaxies fainter than M_B = -10.5 mag can possess at least one GC and that the faint end slope of the initial LF is at least as steep as $\alpha = -1.4$. The dissolved light then comprises about 60-90% of the present day cD halo light (within $10\hbox{$^\prime$}$). However, the number of dissolved galaxies in these cases, 3000-14000, is very high. It has to be shown whether theoretical simulations of cluster evolution can reproduce such high destruction rates, when including also very low mass dwarf galaxies. Moreover, the mean metallicity of the accreted GCs for the cases with high S_N values would be about 0.5 dex lower than the observed metal-poor peak at -1.3 dex. In Sect. 9 we discuss, whether the mixture of the presented accretion process with stripping of GCs and new formation from infalling gas can explain the luminosity of the cD halo together with the observed S_N of the central GCS in the Fornax cluster.