7 Efficiency of new cluster formation by the accretion of gas-rich dwarf galaxies

In this section we assume that the gas of stripped dwarfs forms stars and clusters with the same proportion as has been determined for merging and starburst galaxies. Many examples for young GC candidates in mergers are known: e.g. NGC 3597 (Lutz 1991), NGC 1275 (Holtzman et al. 1992; Nørgaard-Nielsen et al. 1993; NGC 5018 (Hilker & Kissler-Patig 1996), NGC 7252 (Whitmore et al. 1993; Schweizer & Seitzer 1993; Whitmore & Schweizer 1995). The number of newly formed clusters differs from case to case and seems to depend on the amount of gas that is involved in the merging process. The precondition that is needed to form a bound cluster is a cold gas cloud with high density in its core (e.g. Larson 1993). Furthermore, the local star formation efficiency has to be very high and has to occur on a short timescale in order to avoid an early disruption by strong stellar winds and by supernova explosions of the most massive stars (Brown et al. 1995; Fritze-v. Alvensleben & Burkert 1995). The best candidates for the progenitors of the clusters are the massive, embedded cores of (super) giant molecular clouds (e.g. Ashman & Zepf 1992; Harris & Pudritz 1994). Elmegreen et al. (1993) have shown that large molecular cloud complexes can form in interacting systems. The high densities in the cores that are necessary for the cluster collapse can be induced by direct cloud-cloud collision as well as by an increase of the ambient gas pressure as a result of a merger (Jog & Solomon 1992). Furthermore, the high velocities of colliding gas during mergers might act as dynamical heating that counteracts a fast cooling which would prevent an efficient cluster formation. In this way metal-rich gas, where the cooling times are normally short, could also efficiently form GCs.

What is the observed cluster formation efficiency in merger and starburst galaxies? Meurer et al. (1995) investigated the ultraviolet (UV) properties of young clusters in nine starburst galaxies (blue compact dwarfs as well as ultraluminous mergers). On average, about 20% of the UV luminosity comes from clusters. But is this percentage sufficient to increase the specific frequency of the GCS? Before answering this question one has to know how many young clusters will survive the evolution of several Gyr.

Fritze v. Alvensleben & Kurth (1997) calculated with the help of stellar population evolutionary models (Fritze v. Alvensleben & Burkert 1995) that the young Antennae (NGC 7252) clusters will evolve into a typical GCS. However, they do not exclude the possibility that up to 60% of the present clusters may be destroyed by dynamical effects during the evolution of the cluster system. This value is the result of semi-analytical model calculations by Vesperini (1997), who simulated the evolution of a original GC population in a spiral. Note that most of the destroyed clusters are low mass clusters. Thus the destroyed cluster mass is a much smaller percentage of the initial total cluster mass. On the other hand, Okazaki & Tosa (1993) estimated that about 60% in mass of an initial GC population, whose initial mass function $\phi$ is approximated by the power law $\phi = {\rm d}N/{\rm d}M \propto M^{-\alpha}$, with $\alpha \simeq 2$, will be destroyed after evolving into the present GCLF. In the following we will assume that a dissolution of 20 to 60% of the cluster mass or light is reasonable.

7.1 Increase of S_N in a starburst galaxy

Coming back to the question, whether a strong starburst like those investigated by Meurer et al. (1995) can increase S_N, we make a simple calculation: we start with a gas-rich dwarf that has an absolute luminosity of M_V = -16.0 mag and 5 GCs, which means S_N = 2 (typical for spirals, e.g. Zepf & Ashman 1993). We assume that a starburst occurs which involves 10% of the total mass, of which 20% will be transformed into clusters. For the duration of the burst this increases M_V of the galaxy to about -17.8 mag (assuming that the young stellar population is about 4 mag brighter than a faded old one, Fritze v. Alvensleben & Burkert 1995). About 12 Gyr after the burst M_V has faded again to -16.1 mag. At this time the total luminosity of the clusters is M_V = -11.8 if no cluster has been destroyed, or M_V = -11.0 if as many clusters as corresponding to about 50% of the total cluster light have been destroyed. Adopting for the evolved GCS a typical GCLF (t5-function) with a turnover magnitude of $M_{V,{\rm TO}} =$ -7.4 mag and a dispersion of $\sigma = 1.0$ (e.g. Kohle et al. 1996), about 30 or 18 GCs have survived, respectively. The "specific frequency'' of the GCS at the time of the starburst is still quite low, S_N = 2.7 for 35 clusters (or cluster candidates), since the galaxy itself is dominated by the young bright stellar light. Such low S_N values were determined for Local Group irregulars including the LMC (Harris 1991). After 12 Gyr S_N has increased significantly, S_N = 8.4 for 23 GCs (or even S_N = 12.7 for 35 GCs).

If the starburst is 10 times weaker (1% of the total mass), only 3-5 clusters would have survived and the resulting S_N is only slightly larger than before, $S_N = 3.5 \pm 0.5$.

7.2 Estimation of the final S_N of a starburst

Furthermore we want to answer the following question. What is the specific frequency of the starburst itself, without an already existing old stellar population? In other words, we consider an isolated gas cloud and assume that some mechanism has triggered a starburst as strong as observed in starburst galaxies. Then we "destroy'' about 20 to 60% of the cluster light, and look how many GCs survived compared to the total luminosity of the whole system. Note that stars and clusters fade in the same way (according to the models by Fritze v. Alvensleben & Burkert 1995). The final GCLF has by definition the shape of a t5-function with $M_{V,{\rm TO}} = -7.4$ mag and $\sigma = 1.0$.We assume that immediately after the burst 20% of the light comes from clusters and that 1000 GCs will survive the evolution. Table 6 summarizes the results. In column 1 the fraction $f_{\rm destr}$ of GC light that has been disrupted during the evolution is given. Columns 2, 3, and 4 are the absolute luminosities of the evolved GCs, stars, and the total system, respectively. Column 5 gives the resulting S_N of the system.

  

Table 6: Specific frequencies of a starburst, in which 1000 GCs are contained in the final GCLF. The values have been derived under the assumption that 20% of the initial starburst light comes from clusters (Meurer et al. 1995) and a fraction of the cluster light $f_{\rm destr}$ has been supplied to the field star light due to cluster destruction

The calculations show that S_N in an isolated starburst is very high, 40 < S_N < 90. We note that there exists no evidence that such a high S_N can be the result of a simple undisturbed galaxy formation. In particular, dEs, whose structural properties are most easily explained by a starburst followed by a supernova-driven wind (e.g. Dekel & Silk 1986), have much lower S_N values. However, in the context of the galaxy infall scenario, our calculations might imply that stripped gas from galaxies - and especially dwarf galaxies expell their gas most easily (i.e. Dekel & Silk 1986) - can significantly increase the GC S_N of the central GCS, if it suffers a starburst comparable to that observed in starburst galaxies. In Sect. 9 we apply these results to NGC 1399.