The difference in metallicity distribution functions of halo stars and globular clusters as a function of galaxy type A tracer of globular cluster formation and evolution

Context. Observations of globular clusters (GCs) and field stars in thehalos of the giant elliptical galaxy Cen A and the spiral galaxy M 31show a large range of cluster-to-star number ratios (or "specificfrequencies"). The cluster-to-star ratio decreases with increasingmetallicity by over a factor of 100-1000, at all galactocentric radiiand with a slope that does not seem to depend on radius. In dwarfgalaxies, the GCs are also more metal-poor than the field stars onaverage. These observations indicate a strong dependence of either thecluster formation efficiency and/or the cluster destruction rate onmetallicity and environment. Aims. We aim to explain the observedtrends by considering the various effects that influence thecluster-to-star ratio as a function of metallicity, environment andcosmological history.
Methods. We discuss the following effectsthat may influence the observed cluster-to-star ratio: (a) the formationefficiency of GCs; (b) the destruction of embedded GCs by gas expulsion;(c) the maximum masses of GCs; (d) the destruction of GCs by tidalstripping, dynamical friction, and tidal shocks as a function ofenvironment; (e) the hierarchical assembly of GC systems during galaxyformation and the dependence on metallicity.
Results. We showthat both the cluster formation efficiency and the maximum cluster massincrease with metallicity, so they cannot explain the observed trend.Destruction of GCs by tidal stripping and dynamical friction destroyclusters mostly within the inner few kpc, whereas the cluster-to-starratio trend is observed over a much larger range of galactocentricradii. We show that cluster destruction by tidal shocks from giantmolecular clouds in the high-density formation environments of GCsbecomes increasingly efficient towards high galaxy masses and, hence,towards high metallicities. The predicted cluster-to-star ratiodecreases by a factor 100-1000 towards high metallicities and shouldonly weakly depend on galactocentric radius due to orbital mixing duringhierarchical galaxy merging, consistent with the observations. Conclusions. The observed, strong dependence of the cluster-to-starratio on metallicity and the independence of its slope on galactocentricradius can be explained by cluster destruction and hierarchical galaxygrowth. During galaxy assembly, GC metallicities remain a good tracer ofthe host galaxy masses in which the GCs formed and experienced most oftheir destruction. As a result, we find that the metallicity-dependenceof the cluster-to-star ratio does not reflect a GC formation efficiency,but a survival fraction.