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Observations of globular clusters (GCs) and field stars in the halos of thegiant elliptical galaxy Cen A and the spiral galaxy M31 show a large range ofcluster-to-star number ratios ('specific frequencies'). The cluster-to-starratio decreases with increasing metallicity by a factor of 100-1000, at allgalactocentric radii and with a slope that does not seem to depend on radius.In dwarf galaxies, the GCs are also more metal-poor than the field stars onaverage. These observations indicate a strong dependence of either the clusterformation efficiency or the cluster destruction rate on metallicity andenvironment. We aim to explain these trends by considering various effects thatmay influence the observed cluster-to-star ratio as a function of metallicity,environment and cosmological history. We show that both the cluster formationefficiency and the maximum cluster mass increase with metallicity, so theycannot explain the observed trend. Destruction of GCs by tidal stripping anddynamical friction destroy clusters over too small a range of galactocentricradii. We show that cluster destruction by tidal shocks from giant molecularclouds in the high-density formation environments of GCs becomes increasinglyefficient towards high galaxy masses and, hence, towards high metallicities.The predicted cluster-to-star ratio decreases by a factor 100-1000 towards highmetallicities and should only weakly depend on galactocentric radius due toorbital mixing during hierarchical galaxy merging, consistent with theobservations. The observed, strong dependence of the cluster-to-star ratio onmetallicity and the independence of its slope on galactocentric radius can beexplained by cluster destruction and hierarchical galaxy growth. As a result,we find that the metallicity-dependence of the cluster-to-star ratio does notreflect a GC formation efficiency, but a survival fraction. (Abridged)

astronomy and astrophysics

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