Globular Cluster Systems in Nearby Dwarf Galaxies: III. Formation Efficiencies of Old Globular Clusters

We investigate the globular cluster (GC) system scaling parameters as a function of galaxy mass, i.e. specific frequency (S_N), specific luminosity (S_L), specific mass (S_M), and specific number (^T) of GCs. We sample the entire range in galaxy luminosity (Mv = -11 to -23 mag = 10^6 - 10^11 L_sol), environment, and morphology. Irrespective of galaxy type, we confirm the increase of the S_N-value above and below a galaxy magnitude of Mv = -20 mag. Over the full mass range, the S_L-value of early-type galaxies is, on average, twice that of late-types. To investigate the observed trends we derive theoretical predictions of GC system scaling parameters as a function of host galaxy mass based on the models of Dekel & Birnboim (2006) in which star-formation processes are regulated by stellar and supernova feedback below a stellar mass of 3x10^10 M_sol, and by virial shocks above it. We find that the analytical model describes remarkably well the shape of the GC system scaling parameter distributions with a universal specific GC formation efficiency, eta, which relates the total mass in GCs to the total galaxy halo mass. Early-type and late-type galaxies show a similar mean value of eta = 5.5e-5, with an increasing scatter towards lower galaxy masses. This can be due to the enhanced stochastic nature of the star and star-cluster formation processes for such systems. Some massive galaxies have excess eta values compared to what is expected from the mean model prediction for galaxies more luminous than Mv = -20 mag (Lv=10^10L_sol). This may be attributed to a very efficient early GC formation, less efficient production of field stars or accretion of predominantly low-mass/luminosity high-eta galaxies, or a mixture of all these effects. (Abridged)

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