The ACS Virgo Cluster Survey. XII. The Luminosity Function of Globular Clusters in Early-Type Galaxies

We analyze the luminosity function of the globular clusters (GCs) belonging to the early-type galaxies observed in the ACS Virgo Cluster Survey. We have obtained maximum likelihood estimates for a Gaussian representation of the globular cluster luminosity function (GCLF) for 89 galaxies. We have also fit the luminosity functions with an "evolved Schechter function", which is meant to reflect the preferential depletion of low-mass GCs, primarily by evaporation due to two-body relaxation, from an initial Schechter mass function similar to that of young massive clusters in local starbursts and mergers. We find a highly significant trend of the GCLF dispersion σ with galaxy luminosity, in the sense that the GC systems in smaller galaxies have narrower luminosity functions. The GCLF dispersions of our Galaxy and M31 are quantitatively in keeping with this trend, and thus the correlation between σ and galaxy luminosity would seem more fundamental than older notions that the GCLF dispersion depends on Hubble type. We show that this narrowing of the GCLF in a Gaussian description is driven by a steepening of the cluster mass function above the classic turnover mass, as one moves to lower luminosity host galaxies. In a Schechter function description, this is reflected by a steady decrease in the value of the exponential cutoff mass scale. We argue that this behavior at the high-mass end of the GC mass function is most likely a consequence of systematic variations of the initial cluster mass function rather than long-term dynamical evolution. The GCLF turnover mass MTO is roughly constant, at MTO ≃ (2.2 ± 0.4) × 105 M☉ in bright galaxies, but it decreases slightly (by ~35% on average, with significant scatter) in dwarf galaxies with MB,gal ≳ -18. It could be important to allow for this effect when using the GCLF as a distance indicator. We show that part, although perhaps not all, of the variation could arise from the shorter dynamical friction timescales in less massive galaxies. We probe the variation of the GCLF to projected galactocentric radii of 20-35 kpc in the Virgo giants M49 and M87, finding that the turnover point is essentially constant over these spatial scales. Our fits of evolved Schechter functions imply average dynamical mass losses (Δ) over a Hubble time that vary more than MTO, and systematically but nonmonotonically as a function of galaxy luminosity. If the initial GC mass distributions rose steeply toward low masses as we assume, then these losses fall in the range 2 × 105 M☉ ≲ Δ < 106 M☉ per GC for all of our galaxies. The trends in Δ are broadly consistent with observed, small variations of the mean GC half-light radius in ACSVCS galaxies, and with rough estimates of the expected scaling of average evaporation rates (galaxy densities) versus total luminosity. We agree with previous suggestions that if the full GCLF is to be understood in more detail, especially alongside other properties of GC systems, the next generation of GCLF models will have to include self-consistent treatments of dynamical evolution inside time-dependent galaxy potentials.