The Efficiency of Globular Cluster Formation

The specific frequencies of globular cluster systems, SN ∝ tot/LV,gal ∝ Mgcs/Mstars, are discussed in terms of their connection to the efficiency of globular cluster formation in galaxy halos, which is claimed to reflect a generic aspect of the star formation process as it operates even at the current epoch. It is demonstrated that the total masses of GCSs are little affected by the dynamical destruction of low-mass clusters at small galactocentric radii. This permits direct, empirical estimates of the cluster formation efficiency by mass, cl ≡ M/M, even after 1010 yr of GCS evolution. However, the standard practice of using only the stellar luminosities of galaxies as indicators of their initial total gas masses (and thus relating SN to cl in one step) leads to serious conceptual problems, which are reviewed here. The first specific frequency problem, which is the well-known tendency for many brightest cluster galaxies to have higher than average SN, is a global one; the second specific frequency problem is a local one, in which the more extended spatial distribution of GCSs relative to halo stars in some (not all) bright ellipticals leads to SN-values that increase with radius inside the galaxies. Extending similar suggestions in the recent literature, it is argued that these trends in SN do not reflect any such behavior in the underlying cl; rather, both of these problems stem from neglecting the hot, X-ray emitting gas in and around many large ellipticals, and both may be alleviated by including this component in estimates of M. This claim is checked and confirmed in each of M87, M49, and NGC 1399, all of which have been thought to suffer from one or the other of these SN problems. Existing data are combined to construct GCS surface density profiles that extend over nearly the whole extents of these three galaxies, and a nonparametric, geometrical deprojection algorithm is developed to afford a direct comparison between the volume density profiles of their GCSs, stars, and gas. It is found, in each case, that ρcl ∝ (ρgas + ρstars) at radii beyond roughly a stellar effective radius, inside of which dynamical evolution may have depleted the initial GCSs. The constant of proportionality is the same in all three galaxies: cl = 0.0026 ± 0.0005. Taken together, these results suggest that GCSs generally should be more spatially extended than stellar halos only in gas-rich galaxies that also have a high global specific frequency. The implication that cl might have had a universal value is supported by global GCS data for a sample of 97 giant ellipticals, brightest cluster galaxies, and faint dwarfs. The total globular cluster populations in all of these early-type systems are in excellent agreement with the predictions of a constant cl at the level observed directly in M87, M49, and NGC 1399; all systematic variations in GCS specific frequency between galaxies are shown to result entirely from different relations, in different magnitude ranges, between M and the present-day LV,gal. An identical cl is also calculated for the Population II spheroid of the Milky Way and is indicated (although less conclusively) for the ongoing formation of open clusters. The inferred universal cluster formation efficiency, of 0.25% by mass, should serve as a strong constraint on general theories of star and cluster formation. The associated inference of a nonuniversal formation efficiency for unclustered stars is considered, particularly in terms of the suggestion that this might result, both in dwarf galaxies and at large galactocentric radii in the brightest ellipticals, from feedback and galactic winds. Implications for a merger-formation model of early-type GCSs, and for the proposed existence of intergalactic globulars in clusters of galaxies, are briefly discussed.