The Efficiency of Globular Cluster Formation

Abstract

The speciÐc frequencies of globular cluster systems, are discussed in S N P N tot /L V,gal P M gcs /M stars , terms of their connection to the efficiency of globular cluster formation in galaxy halos, which is claimed to reÑect 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 a †ected by the dynamical destruction of low-mass clusters at small galactocentric radii. This permits direct, empirical estimates of the cluster formation efficiency by mass, even after 1010 yr of GCS evolution. However, the standard practice v cl 4 M gcs init/M gas init, of using only the stellar luminosities of galaxies as indicators of their initial total gas masses (and thus relating to in one step) leads to serious conceptual problems, which are reviewed here. The Ðrst S N v cl speciÐc frequency problem, which is the well-known tendency for many brightest cluster galaxies to have higher than average is a global one ; the second speciÐc frequency problem is a local one, in which the S N , more extended spatial distribution of GCSs relative to halo stars in some (not all) bright ellipticals leads to that increase with radius inside the galaxies. Extending similar suggestions in the recent S N-values literature, it is argued that these trends in do not reÑect any such behavior in the underlying S N v 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 gas init. This claim is checked and conÐrmed in each of M87, M49, and NGC 1399, all of which have been thought to su †er from one or the other of these problems. Existing data are combined to construct S N GCS surface density proÐles that extend over nearly the whole extents of these three galaxies, and a nonparametric, geometrical deprojection algorithm is developed to a †ord a direct comparison between the volume density proÐles of their GCSs, stars, and gas. It is found, in each case, that o cl P (o gas ] o stars) at radii beyond roughly a stellar e †ective radius, inside of which dynamical evolution may have depleted the initial GCSs. The constant of proportionality is the same in all three galaxies : v 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 speciÐc frequency. The implication that might have had a universal value is supported by global GCS data for a v cl 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 v cl at the level observed directly in M87, M49, and NGC 1399 ; all systematic variations in GCS speciÐc frequency between galaxies are shown to result entirely from di †erent relations, in di †erent magnitude ranges, between and the present-day An identical is also calculated for the Population II M gas init L V,gal. v cl 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 non-universal 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 brieÑy discussed.