4.3 Physical Basis
So far, the motivation for the GCLF as a standard candle is almost totally empirical rather than theoretical. The astrophysical basis for its similarity from one galaxy to another is a challenging problem, and is probably less well understood than for any other standard candle currently in use. Because globular clusters are old-halo objects that probably predate the formation of most of the other stellar populations in galaxies (e.g. Harris 1986, 1988b, 1991; Fall and Rees 1988), to first order it is not surprising that they look far more similar from place to place than their parent galaxies do. Methods for allowing clusters to form with average masses that are nearly independent of galaxy size or type have been put forward by Fall and Rees (1985, 1988), Larson (1988, 1990), Rosenblatt et al. (1988), and Ashman and Zepf (1992) under various initial assumptions. Other constraints arising from cluster metallicity distributions and the early chemical evolution of the galaxies are discussed by Lin and Murray (1991) Brown et al. (1991). None of these yet serve as more than general guidelines for understanding why the early cluster formation process should be so nearly invariant in the early universe.
After the initial formation epoch, dynamical effects on the clusters including tidal shocking and dynamical friction, and evaporation of stars driven by internal relaxation and the surrounding tidal field, must also affect the GCLF within a galaxy over many Gyr, and these mechanisms might well behave rather similarly in large galaxies of many different types. Recent models incorporating these effects (e.g. Aguilar et al. 1988; Lee and Ostriker 1987; Chernoff and Shapiro 1987; Allen and Richstone 1988) show that their importance decreases dramatically for distances 2-3 kpc from the galaxy nucleus, and for the more massive, compact clusters like present-day globulars. In addition, recent photometry (Grillmair et al. 1986; Lauer and Kormendy 1986; Harris et al. 1991) extending in close to the centers of the Virgo ellipticals has shown no detectable GCLF differences with radius. The implication is therefore that today's GCLF resembles the original mass formation spectrum of at least the brighter clusters, perhaps only slightly modified by dynamical processes. Many qualitative arguments can be constructed as to why the GCLFs should, or should not, resemble each other in different galaxies, but at the present time these must take a distant second place to the actual data.