Evolution of the Mass and Luminosity Functions of Globular Star Clusters
  We reexamine the dynamical evolution of the mass and luminosity functions of
globular star clusters (GCMF and GCLF). Fall & Zhang (2001, hereafter FZ01)
showed that a power-law MF, as commonly seen among young cluster systems, would
evolve by dynamical processes over a Hubble time into a peaked MF with a shape
very similar to the observed GCMF in the Milky Way and other galaxies. To
simplify the calculations, the semi-analytical FZ01 model adopted the
"classical" theory of stellar escape from clusters, and neglected variations in
the $M/L$ ratios of clusters. Kruijssen & Portegies Zwart (2009, hereafter
KPZ09) modified the FZ01 model to include "retarded" and mass-dependent stellar
escape, the latter causing significant $M/L$ variations. KPZ09 asserted that
their model was compatible with observations whereas the FZ01 model was not. We
show here that this claim is not correct; the FZ01 and KPZ09 models fit the
observed Galactic GCLF equally well. We also show that there is no detectable
correlation between $M/L$ and $L$ for GCs in the Milky Way and Andromeda
galaxies, in contradiction with the KPZ09 model. Our comparisons of the FZ01
and KPZ09 models with observations can be explained most simply if stars escape
at rates approaching the classical limit for high-mass clusters, as expected on
theoretical grounds.
