Color-Magnitude Relations within Globular Cluster Systems of Giant
  Elliptical Galaxies: The Effects of Globular Cluster Mass Loss and the
  Stellar Initial Mass Function
  Several recent studies have provided evidence for a `bottom-heavy' stellar
initial mass function (IMF) in massive elliptical galaxies. Here we investigate
the influence of the IMF shape on the recently discovered color-magnitude
relation (CMR) among globular clusters (GCs) in such galaxies. To this end we
use calculations of GC mass loss due to stellar and dynamical evolution to
evaluate (i) the shapes of stellar mass functions in GCs after 12 Gyr of
evolution as a function of current GC mass along with their effects on
integrated-light colors and mass-to-light ratios, and (ii) their impact on the
effects of GC self-enrichment using the 2009 `reference' model of Bailin &
Harris. As to the class of metal-poor GCs, we find the observed shape of the
CMR (often referred to as the `blue tilt') to be very well reproduced by Bailin
& Harris' reference self-enrichment model once 12 Gyr of GC mass loss is taken
into account. The influence of the IMF on this result is found to be
insignificant. However, we find that the observed CMR among the class of
metal-rich GCs (the `red tilt') can only be adequately reproduced if the IMF
was bottom-heavy (e.g., $-3.0 <~ \alpha <~ -2.3$ in $dN/dM \propto
M^{\alpha}$), which causes the stellar mass function at subsolar masses to
depend relatively strongly on GC mass. This constitutes additional evidence
that the metal-rich stellar populations in giant elliptical galaxies were
formed with a bottom-heavy IMF.
