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 ( -3.0 \la \alpha \la - 2.3 in dN / d { \cal { M } } \propto { \cal { 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 .