A comparison of the globular cluster luminosity functions of the inner and outer halo of the Milky Way and M31

We show that the globular cluster luminosity function (GCLF) of the inner halo of the Milky Way is statistically different from the GCLF of the outer halo. We also find a similar difference between the inner and outer halo population of M31. We assert that this difference is evidence for some form of dynamical evolution of the cluster population and/or a dependence of GCLF shape on the environment in which the cluster population formed. We also find that the turnover luminosity of the GCLF is unaffected by these differences and further assert that this stability of the turnover luminosity affirms its usefulness as an indicator of cosmic distance.