Evolution of the mass function (MF) and radial distribution (RD) of the globular cluster (GC) systems of the Milky Way and M87 are calculated using an advanced and realistic Fokker-Planck (FP) model that considers dynamical friction, disk/bulge shocks, and eccentric cluster orbits. We perform hundreds of FP calculations with different initial cluster conditions, and then search a wide parameter space for the best-fit initial GC MF and RD that evolves into the observed present-day GC MF and RD. By allowing both MF and RD of the initial GC system to vary, we find that our best-fit models have a higher peak mass for a log-normal initial MF and a higher cutoff mass for a power-law initial MF than previous estimates. We also find that our results are insensitive to the initial distribution of orbit eccentricity and inclination, but are rather sensitive to the initial concentration of the clusters and to how the initial tidal radius is defined. We discuss the possibility of using the peak mass of the GCMF in a galaxy as a standard candle.
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