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We have derived the global mass functions of a sample of 35 Galactic globularclusters by comparing deep Hubble Space Telescope photometry with suitablemultimass dynamical models. For a subset of 29 clusters with available radialvelocity information we were also able to determine dynamical parameters,mass-to-light ratios and the mass fraction of dark remnants. The derived globalmass functions are well described by single power-laws in the mass range $0.2 <m/M_\odot < 0.8$ with mass function slopes $\alpha>-1$. Less evolved clustersshow deviations from a single-power law, indicating that the original shape oftheir mass distribution was not a power-law. We find a tight anticorrelationbetween the present-day mass function slopes and the half-mass relaxationtimes, which can be understood if clusters started from the same universal IMFand internal dynamical evolution is the main driver in shaping the present-daymass functions. Alternatively, IMF differences correlated with the present-dayhalf-mass relaxation time are needed to explain the observed correlation. Thelarge range of mass function slopes seen for our clusters implies that mostglobular clusters are dynamically highly evolved, a fact that seems difficultto reconcile with standard estimates for the dynamical evolution of clusters.The mass function slopes also correlate with the dark remnant fractionsindicating a preferential retention of massive remnants in clusters subject tohigh mass-loss rates.

The global mass functions of 35 Galactic globular clusters: I. Observational data and correlations with cluster parameters