Dynamical Evolution of the Mass Function of Globular Star Clusters

We present a series of simple, largely analytical models to compute the effects of disruption on the mass function of star clusters. Our calculations include evaporation by two-body relaxation and gravitational shocks and mass loss by stellar evolution. We find that, for a wide variety of initial conditions, the mass function develops a turnover or peak and that, after 12 Gyr, this is remarkably close to the observed peak for globular clusters, at M_p = 2 10^5 solar masses. Below the peak, the evolution is dominated by two-body relaxation, and the mass function always develops a tail of the form psi(M) = const, reflecting that the masses of tidally limited clusters decrease linearly with time just before they are destroyed. This also agrees well with the empirical mass function of globular clusters in the Milky Way. Above the peak, the evolution is dominated by stellar evolution at early times and gravitational shocks at late times. These processes shift the mass function to lower masses while nearly preserving its shape. The radial variation of the mass function within a galaxy depends on the initial position-velocity distribution of the clusters. We find that some radial anisotropy in the initial velocity distribution, especially when this increases outward, is needed to account for the observed near-uniformity of the mass functions of globular clusters. This may be consistent with the observed near-isotropy of the present velocity distributions because clusters on elongated orbits are preferentially destroyed. These results are based on models with static, spherical galactic potentials. We point out that there would be even more radial mixing of the orbits and hence more uniformity of the mass function if the galactic potentials were time-dependent and/or non-spherical.