Dynamical evolution of the mass function of globular star clusters

We present a series of simple, largely analytical models to compute the eff ects of disruption on the mass function of star clusters. Our calculations include evaporation by two-body relaxation and gravitational shocks and mas s loss by stellar evolution. We find that, for a wide variety of initial co nditions, the mass function develops a turnover or peak and that, after 12 Gyr, this is remarkably close to the observed peak for globular clusters, a t M-p approximate to 2 x 10(5) M-circle dot. 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 l imited clusters decrease linearly with time just before they are destroyed. This also agrees well with the empirical mass function of globular cluster s in the Milky Way. Above the peak, the evolution is dominated by stellar e volution at early times and by gravitational shocks at late times. These pr ocesses shift the mass function to lower masses, while nearly preserving it s 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 wh en this increases outward, is needed to account for the observed near-unifo rmity of the mass functions of globular clusters. This may be consistent wi th the observed near-isotropy of the present velocity distributions, becaus e clusters on elongated orbits are preferentially destroyed. These results are based on models with static, spherical galactic potentials. We point ou t 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-depend ent and/or nonspherical.