Shaping the globular cluster mass function by stellar-dynamical evaporation

We show that the globular cluster mass function (GCMF) in the Milky Way depends on cluster half-mass density, rho(h), in the sense that the turnover mass M-TO increases with rho(h) while the width of the GCMF decreases. We argue that this is the expected signature of the slow erosion of a mass function that initially rose toward low masses, predominantly through cluster evaporation driven by internal two-body relaxation. We find excellent agreement between the observed GCMF-including its dependence on internal density rho(h), central concentration c, and Galactocentric distance r(gc) - and a simple model in which the relaxation-driven mass-loss rates of clusters are approximated by -dM/dt = mu(ev) proportional to rho(1/2)(h) h. In particular, we recover the well-known insensitivity of M-TO to r(gc). This feature does not derive from a literal universality'' of the GCMF turnover mass, but rather from a significant variation of M-TO with rho(h) - the expected outcome of relaxation-driven cluster disruption - plus significant scatter in rho(h) as a function of rgc. Our conclusions are the same if the evaporation rates are assumed to depend instead on the mean volume or surface densities of clusters inside their tidal radii, as mu(ev) proportional to rho(1/2)(t) or mu(ev) proportional to Sigma(3/4)(t) -alternative prescriptions that are physically motivated but involve cluster properties (rho(t) and Sigma(t)) that are not as well defined or as readily observable as rho(h). In all cases the normalization of mu(ev) required to fit the GCMF implies cluster lifetimes that are within the range of standard values (although falling toward the low end of this range). Our analysis does not depend on any assumptions or information about velocity anisotropy in the globular cluster system.