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Fokker-Planck models and globular cluster evolution Drukier, Gordon A.


Numerical models for globular cluster evolution using the orbit-averaged Fokker-Planck equation are compared with observations of the globular clusters M71 and NGC 6397. The first set of models studied includes a mass spectrum, a tidal boundary and allows for a central energy source from the formation, hardening and destruction of binaries formed in three-body interactions. These models are compared to star-count mass functions and surface density profiles for M71. It is possible to reproduce the tidal boundary and degree of mass segregation using these models but the central density profiles of the fitted models are much steeper than is observed. On the basis of the degree of mass segregation and the short relaxation time, M71 is dynamically a highly evolved object, but the surface density profile contradicts this. Several modifications of the model are considered to resolve this difficulty, and an additional energy source, which does not require extreme densities to operate, appears to be required. New observations of the cluster NGC 6397 are presented. This cluster is presently at a similar position in the galaxy as M71, and has a similar mass and mass function, but is much more centrally concentrated. NGC 6397 is a low metallicity cluster with halo kinematics, in contrast to the metal-rich disk cluster M71. The observations have been reduced to give a surface density profile, and mass functions at two distances from the cluster centre. The surface density profile is fit by a power-law with slope —0.8 in the central arc minute. The mass functions give some evidence for mass segregation, but the low signal-to-noise of the outer mass function limits the significance of this observation. A second set of models, augmented to include the effects of mass loss due to stellar evolution, are used to find matches for the observations of M71 and NGC 6397. A diagram showing the evolution with time of the amount of mass segregation and the half-density radius is shown to be useful in identifying good candidate models. Stellar evolution appears not to solve the problem ofM71 as no satisfactorily matching model has been found. Possible solutions to this problem are discussed. The observations of NGC 6397 can be reproduced by the models and the best such model is described. This model has an initial mass function with a Salpeter-like slope and is undergoing core-collapse. This demonstrates that a numerical model based on the orbit-averaged Fokker-Planck equation, and including an evolving mass spectrum, a tidal boundary and the binary energy source, is a useful model for the dynamical evolution of some globular clusters.

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