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This is the third paper of a series of our works on the self-similarorbit-averaged Fokker-Planck (OAFP) equation. The first paper provided anaccurate spectral solution of the equation for isotropic pre-collapse starclusters and the second detailed the physical feature of the model. Based onthe works, the present work applies the solution to the observed structuralprofiles of Galactic globular clusters. For fitting to the profiles, the mostfundamental (quasi-)stationary model, the King model, and the variants haveshown successful results while they can not apply to core-collapsing andcore-collapsed clusters at the late stage of the relaxation evolution. Wepropose an energy-truncated self-similar OAFP model that can apply to clustersat both the early and late stages of the evolution. This new model fits thestructural profiles of at least half of Galactic globular clusters while italso applies to core-collapsed stars with resolved cores. As a main result, weprovide the completion rate of core collapse against concentration for theclusters. Also, we show our new model can apply to the globular clusters evenin a broad range of radii (0.01$\sim$10 arcminutes). However, since our modelincludes polytrope (elongated outer halo), the tidal radius of the modelbecomes unrealistically large for some clusters. To avoid the issue, we alsopropose an approximated form of the new model. Lastly, we report that Milky Wayglobular clusters with low concentrations have the same spatial structures asstellar polytropes and discuss whether such polytropic cluster is a reasonableconcept.

research in astronomy and astrophysics/research in astronomy and astrophysics

Self-similar orbit-averaged Fokker-Planck equation for isotropic  spherical dense clusters (iii) application of pre-collapse solution to  Galactic globular clusters