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

Abstract

This is the third paper of a series of our works on the self-similar orbit-averaged Fokker-Planck (OAFP) equation. The first paper provided an accurate spectral solution of the equation for isotropic pre-collapse star clusters and the second detailed the physical feature of the model. Based on the works, the present work applies the solution to the observed structural profiles of Galactic globular clusters. For fitting to the profiles, the most fundamental (quasi-)stationary model, the King model, and the variants have shown successful results while they can not apply to core-collapsing and core-collapsed clusters at the late stage of the relaxation evolution. We propose an energy-truncated self-similar OAFP model that can apply to clusters at both the early and late stages of the evolution. This new model fits the structural profiles of at least half of Galactic globular clusters while it also applies to core-collapsed stars with resolved cores. As a main result, we provide the completion rate of core collapse against concentration for the clusters. Also, we show our new model can apply to the globular clusters even in a broad range of radii (0.01$\sim$10 arcminutes). However, since our model includes polytrope (elongated outer halo), the tidal radius of the model becomes unrealistically large for some clusters. To avoid the issue, we also propose an approximated form of the new model. Lastly, we report that Milky Way globular clusters with low concentrations have the same spatial structures as stellar polytropes and discuss whether such polytropic cluster is a reasonable concept.