Self-similar orbit-averaged Fokker-Planck equation for isotropic spherical dense clusters (iii) Application to Galactic globular clusters

Yuta Ito

Published 2020-03-31Version 1

This is the third paper of a series of our works on the self-similar orbit-averaged Fokker-Planck (OAFP) equation. The first paper shows an accurate spectral solution of the equation for isotropic pre-collape cluster and the second details the physical feature of the model and negative specific heat. Based on the works, the present work applies the solution to observed the structural profiles of Galactic globular clusters. For fitting to the structures, the most fundamental (quasi-)stationary model, the King model, and the variants have shown successful results while they can not apply to clusters just before or after core-collapse phase at the late stage of the relaxation evolution. We aim at establishing an energy-truncated self-similar OAFP model that can apply to clusters at both the early- and late stage 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 at broad radii (0.01$\sim$10 arcminutes). However, due to the nature of polytrope (elongated outer halo) the tidal radius of the model becomes unrealistically large for some clusters. To avoid the issue, we propose an approximated form of the new model. Lastly, we suggest that Milky Way globular clusters with low concentrations have the same spatial structures as stellar polytropes and discuss whether such polytropic globular cluster can exist.