Self-similar orbit-averaged Fokker-Planck equation for isotropic spherical dense clusters (iii) Application to Galactic globular clusters. (arXiv:2004.00747v1 [astro-ph.GA])

Self-similar orbit-averaged Fokker-Planck equation for isotropic spherical dense clusters (iii) Application to Galactic globular clusters. (arXiv:2004.00747v1 [astro-ph.GA])
<a href="http://arxiv.org/find/astro-ph/1/au:+Ito_Y/0/1/0/all/0/1">Yuta Ito</a>

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.

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.

http://arxiv.org/icons/sfx.gif