Comparative study between N-body and Fokker-Planck simulations for rotating star clusters - II. 2-component models

TL;DR

This study compares N-body and Fokker-Planck simulations of rotating, two-component star clusters, revealing how initial rotation and mass spectrum influence cluster evolution and shape, especially during bar instability phases.

Contribution

It provides a detailed comparison of N-body and Fokker-Planck methods for rotating star clusters with mass spectrum, highlighting differences during early bar instability development.

Findings

N-body and FP simulations agree well for slow rotation.

Rapid rotation leads to bar instability in N-body simulations.

Cluster shape becomes tri-axial or prolate during instability.

Abstract

To understand the effects of the initial rotation on the evolution of the tidally limited clusters with mass spectrum, we have performed N-body simulations of the clusters with different initial rotations and compared the results with those of the Fokker-Planck (FP) simulations. We confirmed that the cluster evolution is accelerated by not only the initial rotation but also the mass spectrum. For the slowly rotating models, the time evolutions of mass, energy and angular momentum show good agreements between N-body and FP simulations. On the other hand, for the rapidly rotating models, there are significant differences between these two approaches at the early stage of the evolutions because of the development of bar instability in N-body simulations. The shape of the cluster for N-body simulations becomes tri-axial or even prolate, which cannot be produced by the 2-dimensional FP simulations. The total angular momentum and the total mass of the cluster decrease rapidly while bar-like structure persists. After the rotational energy becomes smaller than the critical value for the bar instability, the shape of the cluster becomes nearly axisymmetric again, and follows the evolutionary track predicted by the FP equation. We have confirmed again that the energy equipartiton is not completely achieved when M2/M1(m2>/m1)^(3/2) > 0.16. By examining the angular momentum at each mass component, we found that the exchange of angular momentum between different mass components occurs, similar to the energy exchange leading to the equipartition.