Star Clusters Under Stress: Why Small Systems Cannot Dynamically Relax

TL;DR

This paper uses N-body simulations to show that small stellar clusters evolve differently from classical theories, with binary formation and heating causing expansion rather than core collapse, especially in modest systems.

Contribution

It demonstrates through simulations and analysis that small clusters do not undergo classical dynamical relaxation, highlighting the roles of binary formation and stellar evolution.

Findings

Massive stars sink and form binaries rapidly.

Binary heating reverses core contraction, causing expansion.

Higher N clusters experience longer relaxation phases.

Abstract

Utilizing a series of N-body simulations, we argue that gravitationally bound stellar clusters of modest population evolve very differently from the picture presented by classical dynamical relaxation theory. The system's most massive stars rapidly sink towards the center and form binary systems. These binaries efficiently heat the cluster, reversing any incipient core contraction and driving a subsequent phase of global expansion. Most previous theoretical studies demonstrating deep and persistent dynamical relaxation have either conflated the process with mass segregation, ignored three-body interactions, or else adopted the artificial assumption that all cluster members are single stars of identical mass. In such a uniform-mass cluster, binary formation is greatly delayed, as we confirm here both numerically and analytically. The relative duration of core contraction and global expansion is effected by stellar evolution, which causes the most massive stars to die out before they form binaries. In clusters of higher N, the epoch of dynamical relaxation lasts for progressively longer periods. By extrapolating our results to much larger populations, we can understand, at least qualitatively, why some globular clusters reach the point of true core collapse.