Title:Star Clusters Under Stress: Why Small Systems Cannot Dynamically Relax

Abstract:
Utilizing a series of N-body simulations, I argue that gravitationally bound clusters of modest population 
evolve very differently from the picture presented by classical dynamical relaxation theory. Dynamical friction 
causes the most massive stars to rapidly sink towards the center of the cluster 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 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 I confirm numerically. 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 these results to much larger populations we can understand, at least qualitatively, why some 
globular clusters reach the point of true core collapse.