No Energy Equipartition in Globular Clusters

TL;DR

Globular clusters do not reach energy equipartition as previously believed; instead, they develop only partial equipartition, with velocity dispersion scaling weakly with stellar mass, a finding supported by direct N-body simulations.

Contribution

This study challenges the long-held assumption that globular clusters evolve toward full energy equipartition, demonstrating instead a state of partial equipartition through detailed simulations.

Findings

No simulated globular cluster reaches full equipartition.

Maximum ta for main-sequence stars is about 0.15.

Presence of an IMBH reduces ta, indicating less mass segregation.

Abstract

It is widely believed that globular clusters evolve over many two-body relaxation times toward a state of energy equipartition, so that velocity dispersion scales with stellar mass as \sigma ~ m^{-\eta} with \eta = 0.5. We show that this is incorrect, using direct N-body simulations with a variety of realistic IMFs and initial conditions. No simulated system ever reaches a state close to equipartition. Near the center, the luminous main-sequence stars reach a maximum \eta_{max} ~ 0.15 \pm 0.03. At large times, all radial bins convergence on an asymptotic value \eta_{\infty} ~ 0.08 \pm 0.02. The development of this "partial equipartition" is strikingly similar across our simulations, despite the range of initial conditions employed. Compact remnants tend to have higher \eta than main-sequence stars (but still \eta < 0.5), due to their steeper (evolved) mass function. The presence of an intermediate-mass black hole (IMBH) decreases \eta, consistent with our previous findings of a quenching of mass segregation under these conditions. All these results can be understood as a consequence of the Spitzer instability for two-component systems, extended by Vishniac to a continuous mass spectrum. Mass segregation (the tendency of heavier stars to sink toward the core) has often been studied observationally, but energy equipartition has not. Due to the advent of high-quality proper motion datasets from the Hubble Space Telescope, it is now possible to measure \eta. Detailed data-model comparisons open up a new observational window on globular cluster dynamics and evolution. Comparison of our simulations to Omega Cen observations yields good agreement, confirming that globular clusters are not generally in energy equipartition. Modeling techniques that assume equipartition by construction (e.g., multi-mass Michie-King models) are approximate at best.