2013MNRAS.435.3272T

It is widely believed that globular clusters evolve over many two-body relaxation times towards a state of energy equipartition, so that velocity dispersion scales with stellar mass as σ ∝ m-η with η = 0.5. We show here that this is incorrect, using a suite of direct N-body simulations with a variety of realistic initial mass functions and initial conditions. No simulated system ever reaches a state close to equipartition. Near the centre, the luminous main-sequence stars reach a maximum ηmax ~ 0.15±0.03. At large times, all radial bins convergence on an asymptotic value η∞ ~ 0.08±0.02. The development of this `partial equipartition' is strikingly similar across our simulations, despite the range of different initial conditions employed. Compact remnants tend to have higher η than main-sequence stars (but still η < 0.5), due to their steeper (evolved) mass function. The presence of an intermediate-mass black hole (IMBH) decreases η, 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 towards the core) has often been studied observationally, but energy equipartition has not. Due to the advent of high-quality proper motion data sets from the Hubble Space Telescope, it is now possible to measure η for real clusters. Detailed data-model comparisons open up a new observational window on globular cluster dynamics and evolution. A first comparison of our simulations to observations of Omega Cen yields good agreement, supporting the view that globular clusters are not generally in energy equipartition. Modelling techniques that assume equipartition by construction (e.g. multi-mass Michie-King models) are approximate at best.