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No energy equipartition in globular clusters
Trenti, Michele; van der Marel, Roeland
AA(Institute of Astronomy, University of Cambridge, Cambridge CB2 1TN, UK; ), AB(Space Telescope Science Institute, Baltimore, MD 21210, USA)
Monthly Notices of the Royal Astronomical Society, Volume 435, Issue 4, p.3272-3282 (MNRAS Homepage)
Publication Date:
Astronomy Keywords:
stars: kinematics and dynamics, globular clusters: general
Abstract Copyright:
2013 The Authors Published by Oxford University Press on behalf of the Royal Astronomical Society
Bibliographic Code:


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 sigma ∝ m-eta with eta = 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 etamax ≈ 0.15 ± 0.03. At large times, all radial bins convergence on an asymptotic value eta ≈ 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 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 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 eta 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.
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