No Energy Equipartition in Globular Clusters
  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.
