Title: The Gaia-ESO Survey: Dynamical models of flattened, rotating globular clusters,
Abstract: We present a family of self-consistent axisymmetric rotating globular cluster
models which are fitted to spectroscopic data for NGC 362, NGC 1851, NGC 2808,
NGC 4372, NGC 5927 and NGC 6752 to provide constraints on their physical and
kinematic properties, including their rotation signals. They are constructed by
flattening Modified Plummer profiles, which have the same asymptotic behaviour
as classical Plummer models, but can provide better fits to young clusters due
to a slower turnover in the density profile. The models are in dynamical
equilibrium as they depend solely on the action variables. We employ a fully
Bayesian scheme to investigate the uncertainty in our model parameters
(including mass-to-light ratios and inclination angles) and evaluate the
Bayesian evidence ratio for rotating to non-rotating models. We find convincing
levels of rotation only in NGC 2808. In the other clusters, there is just a
hint of rotation (in particular, NGC 4372 and NGC 5927), as the data quality
does not allow us to draw strong conclusions. Where rotation is present, we
find that it is confined to the central regions, within radii of $R \leq 2
r_h$. As part of this work, we have developed a novel q-Gaussian basis
expansion of the line-of-sight velocity distributions, from which general
models can be constructed via interpolation on the basis coefficients.