Dynamical Modeling of NGC 6809: Selecting the best model using Bayesian
  Inference
  The precise cosmological origin of globular clusters remains uncertain, a
situation hampered by the struggle of observational approaches in conclusively
identifying the presence, or not, of dark matter in these systems. In this
paper, we address this question through an analysis of the particular case of
NGC 6809. While previous studies have performed dynamical modeling of this
globular cluster using a small number of available kinematic data, they did not
perform appropriate statistical inference tests for the choice of best model
description; such statistical inference for model selection is important since,
in general, different models can result in significantly different inferred
quantities. With the latest kinematic data, we use Bayesian inference tests for
model selection and thus obtain the best fitting models, as well as mass and
dynamic mass-to-light ratio estimates. For this, we introduce a new likelihood
function that provides more constrained distributions for the defining
parameters of dynamical models. Initially we consider models with a known
distribution function, and then model the cluster using solutions of the
spherically symmetric Jeans equation; this latter approach depends upon the
mass density profile and anisotropy $\beta$ parameter. In order to find the
best description for the cluster we compare these models by calculating their
Bayesian evidence. We find smaller mass and dynamic mass-to-light ratio values
than previous studies, with the best fitting Michie model for a constant
mass-to-light ratio of $\Upsilon = 0.90^{+0.14}_{-0.14}$ and
$M_{\text{dyn}}=6.10^{+0.51}_{-0.88} \times 10^4 M_{\odot}$. We exclude the
significant presence of dark matter throughout the cluster, showing that no
physically motivated distribution of dark matter can be present away from the
cluster core.
