Application of three-body stability to globular clusters: II. Observed
  velocity dispersions
  The velocity dispersion profile in globular clusters (GCs) is explained here
without having to rely on dark matter or a modification of Newtonian dynamics
(MOND). The flattening of the velocity dispersion at large radii in certain
Milky Way GCs, or lack thereof, is explained by recourse to the stability of
the three-body problem in Newtonian dynamics. The previous paper in this series
determined an analytical formula for the transition radius between stable and
unstable orbits for a star in a GC. This stability boundary is used here to
predict where the velocity dispersion profile is expected to flatten in GCs,
given known orbital parameters of the GC-galaxy orbit. Published observational
data for the velocity dispersion as a function of radius of 15 Milky Way GCs
with approximately known orbital parameters are used here. We find that the
stability boundary predicts flattening in the majority of clusters. While
observational uncertainties in the orbital parameters prevent MOND from being
ruled out entirely for some clusters, it is not the preferred model in any
cluster. Based on the results of this study, we recommend further velocity
dispersion observations and orbital determination for NGC 6171 and NGC 6341 as
these are promising candidates for distinguishing Newtonian and MOND models. In
particular, NGC 6171 may already be showing evidence of the chaotic diffusion
of stars leading to flattening at the predicted stability boundary.
