Flattened velocity dispersion profiles in Globular Clusters: Newtonian
  tides or modified gravity?
  Over the past couple of years, a number of observational studies have
confirmed the flattening of the radial velocity dispersion profiles for stars
in various nearby globular clusters. As the projected radial coordinate is
increased, a radius appears beyond which, the measured velocity dispersion
ceases to drop and settles at a fixed value, $\sigma_{\infty}$. Under Newtonian
gravity, this is explained by invoking tidal heating from the overall Milky Way
potential on the outer, more loosely bound stars, of the globular clusters in
question. From the point of view of modified gravity theories, such an outer
flattening is expected on crossing the critical acceleration threshold $a_{0}$,
beyond which, a transition to MONDian dynamics is expected, were equilibrium
velocities cease to be a function of distance. In this paper we attempt to sort
out between the above competing explanations, by looking at their plausibility
in terms of an strictly empirical approach. We determine Newtonian tidal radii
using masses accurately calculated through stellar population modelling, and
hence independent of any dynamical assumptions, distances, size and orbital
determinations for a sample of 16 globular clusters. We show that their
Newtonian tidal radii at perigalacticon are generally larger that the radii at
which the flattening in the velocity dispersion profiles occurs, by large
factors of 4, on average. While this point makes the Newtonian tidal
explanation suspect, it is found that the radii at which the flattening is
observed on average correlate with the radii where the $a_{0}$ threshold is
crossed, and that $\sigma_{\infty}$ values scale with the fourth root of the
total masses, all features predicted under modified gravity theories.
