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.