X. Hernandez, M. A. Jimenez, C. Allen
Over the past couple of years, a number of observational studies have confirmed the outer flattening of the radial velocity dispersion profiles for stars in various nearby globular clusters. 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 the sample of 8 globular clusters studied. We show that their Newtonian tidal radii, in all cases, at perigalacticon, are larger that the radii at which the flattening in the velocity dispersion profiles occur, by large factors of 2-10. While this point makes the Newtonian tidal explanation extremely suspect, it is found that the radii at which the flattening is observed nicely correlates with the radii where the $a_{0}$ threshold is crossed, that the fractional fall in the velocity dispersion profile correlates with the fraction of the cluster lying within the $a_{0}$ threshold, and that $\sigma_{\infty}$ values scale with the fourth root of the total masses, all features predicted under modified gravity theories.
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http://arxiv.org/abs/1206.5024
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