The outskirts of globular clusters as modified gravity probes
  In the context of theories of gravity modified to account for the observed
dynamics of galactic systems without the need to invoke the existence of dark
matter, a prediction often appears regarding low acceleration systems: wherever
$a$ falls below $a_{0}$ one should expect a transition from the classical to
the modified gravity regime.This modified gravity regime will be characterised
by equilibrium velocities which become independent of distance, and which scale
with the fourth root of the total baryonic mass, $V^{4} \propto M$. The two
above conditions are the well known flat rotation curves and Tully-Fisher
relations of the galactic regime. Recently however, a similar phenomenology has
been hinted at, at the outskirts of Galactic globular clusters, precisely in
the region where $a<a_{0}$. Radial profiles of the projected velocity
dispersion have been observed to stop decreasing along Keplerian expectations,
and to level off at constant values beyond the radii where $a<a_{0}$. We have
constructed gravitational equilibrium dynamical models for a number of globular
clusters for which the above gravitational anomaly has been reported, using a
modified Newtonian force law which yields equilibrium velocities equivalent to
MOND. We find models can be easily constructed having an inner Newtonian region
and an outer modified gravity regime, which reproduce all observational
constraints, surface brightness profiles, total masses and line of sight
velocity dispersion profiles. Through the use of detailed single stellar
population models tuned individually to each of the globular clusters in
question, we derive estimates of the total masses for these systems.
Interestingly, we find that the asymptotic values of the velocity dispersion
profiles are consistent with scaling with the fourth root of the total masses,
as expected under modified gravity scenarios.
