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Tidal radii and escape speeds in dwarf spheroidal galaxies under MOND and dark halos compared

We investigate the success and problems of MOdified Newtonian Dynamics (MOND) in explaining the structural parameters and dynamics of remote Galactic globular clusters (GCs) and dwarf spheroidal (dSph) galaxies. Using the MOND value for the mass of the Milky Way as inferred from the Galactic rotation curve, we derive the tidal radii of Galactic GCs, and compare to observed values. Except for Pal 14, the predicted tidal radii of GCs are systematically larger than the observed nominal values. However, the associated uncertainties are so large that tidal radii are consistent on the $1σ$ level. We have considered the importance of the Galactic tidal force on the survival of dSphs under MOND. Assuming mass-to-light ratios compatible with a naked stellar population, we found that the present Galactic dSphs preserve their integrity over one Hubble time, except Sextans which may survive the tidal interaction only for several Gyr. Mass-to-light ratios as inferred from the internal kinematics of dSph galaxies can be used, but they appear too large to be accounted for only by the stellar population in Willman 1, Coma Berenice, Ursa Minor, Draco, Ursa Major and possibly Boötes dwarves. Finally, the ability of the Sculptor dwarf to retain the observed population of low-mass X-ray binaries (LMXBs) is examined. Under the MOND paradigm, we find that the retention fraction in Sculptor is likely not larger than a few percent. Compared to the dark matter scenario, it turns out that MOND makes the retention problem worse. We propose that measurements of the radial velocities of the observed LMXBs in Sculptor could provide a way to distinguish between modified gravities or extended and massive dark matter halos.