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 Galactic globular clusters (GCs) and Local dwarf spheroidal (dSph) galaxies. Tidal radii of remote GCs are used to calibrate the mass of the Milky Way under MOND. We find a mass consistent with the baryonic mass, $\sim 10^{11}$ M$_{\odot}$, obtained from kinematic data, on the $1\sigma$ level. Using this value for the mass of the Milky Way, the tidal radii of dSph galaxies have been derived assuming mass-to-light ratios compatible with a naked stellar population and are found to be fully consistent with the observed tidal radii. 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 Ursa Minor, Draco, Ursa Major and probably Bo\"{o}tes dwarfs. 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