Roche lobe sizes in deep-MOND gravity

MOdified Newtonian Dynamics survived the test over two decades, fitting the ups and downs of a variety of galaxy velocity curves without fine , tuning (Sanders & McGaugh 2002, ARA&A, 40, 263). MOND is also evolving from an empirical to a decent theory respecting fundamental physics after Bekenstein (2004, Phys. Rev. D, 70, 3509) showed that le and Hubble expansion can be modeled rigourously in a Modified Relativity. However, many properties of MOND are obscured by its non-linear Poisson's equation. Here we study the effect of tides for a binary stellar system or a baryonic satellite-host galaxy system. We show that the Roche lobe is more squashed than the Newtonian case due to the anisotropic dilation effect in deep-MOND. We prove analytically that the Roche lobe volume scales linearly with the "true" baryonic mass ratio in both Newtonian and deep-MOND regimes, insensitive to the modification to the inertia mass. Hence accurate Roche radii of satellites can break the degeneracy of MOND and dark matter theory. Globular clusters and dwarf galaxies of comparable luminosities and distances show a factor of ten scatter in limiting radii; this is difficult to explain in any "mass-tracing-light" universe.