Roche Lobe Shapes in MOND-like Modified Gravity

We consider how to break the near degeneracy between dark matter and baryonic MOdified Newtonian Dynamics (MOND). We show that the Roche Lobes of a two-body baryonic system (e.g., a globular cluster orbiting a host galaxy) are sensitive to modifications of the law of gravity. We generalise the analytical results obtained in the deep-MOND limit by Zhao (2005, astro-ph/0511713), consider in the framework of a general non-Newtonian law g ∝ R . We give analytical expressions for the inner Lagrange point and Robe lobe axis ratios. The Roche lobe volume is proven to scale linearly with the baryonic mass ratio which applies to any modification function μ(g) or power-law function ζ. The lobes are squashed, with the aspect ratio varying with μ(g) due to the anisotropic dilation effect in MOND-like gravity. We generalise these results for extended mass distribution. Precise measurement of Roche lobe shapes for different satellite-host separations could constrain the law of gravity.