On the tension between the Radial Acceleration Relation and Solar System quadrupole in modified gravity MOND

Modified Newtonian Dynamics (MOND), postulating a breakdown of Newtonian mechanics at low accelerations, has considerable success at explaining galaxy kinematics. However, the quadrupole of the gravitational field of the Solar System (SS) provides a strong constraint on the way in which Newtonian gravity can be modified. In this paper we assess the extent to which the AQUAL and QUMOND modified gravity formulations of MOND are capable of accounting simultaneously for the Radial Acceleration Relation (RAR), the Cassini measurement of the SS quadrupole and the kinematics of wide binaries in the Solar neighbourhood. We achieve this by inferring the location and sharpness of the MOND transition from the SPARC RAR under broad assumptions for the behaviour of the interpolating function and external field effect. We constrain the same quantities from the SS quadrupole, finding that this requires a significantly sharper transition between the deep-MOND and Newtonian regimes than is allowed by the RAR (an 8.7$\sigma$ tension under fiducial model assumptions). This may be relieved somewhat by allowing additional freedom in galaxies' mass-to-light ratios -- which also improves the RAR fit -- and more significantly (to 1.9$\sigma$) by removing galaxies with bulges. For the first time, we also apply to the SPARC RAR fit an AQUAL correction for flattened systems, obtaining similar results. Finally we show that the SS quadrupole constraint implies, to high precision, no deviation from Newtonian gravity in nearby wide binaries, and speculate on possible resolutions of this tension between SS and galaxy data within the MOND paradigm.