On the incompatibility of the Radial Acceleration Relation and Solar System quadrupole in modified gravity MOND

Modified Newtonian Dynamics (MOND), postulating a breakdown of Newtonianmechanics at low accelerations, has considerable success at explaining galaxykinematics. However, the quadrupole of the gravitational field of the SolarSystem (SS) provides a strong constraint on the way in which Newtonian gravitycan be modified. In this paper we assess the extent to which modified gravityformulations of MOND are capable of accounting simultaneously for the RadialAcceleration Relation (RAR) -- encapsulating late-type galaxy dynamics -- theCassini measurement of the SS quadrupole and the kinematics of wide binaries inthe Solar neighbourhood. We achieve this by extending the method of Desmond(2023) to infer the location and sharpness of the MOND transition from theSPARC RAR under broad assumptions for the behaviour of the interpolatingfunction and external field effect. We constrain the same quantities from theSS quadrupole, finding that it requires a significantly sharper transitionbetween the deep-MOND and Newtonian regimes than is allowed by the RAR (an8.7$\sigma$ tension under fiducial model assumptions). This may be relieved byallowing additional freedom in galaxies' mass-to-light ratios -- which alsoprovides a better RAR fit -- and more significantly by removing galaxies withbulges. We show that the SS quadrupole constraint implies, to high precision,no deviation from Newtonian gravity in wide binaries in the Solarneighbourhood, and speculate on possible resolutions of this incompatibilitybetween SS and galaxy data within the MOND paradigm.