A novel MOND effect in isolated high-acceleration systems


E-mail: moti.milgrom@weizmann.ac.il


We discuss a novel MOND effect that entails a correction to the dynamics of isolated mass systems even when they are deep in the Newtonian regime: systems whose extent RrM, where rM ≡ (GMt/a0)1/2 is the MOND radius and Mt is the total mass. Interestingly, even if the MOND equations approach Newtonian dynamics arbitrarily fast at high accelerations, this correction decreases only as a power of R/rM. The effect appears in formulations of MOND as modified gravity, governed by generalizations of the Poisson equation. The MOND correction to the potential is a quadrupole field math formula, where r is the radius from the centre of mass. In quasilinear MOND (QUMOND), math formula, where Qij is the quadrupole moment of the system and α > 0 is a numerical factor that depends on the interpolating function. For example, the correction to the Newtonian force between two masses, m and M, a distance ℓ apart (ℓ ≪ rM) is math formula (attractive). Its strength relative to the Newtonian force is math formula (gNGMt/ℓ2). For generic MOND theories, which approach Newtonian dynamics quickly for accelerations beyond a0, the predicted strength of the effect in the Solar system is rather much below present testing capabilities. In MOND theories that become Newtonian only beyond κa0, the effect is enhanced by κ2.