A novel MOND effect in isolated high-acceleration systems

Abstract

I 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 R<<Rm, where Rm=sqrt(GM/a0) is the MOND radius, and M 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 G*Pij*Ri*Rj, where R is the radius from the center of mass. In QUMOND (quasilinear MOND), Pij=-qQij/Rm^5, where Qij is the quadrupole moment of the system, and q>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 Fa=2q(L/Rm)^3(mM)^2(M+m)^{-3}a0 (attractive). 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 k*a0, the effect is enhanced by k^2.