A novel MOND effect in isolated high-acceleration systems

作者：Milgrom Mordehai^*

来源：Monthly Notices of the Royal Astronomical Society, 2012, 426(1): 673-678.

DOI：10.1111/j.1365-2966.2012.21719.x

• galaxies: kinematics and dynamics

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 R less than or greater than r(M), where r(M) equivalent to (GM(t)/a(0))(1/2) is the MOND radius and M-t 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/r(M). 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 phi(a)approximate to G(Q)over-cap(ij)r(i)r(j), where r is the radius from the centre of mass. In quasilinear MOND (QUMOND), (Q)over-cap(ij)=-alpha Q(ij)r(M)(-5), where Q(ij) is the quadrupole moment of the system and alpha > 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 greater than or less than r(M)) is F-a=2 alpha(l/r(M))(3)(mM)(2)M(t)(-3)a(0) (attractive). Its strength relative to the Newtonian force is 2 alpha(mM/M-t(2))(a(0)/gN)(5/2) (gN equivalent to GM(t)/l(2)). For generic MOND theories, which approach Newtonian dynamics quickly for accelerations beyond a(0), 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 kappa a(0), the effect is enhanced by kappa(2).

• 出版日期2012-10