Exact solutions and approximations of MOND fields of disc galaxies

Abstract We Consider models of thin disks (with and without bulges) in the Bekenstein-Milgrom formulation of MOND as a modification of Newtonian gravity. Analytic solutions are found for the full gravitational fields of Kuzmin disks, and of disk-plus-bulge generalizations of them. For all these models a simple relation between the MOND potential field, ψ, and the Newtonian potential, ϕ N, holds everywhere outside the disk: µ( | ∇ψ|/a o) ∇ψ = ∇ϕ N. We give exact expressions for the rotation curves for these models. We also find that this algebraic relation is a very good approximation for exponential disks. The algebraic relation outside the disk is then extended into the disk to derive an improved approximation for the MOND rotation curve of disk galaxies that requires only knowledge of the Newtonian curve and the surface density. I.