Axisymmetric and Triaxial MOND Density‐Potential Pairs

We present a simple method, based on the deformation of spherically symmetricpotentials, to construct explicit axisymmetric and triaxial MONDdensity-potential pairs. General guidelines to the choice of suitabledeformations, so that the resulting density distribution is nowhere negative,are presented. This flexible method offers for the first time the possibilityto study the MOND gravitational field for sufficiently general and realisticdensity distributions without resorting to sophisticated numerical codes. Thetechnique is illustrated by constructing the MOND density-potential pair for atriaxial galaxy model that, in the absence of deformation, reduces to theHernquist sphere. Such analytical solutions are also relevant to test andvalidate numerical codes. Here we present a new numerical potential solverdesigned to solve the MOND field equation for arbitrary density distributions:the code is tested with excellent results against the analytic MOND triaxialHernquist model and the MOND razor-thin Kuzmin disk, and a simple applicationis finally presented.Comment: 21 pages, 5 figures. Accepted for publication in the Astrophysical Journa