Modified Clutton-Brock Basis Potential Functions in MOND Formulation

In this paper a set of basis potential functions is introduced which could be used in expanding the MONDian potentials of razor-thin galactic disks. We modify Clutton-Brock basis potential functions in Milgrom’s formulation of Modified Newtonian Dynamics (MOND), for razor-thin galactic disks. Then, we use these new modified basis functions to expand modified potential functions of Kuzmin and exponential disks. We calculate expansion coefficients and Kouchi convergence to show that the MONDian potential functions expansions of these two sample disks, versus modified Clutton-Brock basis potential functions, with limited increase of expansion’s terms (up to 30 terms), converge to the exact values of their potentials. Therefore, Modified Clutton-Brock basis potential functions could be used as a set of basis functions for expansion of other MONDian potential functions of razor-thin galactic disks. These basis functions could also be applicable in simulations and codes which are used to study the dynamics of disk galaxies, especially in the methods like N-body simulations and particle mesh.