Modeling the Rotation Curve of Disk Galaxies

Abstract The present paper suggests an exact solution of the Poisson equation which appears infrequently addressed in applications regarding the calculation of the gravitational potential of disk galaxies. We suggest an analytical solution for the problem in cylindrical coordinates by using the finite integral transform technique. The final solution is presented as an expansion on the eigenfunctions of the corresponding Sturm–Liouville problem. The Green’s function of the problem is constructed for an arbitrary density distribution function of matter in a galaxy. Based on the obtained results, we propose an expression for the rotation curve. As an example, this paper suggests the calculations of the rotation curve for the Galaxy.