Astrophysics Modeling the Newtonian dynamics for rotation curve analysis of thin-disk galaxies

Abstract We present an efficient, robust computational method for modeling the Newtonian dynamics for rotation curve analysis of thin-disk galaxies. With appropri-ate mathematical treatments, the apparent numerical difficulties associated with sin-gularities in computing elliptic integrals are completely removed. Using a boundary element discretization procedure, the governing equations are transformed into a lin-ear algebra matrix equation that can be solved by straightforward Gauss elimination in one step without further iterations. The numerical code implemented according to our algorithm can accurately determine the surface mass density distribution in a disk galaxy from a measured rotation curve (or vice versa). For a disk galaxy with a typical flat rotation curve, our modeling results show that the surface mass density monotoni-cally decreases from the galactic center toward the periphery, according to Newtonian dynamics. In a large portion of the galaxy, the surface mass density follows an ap-proximately exponential law of decay with respect to the galactic radial coordinate. Yet the radial scale length for the surface mass density seems to be generally larger than that of the measured brightness distribution, suggesting an increasing mass-to