Structural properties of spherical galaxies: A semi-analytical approach

Since the distribution of light measured along any galactocentric radius of an elliptical galaxy has the same functional form exp[-R-1/n] (Sersic profile) for almost all galaxies, and since this profile is the Abel integral of the luminous density, it looks worth-while to seek the way to derive the latter from the former. We propose in this paper a "discrete ordinate" method, which yields, for any value of n > 1, an explicit expression for the luminous density, (rhoL)(r), that can be evaluated numerically to any required degree of precision. Once we have obtained such an expresion for the spatial density, (rhoL)(r), we can compute straightforwardly the mass distribution, M(r), the potential, phi(r), and the velocity dispersions, sigma(s)(2)(r), in space and on the observational plane, sigma(p)(2)(R).