Elements of a gravitational lens system assuming an elliptical galaxy model

Abstract

This work studies some elements of gravitational lensing by galaxies such as the lens equation, deflection angle, lensing potential and time delay, modeling the mass distribution of the lensing galaxy as an elliptical galaxy. The mass distribution function ρ of the deflecting galaxy indicates that it has a nucleus with radius a in its core, a free-form parameter b (b > a), and that the mass density of the nucleus is ρ0. The mass density distribution ρ allows us to find the surface mass density Σ (projected on the plane of the lens), followed by general elements of the gravitational lens expressed in terms of the geometric parameters a and b. The relation between these parameters is defined by the adimensional factor n = b/a > 1. The results of this work can be applied to any galactic lens system to conduct an analysis based on the temporal delay between two images and to determine the conditions that must be satisfied by the parameter n.