Gravitational lensing by a smoothly variable three-dimensional mass distribution

Abstract

A smooth three-dimensional mass distribution is approximated by a model with multiple thin screens, with surface mass density varying smoothly on each screen. We find that 16 screens are sufficient for a good approximation of the three-dimensional distribution of matter. We also find that in this multiscreen model the distribution of amplifications of single images is dominated by the convergence due to matter within the beam. The shear caused by matter outside the beam has no significant effect. This finding considerably simplifies the modeling of lensing by a smooth three-dimensional mass distribution by effectively reducing the problem to one dimension, as it is sufficient to know the mass distribution along a straight light ray.