Systematic Effects on Tangential and Radial Arc Statistics: The Finite Source Size and Ellipticities of the Lens and Source

Abstract

It has been recognized that the arc statistics of gravitational lensing are a useful probe of the density profile of clusters of galaxies. We examine several systematic effects that are important in predicting the number of arcs, with particular attention to the difference between tangential and radial arcs. First, we derive an analytic expression for the cross section for radial arcs taking account of the source size and find that a moderate source size enhances the cross section for radial arcs, while a larger source size (≳1'' in our example) suppresses the number of radial arcs. On the other hand, tangential arcs are much less sensitive to the source size. Next, we numerically calculate the cross section for arcs considering the lens and source ellipticities. We find that the numbers of both tangential and radial arcs are highly enhanced by both ellipticities, by 1 or 2 orders of magnitude. The number ratio of radial to tangential arcs is, however, not so affected if the threshold axis ratio of arcs is large (≳7). The number ratio therefore still remains a good statistic for probing the density profile of lens objects if the source-size effect is correctly taken into account.