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

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

2002-03-09

arxiv.org/abs/astro-ph/0203142v3

Astrophys.J. 573 (2002) 51

Astronomy and Astrophysics

Astrophysics

8 pages, 9 figures, emulateapj5, accepted for publication in ApJ; minor typos corrected

Scientific paper

10.1086/340594

It has been recognized that the arc statistics of gravitational lensing is a useful probe of the density profile of clusters of galaxies. We examine several systematic effects which 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 of the cross section for radial arcs taking account of the source size and find that the moderate source size enhances the cross section for radial arcs while larger source size (\gtrsim 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 one or two 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 (\gtrsim 7). The number ratio therefore still remains good statistics which probe the density profile of the lens objects, if the source size effect is correctly taken into account.

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