Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Systematic Effects on Tangential and Radial Arc Statistics: The Finite
  Source Size and Ellipticities of the Lens and Source   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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The categories of this paper are: stat
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The categories of this paper are: nucl-th
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The categories of this paper are: bayes-an
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The categories of this paper are: atom-ph
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The categories of this paper are: eess
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The categories of this paper are: q-bio
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The categories of this paper are: cond-mat
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The categories of this paper are: comp-gas
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The categories of this paper are: funct-an
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The categories of this paper are: q-alg
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The categories of this paper are: chao-dyn
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The categories of this paper are: solv-int
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The categories of this paper are: nlin
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The categories of this paper are: gr-qc
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The categories of this paper are: patt-sol
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The categories of this paper are: dg-ga