Is the Number of Giant Arcs in ΛCDM Consistent With Observations?

We use high-resolution N-body simulations to study the galaxy-cluster crosssections and the abundance of giant arcs in the ΛCDM model. Clusters are selected from the simulations using the friends-of-friends method, and their crosssections for forming giant arcs are analyzed. The background sources are assumed to follow a uniform ellipticity distribution from 0 to 0.5 and to have an area identical to a circular source with diameter 1. We find that the optical depth scales as the source redshift approximately as τ1′′ = 2.25×10 /[1+(zs/3.14) ] (0.6 < zs < 7). The amplitude is about 50% higher for an effective source diameter of 0.5. The optimal lens redshift for giant arcs with the length-towidth ratio (L/W ) larger than 10 increases from 0.3 for zs = 1, to 0.5 for zs = 2, and to 0.7-0.8 for zs > 3. The optical depth is sensitive to the source redshift, in qualitative agreement with Wambsganss et al. (2004). However, our overall optical depth appears to be only ∼ 10% to 70% of those from previous studies. The differences can be mostly explained by different power spectrum normalizations (σ8) used and different ways of determining the L/W ratio. Finite source size and ellipticity have modest effects on the optical depth. We also found that the number of highly magnified (with magnification |μ| > 10) and “undistorted” images (with L/W < 3) is comparable to the number of giant arcs with |μ| > 10 and L/W > 10. We conclude that our predicted rate of giant arcs may be lower than the observed rate, although the precise ‘discrepancy’ is still unclear due to uncertainties both in theory and observations. Shanghai Astronomical Observatory; the Partner Group of MPA, Nandan Road 80, Shanghai 200030, China; Email: (lgl,ypjing, kangx)@center.shao.ac.cn 2 University of Manchester, Jodrell Bank Observatory, Macclesfield, Cheshire SK11 9DL, UK; Email: [email protected] Zentrum für Astronomie, ITA, Universität Heidelberg, Albert-Überle-Str. 2, 69120 Heidelberg, Germany; Email: (mbartelmann, meneghetti)@ita.uni-heidelberg.de Graduate School of Chinese Academy of Sciences, Beijing 100039, China