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

Details Is the Number of Giant Arcs in LCDM Consistent With Observations? Is the Number of Giant Arcs in LCDM Consistent With Observations?

2005-03-08

arxiv.org/abs/astro-ph/0503172v4

Astrophys.J. 635 (2005) 795-805

Astronomy and Astrophysics

Astrophysics

Revised version after the referee's reports (32 pages,13figures). The paper has been significantly revised with many additions

Scientific paper

10.1086/497583

We use high-resolution N-body simulations to study the galaxy-cluster cross-sections and the abundance of giant arcs in the $\Lambda$CDM model. Clusters are selected from the simulations using the friends-of-friends method, and their cross-sections 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 $1\arcsec$. We find that the optical depth scales as the source redshift approximately as $\tau_{1''} = 2.25 \times 10^{-6}/[1+(\zs/3.14)^{-3.42}]$ ($0.6<\zs<7$). The amplitude is about 50% higher for an effective source diameter of $0.5\arcsec$. The optimal lens redshift for giant arcs with the length-to-width 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 $\sim$ 10% to 70% of those from previous studies. The differences can be mostly explained by different power spectrum normalizations ($\sigma_8$) 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 $|\mu|>10$) and ``undistorted'' images (with $L/W<3$) is comparable to the number of giant arcs with $|\mu|>10$ 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.

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