XXXIV Reunião Anual da Sociedade Astronômica Brasileira

We study the abundance of gravitational arcs in galaxy clusters, focusing in particular on its variation with respect to the cluster redshift (z_L). We present a method to include observational effects, such as the seeing and the signal to noise ratio (s/n) of the images, in semi-analytic calculations of arc statistics. Since the magnification (mu) enhances the s/n of the arcs, we must obtain the cross section as a function of mu, for arbitrary length to width ratios (L/W) of the images. The cross section (sigma) for arc formation is computed by mapping circular sources and with a semi-analytic method based on the eigenvalue ratio of the magnification tensor. Using this last approach we obtained the scaling of sigma with respect to mu, L/W, and other parameters, which allows for a fast computation of the cross section. We apply this method to evaluate the expected number of arcs per cluster (f_arcs) using an elliptical Navarro-Frenk-White matter distribution, explicitly including the effect of magnification. We find that f_arcs increases with cluster redshift for low z_L and then has a turnover, decaying for higher z_L. The behavior of cluster abundance at higher z_L as well as the turnover redshift are sensitive to the high redshift source distribution and limiting magnitude of the image. This stresses the importance of the magnification, which effectively increases the limiting magnitude in strongly lensed regions. For a survey with similar depth as the Red Sequence Cluster Survey (RCS) we predict that the number of arcs increases substantially up to z_L ~0.6, which is consistent with the excess of arcs found in this survey for clusters at higher redshifts. The overall arc abundance is much lower for the Sloan Digital Sky Survey (SDSS) depths and f_arcs has an significant drop below z_L ~ 0.3, which is also consistent with an arc search in SDSS.