Broadband Photometry of 105 Giant Arcs: Redshift Constraints and Implications for Giant Arc Statistics

We measure the photometric properties of 105 giant arcs that were identified in systematic searches for galaxy-cluster-scale strong lenses in the Second Red-Sequence Cluster Survey and the Sloan Digital Sky Survey. The cluster lenses span 0.2 < z_l < 1.2 in redshift, with a median \bar{z}_{l}=0.58. Using broadband color criteria we sort the entire arc sample into redshift bins based on u-g and g-r colors, and also r-z colors for the ~90% of arcs that have z-band data. This analysis yields broad redshift constraints with 71⁺⁵ _{- 4}% of the arcs at z >= 1.0, 64⁺⁶ _{- 4}% at z >= 1.4, 56⁺⁵ _{- 4}% at z >= 1.9, and 21⁺⁴ _{- 2}% at z >= 2.7. The remaining 29⁺⁰³ _{- 5}% have z < 1. The inferred median redshift is \bar{z}_{s} = 2.0+/- 0.1, in good agreement with a previous determination from a smaller sample of brighter arcs (g <~ 22.5). This agreement confirms that z_s = 2.0 ± 0.1 is the typical redshift for giant arcs with g <~ 24 that are produced by cluster-scale strong lenses and that there is no evidence for strong evolution in the redshift distribution of arcs over a wide range of g-band magnitudes (20 <= g <=24). Establishing that half of all giant arcs are at z >~ 2 contributes significantly toward relieving the tension between the number of arcs observed and the number expected in a ΛCDM cosmology, but there is considerable evidence to suggest that a discrepancy persists. Additionally, this work confirms that forthcoming large samples of giant arcs will supply the observational community with many magnified galaxies at z >~ 2.

Based on observations taken at the Southern Astrophysical Research Telescope (SOAR), a collaboration between CNP-Brazil, NOAO, The University of North Carolina at Chapel Hill, and Michigan State University and the Canada-France-Hawaii Telescope (CFHT) on Mauna Kea, which is operated by the National Research Council of Canada, the Institut National des Sciences de l'Univers of the Centre National de la Recherche Scientifique of France, and the University of Hawaii. Additional supporting observations come from the 2.5 m Nordic Optical Telescope, operated on the island of La Palma jointly by Denmark, Finland, Iceland, Norway, and Sweden, in the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofisica de Canarias, and the Gemini Observatory, which is operated by the Association of Universities for Research in Astronomy, Inc., under a cooperative agreement with the NSF on behalf of the Gemini partnership: The United States, The United Kingdom, Canada, Chile, Australia, Brazil, and Argentina.