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

We measure the bulk photometric properties of a sample of 105 giant arcs that were identified in systematic searches for galaxy-cluster-scale strong lenses in the Second Red-Sequence Cluster Survey (RCS-2) and the Sloan Digital Sky Survey (SDSS). Using well-established optical 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 the arcs that have z-band data. This analysis yields broad redshift constraints with 85 +4 -5 % at z > 1.0, 65 +6 -4 % at z > 1.4, 56 +5 -4 % at z > 1.9, and 21 +4 -2 % at z > 2.7. The inferred median redshift of z = 2.0 +/- 0.1 is in good agreement with a previous determination of the redshift distribution of a smaller sample of brighter arcs. This agreement confirms that z = 2.0 +/- 0.1 is the typical redshift for giant arcs produced by cluster-scale strong lensing, independent of typical brightness of the arcs, and that this observed redshift distribution should therefore provide a good description of samples of lensed arcs over a wide range of arc brightnesses. Establishing that half of all giant arcs are galaxies at z >~ 2 contributes significantly toward relieving the tension of the order of magnitude discrepancy between the number of giant arcs observed and the number expected in a Lambda-CDM 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 a large number of strongly lensed galaxies at z >~ 2