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 (RCS-2) and the Sloan Digital Sky Survey (SDSS). The cluster lenses span 0.2 < z_lens < 1.2 in redshift, with a median z_lens = 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 +3 -5 % have z < 1. The inferred median redshift is 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 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 many magnified galaxies at z > 2.