Broadband photometry of 105 giant arcs: Redshift distribution 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 for approximately 90% of the full giant arc sample we also measure z-band photometry and r-z colors. This analysis yields broad redshift constraints and linear brightness measurements for the entire sample of arcs, confirming that a majority these objects reside at high redshift, with ∼85% at z > 1, ∼65% at z > 1.4, ∼56% at z ≥ 1.9, and ∼21% at z ≥ 2.7. The arcs have an inferred median redshift of z = 2, in good agreement with a previous determination of the redshift distribution of a smaller sample of much brighter arcs. The agreement between the two measurements suggests that z = 2 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. Both the redshift distribution and linear brightness distribution of giant arcs are direct observables that inform efforts to accurately simulate the statistics of giant arcs as a function of cosmology. Establishing that half of all giant arcs are galaxies at z > 2 contributes significantly toward relieving the tension between past claims of an order of magnitude discrepancy between the number of giant arcs observed and the number expected in a DeltaCDM 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. These sources will be significantly magnified and therefore provide an opportunity to investigate the individual properties of intrinsically faint galaxies at much higher signal-to-noise than can be achieved ix for individual sources in the field.