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 _ { 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 \sim 90 \% of arcs that have z - band data .
This analysis yields broad redshift constraints with 71 ^ { +5 } _ { -4 } ~ { } \% of the arcs at z \geq 1.0 , 64 ^ { +6 } _ { -4 } ~ { } \% at z \geq 1.4 , 56 ^ { +5 } _ { -4 } ~ { } \% at z \geq 1.9 , and 21 ^ { +4 } _ { -2 } ~ { } \% at z \geq 2.7 .
The remaining 29 ^ { +03 } _ { -5 } % have z < 1 .
The inferred median redshift is \bar { z } _ { s } = 2.0 \pm 0.1 , in good agreement with a previous determination from a smaller sample of brighter arcs ( g \lesssim 22.5 ) .
This agreement confirms that z _ { s } = 2.0 \pm 0.1 is the typical redshift for giant arcs with g \lesssim 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 \leq g \leq 24 ) .
Establishing that half of all giant arcs are at z \gtrsim 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 \gtrsim 2 .