The Redshift Distribution of Giant Arcs in the Sloan Giant Arcs Survey

We measure the redshift distribution of a sample of 28 giant arcs discovered as a part of the Sloan Giant Arcs Survey. Gemini/GMOS-North spectroscopy provides precise redshifts for 24 arcs, and "redshift desert" constrains for the remaining 4 arcs. This is a direct measurement of the redshift distribution of a uniformly selected sample of bright giant arcs, which is an observable that can be used to inform efforts to predict giant arc statistics. Our primary giant arc sample has a median redshift z = 1.821 and nearly two-thirds of the arcs, 64%, are sources at z >~ 1.4, indicating that the population of background sources that are strongly lensed into bright giant arcs resides primarily at high redshift. We also analyze the distribution of redshifts for 19 secondary strongly lensed background sources that are not visually apparent in Sloan Digital Sky Survey imaging, but were identified in deeper follow-up imaging of the lensing cluster fields. Our redshift sample for the secondary sources is not spectroscopically complete, but combining it with our primary giant arc sample suggests that a large fraction of all background galaxies that are strongly lensed by foreground clusters reside at z >~ 1.4. Kolmogorov-Smirnov tests indicate that our well-selected, spectroscopically complete primary giant arc redshift sample can be reproduced with a model distribution that is constructed from a combination of results from studies of strong-lensing clusters in numerical simulations and observational constraints on the galaxy luminosity function.