A systematic search for high surface brightness giant arcs in a Sloan Digital Sky Survey cluster sample

We present the results of a search for gravitationally lensed giant arcs conducted on a sample of 825 SDSS galaxy clusters. Both a visual inspection of the images and an automated search were performed, and no arcs were found. This result is used to set an upper limit on the arc probability per cluster. We present selection functions for our survey, in the form of arc detection efficiency curves plotted as functions of arc parameters, for both the visual inspection and the automated search. The selection function is such that we are sensitive only to long, high surface brightness arcs with g-band surface brightness mu g <= 24.8 and length-to-width ratio l/w >= 10. Our upper limits on the arc probability are compatible with previous arc searches. Finally, we report on a serendipitous discovery of a giant arc in the SDSS data, known inside the SDSS Collaboration as Hall's arc.