A Snapshot Survey for Gravitational Lenses amongz4.0 Quasars. I. Thez>5.7 Sample

Over the last few years, the Sloan Digital Sky Survey (SDSS) has discoveredseveral hundred quasars with redshift between 4.0 and 6.4. Including theeffects of magnification bias, one expects a priori that an appreciablefraction of these objects are gravitationally lensed. We have used the AdvancedCamera for Surveys on the Hubble Space Telescope to carry out a snapshotimaging survey of high-redshift SDSS quasars to search for gravitationallysplit lenses. This paper, the first in a series reporting the results of thesurvey, describes snapshot observations of four quasars at z = 5.74, 5.82, 5.99and 6.30, respectively. We find that none of these objects has a lensedcompanion within 5 magnitudes with a separation larger than 0.3 arcseconds;within 2.5 magnitudes, we can rule out companions within 0.1 arcseconds. Basedon the non-detection of strong lensing in these four systems, we constrain thez~6 luminosity function to a slope of beta>-4.63 (3 sigma), assuming a break inthe quasar luminosity function at M_{1450}^*=-24.0. We discuss the implicationsof this constraint on the ionizing background due to quasars in the earlyuniverse. Given that these quasars are not highly magnified, estimates of themasses of their central engines by the Eddington argument must be takenseriously, possibly challenging models of black hole formation.Comment: 23 pages, 8 figures, 2 tables, submitted to A