A Snapshot Survey for Gravitational Lenses Among z ≥ 4 . 0 Quasars : I . The z > 5 . 7 Sample

Over the last few years, the Sloan Digital Sky Survey (SDSS) has discovered several hundred quasars with redshift between 4.0 and 6.4. Including the effects of magnification bias, one expects a priori that an appreciable fraction of these objects are gravitationally lensed. We have used the Advanced Camera for Surveys on the Hubble Space Telescope to carry out a snapshot imaging survey of high-redshift SDSS quasars to search for gravitationally split lenses. This paper, the first in a series reporting the results of the survey, describes snapshot observations of four quasars at z = 5.74, 5.82, 5.99 and 6.30, respectively. We find that none of these objects has a lensed companion within 5 magnitudes with a separation larger than 0.3 arcseconds; within 2.5 magnitudes, we can rule out companions within 0.1 arcseconds. Based on the non-detection of strong lensing in these four systems, we constrain the z ∼ 6 luminosity function to a slope of β > −4.63 (3σ), assuming a break in the quasar luminosity function at M 1450 = −24.0. We discuss the implications of this constraint on the ionizing background due to quasars in the early universe. Given that these quasars are not highly magnified, estimates of the masses of their central engines by the Eddington argument must be taken seriously, possibly challenging models of black hole formation. Subject headings: gravitational lensing — early universe — quasars: general — quasars: individual (SDSSp J104433.04–012502.2, SDSSp J083643.85+005453.3, SDSSp J130608.26+035626.3, SDSSp J103027.10+052455.0) — galaxies: luminosity function Princeton University Observatory, Peyton Hall, Princeton, NJ 08544. Department of Astronomy, Columbia University, 550 West 120th Street, New York, NY 10027. Steward Observatory, University of Arizona, 933 North Cherry Avenue, Tucson, AZ 85721. Department of Astronomy and Astrophysics, The Pennsylvania State University, 525 Davey Laboratory, University Park, PA 16802. Apache Point Observatory, P.O. Box 59, Sunspot, NM 88349. Department of Astronomy, University of Illinois at Urbana-Champaign, 1002 West Green Street, Urbana, IL 61801-3080.