CORRECTING THEz∼ 8 GALAXY LUMINOSITY FUNCTION FOR GRAVITATIONAL LENSING MAGNIFICATION BIAS

We present a Bayesian framework to account for the magnification bias from both strong and weak gravitational lensing in estimates of high-redshift galaxy luminosity functions (LFs). We illustrate our method by estimating the z ∼ 8 UV LF using a sample of 97 Y-band dropouts (Lyman break galaxies) found in the Brightest of Reionizing Galaxies (BoRG) survey and from the literature. We find the LF is well described by a Schechter function with characteristic magnitude of , faint-end slope of , and number density of . These parameters are consistent within the uncertainties with those inferred from the same sample without accounting for the magnification bias, demonstrating that the effect is small for current surveys at z ∼ 8, and cannot account for the apparent overdensity of bright galaxies compared to a Schechter function found recently by Bowler et al. and Finkelstein et al. We estimate that the probability of finding a strongly lensed z ∼ 8 source in our sample is in the range ∼3–15% depending on limiting magnitude. We identify one strongly lensed candidate and three cases of intermediate lensing in BoRG (estimated magnification μ > 1.4) in addition to the previously known candidate group-scale strong lens. Using a range of theoretical LFs we conclude that magnification bias will dominate wide field surveys—such as those planned for the Euclid and WFIRST missions—especially at z > 10. Magnification bias will need to be accounted for in order to derive accurate estimates of high-redshift LFs in these surveys and to distinguish between galaxy formation models.