2015ApJ...805...79M

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.