Correcting the z~8 Galaxy Luminosity Function for Gravitational Lensing Magnification Bias

Abstract

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. We illustrate our method by estimating the $z\sim 8$ UV luminosity function 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 luminosity function is well described by a Schechter function with characteristic magnitude of $M^{\star }=-19.85_{-0.35}^{+0.30}$, faint-end slope of $\alpha =-1.72_{-0.29}^{+0.30}$, and number density of ${\log }_{10}{\Psi }^{\star }[{\text{Mpc}}^{-3}]=-3.00_{-0.31}^{+0.23}$. 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 $z\sim 8$, and cannot account for the apparent overdensity of bright galaxies compared to a Schechter function found recently by Bowler et al. (2014a,b) and Finkelstein et al. (2014). We estimate that the probability of finding a strongly lensed $z\sim 8$ source in our sample is in the range $\sim 3-15\%$ depending on limiting magnitude. We identify one strongly-lensed candidate and three cases of intermediate lensing in BoRG (estimated magnification $\mu >1.4$) in addition to the previously known candidate group-scale strong lens. Using a range of theoretical luminosity functions 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 luminosity functions in these surveys and to distinguish between galaxy formation models.

Accepted for publication in ApJ. 20 pages, 13 figures

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