The Impact of Strong Gravitational Lensing on Observed Lyman-Break Galaxy Numbers at 4<z<8 in the GOODS and the XDF Blank Fields

Detection of Lyman-Break Galaxies (LBGs) at high-redshift can be affected by gravitational lensing induced by foreground deflectors not only in galaxy clusters, but also in blank fields. We quantify the impact of strong magnification in the samples of $B$, $V$, $i$, $z$ $\&$ $Y$ LBGs ($4\lesssim z \lesssim8$) observed in the XDF and GOODS/CANDELS fields, by investigating the proximity of dropouts to foreground objects. We find that $\sim6\%$ of bright LBGs ($m_{H_{160}}<26$) at $z\sim7$ have been strongly lensed ($\mu>2$) by foreground objects. This fraction decreases from $\sim 3.5\%$ at $z\sim6$ to $\sim1.5\%$ at $z\sim4$. Since the observed fraction of strongly lensed galaxies is a function of the shape of the luminosity function (LF), it can be used to derive Schechter parameters, $\alpha$ and $M_{\star}$, independently from galaxy number counts. Our magnification bias analysis yields Schechter-function parameters in close agreement with those determined from galaxy counts albeit with larger uncertainties. Extrapolation of our analysis to $z\gtrsim 8$ suggests that future surveys with JSWT, WFIRST and EUCLID should find excess LBGs at the bright-end, even if there is an intrinsic exponential cutoff of number counts. Finally, we highlight how the magnification bias measurement near the detection limit can be used as probe of the population of galaxies too faint to be detected. Preliminary results using this novel idea suggest that the magnification bias at $M_{UV}\sim -18$ is not as strong as expected if $\alpha\lesssim -1.7$ extends well below the current detection limits in the XDF. At face value this implies a flattening of the LF at $M_{UV}\gtrsim-16.5$. However, selection effects and completeness estimates are difficult to quantify precisely. Thus, we do not rule out a steep LF extending to $M_{UV}\gtrsim -15$.