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 $zsim8$ 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 $M^star = -19.85^{+0.30}_{-0.35}$, faint-end slope of $alpha = -1.72^{+0.30}_{-0.29}$, and number density of $log_{10} Psi^star [textrm{Mpc}^{-3}] = -3.00^{+0.23}_{-0.31}$. 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 $zsim8$, 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 $zsim8$ 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.
We present an analysis of the spatial distribution of star formation in a sample of 60 visually identified galaxy merger candidates at z>1. Our sample, drawn from the 3D-HST survey, is flux-limited and was selected to have high star formation rates b
ased on fits of their broad-band, low spatial resolution spectral energy distributions. It includes plausible pre-merger (close pairs) and post-merger (single objects with tidal features) systems, with total stellar masses and star formation rates derived from multi-wavelength photometry. Here we use near-infrared slitless spectra from 3D-HST which produce Halpha or [OIII] emission line maps as proxies for star-formation maps. This provides a first comprehensive high-resolution, empirical picture of where star formation occurred in galaxy mergers at the epoch of peak cosmic star formation rate. We find that detectable star formation can occur in one or both galaxy centres, or in tidal tails. The most common case (58%) is that star formation is largely concentrated in a single, compact region, coincident with the centre of (one of) the merger components. No correlations between star formation morphology and redshift, total stellar mass, or star formation rate are found. A restricted set of hydrodynamical merger simulations between similarly massive and gas-rich objects implies that star formation should be detectable in both merger components, when the gas fractions of the individual components are the same. This suggests that z~1.5 mergers typically occur between galaxies whose gas fractions, masses, and/or star formation rates are distinctly different from one another.
