High-redshift galaxies: Their predicted size and surface brightness distributions and their gravitational lensing probability

Direct observations of the first generation of luminous objects will likely become feasible over the next decade. The advent of the Next Generation Space Telescope (NGST) will allow imaging of numerous galaxies and mini-quasars at redshifts z greater than or similar to 5. We apply semianalytic models of structure formation to estimate the rate of multiple imaging of these sources by intervening gravitational lenses. Popular cold dark matter (CDM) models for galaxy formation yield a lensing optical depth of similar to 1% for sources at z similar to 10. The expected slope of the luminosity function of the early sources implies an additional magnification bias of similar to 5, bringing the fraction of lensed sources at z = 10 to similar to 5%. We estimate the angular size distribution of high-redshift disk galaxies and find that most of them are more extended than the resolution limit of NGST, similar to 0 ".06. We also show that there is only a modest redshift evolution in the observed mean surface brightness of galaxies at z greater than or similar to 2. The expected increase by 1-2 orders of magnitude in the number of resolved sources on the sky, due to observations with NGST, will dramatically improve upon the statistical significance of existing weak-lensing measurements. We show that despite this increase in the density of sources, confusion noise from z > 2 galaxies is expected to be small for NGST observations.