Galaxy statistics in pencil-beam surveys at high redshifts

Surveys of faint galaxies at high redshifts often result in a 'pencil- beam' geometry that is much longer along the line of sight than across the sky. We explore the effects of this geometry on the abundance and clustering of Lyman-break galaxies (LBGs) and Lyman alpha emitters (LAEs) in current and future surveys based on cosmological N-body simulations which adequately describe the non-linear growth of structure on small scales and compare to linear theory. We find that the probability distribution of the LBG abundance is skewed towards low values since the narrow transverse dimension of the survey is more likely to probe underdense regions. Over a range that spans 1-2 orders of magnitude in galaxy luminosities, the variance in the number of objects differs from the commonly used analytic prediction and is not dominated by Poisson noise. Additionally, non-linear bias on small scales results in a 1D power spectrum of LAEs using a James Webb Space Telescope field of view that is relatively flat, markedly different from the expectation of linear perturbation theory. We discuss how these results may affect attempts to measure the UV background at high redshifts, estimate the relationship between halo mass and galaxy luminosity, and probe re-ionization by measuring the power-modulating effect of ionized regions.