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 nonlinear growth of structure on small scales and compare to
linear theory. We find that the probability distribution of the LBG abundance
is skewed toward 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, nonlinear bias on small scales results in a
one-dimensional 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 reionization by measuring
the power-modulating effect of ionized regions.
