The distribution of high-redshift galaxy colors: Line-of-sight variations in neutral hydrogen absorption

We model, via Monte Carlo simulations, the distribution of observed U-B, B- V, and V-I galaxy colors in the range 1.75 < z < 5 caused by variations in the line-of-sight opacity due to neutral hydrogen (H I). We also include H I internal to the source galaxies. Even without internal H I absorption, co mparison of the distribution of simulated colors with the analytic approxim ations of Madau et al, reveals systematically different mean colors and sca tter. Differences arise in part because we use more realistic distributions of column densities and Doppler parameters. However, there are also mathem atical problems of applying mean and standard deviation opacities, and such application yields unphysical results. These problems are corrected using our Monte Carlo approach. Including H I absorption internal to the galaxies generally diminishes the scatter in the observed colors at a given redshif t, but for redshifts of interest this diminution only occurs in the colors using the bluest bandpass. Internal column densities less than 10(17) cm(2) do not affect the observed colors, while column densities greater than 10( 18) cm(2) yield a limiting distribution of high-redshift galaxy colors. As one application of our analysis, we consider the sample completeness as a f unction of redshift for a single spectral energy distribution (SED) given t he multicolor selection boundaries for the Hubble Deep Field proposed by Ma dau et al. We argue that the only correct procedure for estimating the z > 3 galaxy luminosity function from color-selected samples is to measure the (observed) distribution of redshifts and intrinsic SED types and then consi der the variation in color for each SED and redshift. A similar argument ap plies to the estimation of the luminosity function of color-selected, high- redshift QSOs.