High-redshift voids in the excursion set formalism
Abstract
Voids are a dominant feature of the low-redshift galaxy distribution. Several recent surveys have found evidence for the existence of large-scale structure at high redshifts as well. We present analytic estimates of galaxy void sizes at redshifts z ~ 5 - 10 using the excursion set formalism. We find that recent narrow-band surveys at z ~ 5 - 6.5 should find voids with characteristic scales of roughly 20 comoving Mpc and maximum diameters approaching 40 Mpc. This is consistent with existing surveys, but a precise comparison is difficult because of the relatively small volumes probed so far. At z ~ 7 - 10, we expect characteristic void scales of ~ 14 - 20 comoving Mpc assuming that all galaxies within dark matter haloes more massive than 1010 Msun are observable. We find that these characteristic scales are similar to the sizes of empty regions resulting from purely random fluctuations in the galaxy counts. As a result, true large-scale structure will be difficult to observe at z ~ 7 - 10, unless galaxies in haloes with masses less than ~ 109 Msun are visible. Galaxy surveys must be deep and only the largest voids will provide meaningful information. Our model provides a convenient picture for estimating the "worst-case" effects of cosmic variance on high-redshift galaxy surveys with limited volumes.