High-redshift voids in the excursion set formalism

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 10^10 M_sun 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 ~ 10^9 M_sun 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.Comment: 12 pages, 9 figures, 1 table, accepted by MNRA

Large Fluctuations in the High-Redshift Metagalactic Ionizing Background

Recent observations have shown that the scatter in opacities among coeval segments of the Lyman-alpha forest increases rapidly at z > 5. In this paper, we assess whether the large scatter can be explained by fluctuations in the ionizing background in the post-reionization intergalactic medium. We find that matching the observed scatter at z ~ 5.5 requires a short spatially averaged mean free path of 3 shorter than direct measurements at z ~ 5.2. We argue that such rapid evolution in the mean free path is difficult to reconcile with our measurements of the global H I photoionization rate, which stay approximately constant over the interval z ~ 4.8 - 5.5. However, we also show that measurements of the mean free path at z > 5 are likely biased towards higher values by the quasar proximity effect. This bias can reconcile the short values of the mean free path that are required to explain the large scatter in opacities. We discuss the implications of this scenario for cosmological reionization. Finally, we investigate whether other statistics applied to the z > 5 Lyman-alpha forest can shed light on the origin of the scatter. Compared to a model with a uniform ionizing background, models that successfully account for the scatter lead to enhanced power in the line-of-sight flux power spectrum on scales k < 0.1 h/Mpc. We find tentative evidence for this enhancement in observations of the high-redshift Lyman-alpha forest.Comment: Matches version published by MNRAS with clarifications and expanded discussio