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

Constraints on the Star Formation Efficiency of Galaxies During the Epoch of Reionization

Reionization is thought to have occurred in the redshift range of $6 < z < 9$, which is now being probed by both deep galaxy surveys and CMB observations. Using halo abundance matching over the redshift range $5<z<8$ and assuming smooth, continuous gas accretion, we develop a model for the star formation efficiency $f_{\star}$ of dark matter halos at $z>6$ that matches the measured galaxy luminosity functions at these redshifts. We find that $f_{\star}$ peaks at $\sim 30\%$ at halo masses $M \sim 10^{11}$--$10^{12}$~M$_\odot$, in qualitative agreement with its behavior at lower redshifts. We then investigate the cosmic star formation histories and the corresponding models of reionization for a range of extrapolations to small halo masses. We use a variety of observations to further constrain the characteristics of the galaxy populations, including the escape fraction of UV photons. Our approach provides an empirically-calibrated, physically-motivated model for the properties of star-forming galaxies sourcing the epoch of reionization. In the case where star formation in low-mass halos is maximally efficient, an average escape fraction $\sim0.1$ can reproduce the optical depth reported by Planck, whereas inefficient star formation in these halos requires either about twice as many UV photons to escape, or an escape fraction that increases towards higher redshifts. Our models also predict how future observations with JWST can improve our understanding of these galaxy populations.Comment: 19 pages, 12 figures, accepted for publication in MNRAS, minor modification

Reionization Through the Lens of Percolation Theory

The reionization of intergalactic hydrogen has received intense theoretical scrutiny over the past two decades. Here, we approach the process formally as a percolation process and phase transition. Using semi-numeric simulations, we demonstrate that an infinitely-large ionized region abruptly appears at an ionized fraction of ~0.1 and quickly grows to encompass most of the ionized gas: by an ionized fraction of 0.3, nearly ninety percent of the ionized material is part of this region. Throughout most of reionization, nearly all of the intergalactic medium is divided into just two regions, one ionized and one neutral, and both infinite in extent. We also show that the discrete ionized regions that exist before and near this transition point follow a near-power law distribution in volume, with equal contributions to the total filling factor per logarithmic interval in size up to a sharp cutoff in volume. These qualities are generic to percolation processes, with the detailed behavior a result of long-range correlations in the underlying density field. These insights will be crucial to understanding the distribution of ionized and neutral gas during reionization and provide precise meaning to the intuitive description of reionization as an "overlap" process.Comment: 16 pages, version accepted by MNRAS (conclusions unchanged from original

Extreme Galaxies During Reionization: Testing ISM and Disk Models

We test the ability of equilibrium galactic disk and one-zone interstellar medium models to describe the physical and emission properties of quasar hosts, submillimeter galaxies, and Lyman-alpha emitters at z>~6. The size, line widths, star formation rates, black hole accretion rates, gas masses and temperatures, and the relationships between these properties are all well-described by our model, and we provide approximate fitting formulae for comparison with future observations. However, comparing our carbon line predictions to observations reveals differences between the ISM at low and high redshifts. Our underestimate of the [CII] line emission indicates either higher star formation efficiencies in high-redshift molecular clouds or less depletion of metals into dust at fixed metallicity. Further, our over-prediction of the CO(6-5)/CO(1-0) ratio suggests that molecular clouds in real high-redshift galaxies have a lower turbulent Mach number and more subthermal CO(6-5) emission than expected owing either to sizes smaller than the local Jeans mass or to a pressure support mechanism other than turbulence.Comment: Accepted in MNRAS; 19 pages; 10 figures; 4 table

The Effect of Fluctuations on the Helium-Ionizing Background

Interpretation of He II Ly{\alpha} absorption spectra after the epoch of He II reionization requires knowledge of the He II ionizing background. While past work has modelled the evolution of the average background, the standard cosmological radiative transfer technique assumes a uniform radiation field despite the discrete nature of the (rare) bright quasars that dominate the background. We implement a cosmological radiative transfer model that includes the most recent constraints on the ionizing spectra and luminosity function of quasars and the distribution of IGM absorbers. We also estimate, for the first time, the effects of fluctuations on the evolving continuum opacity in two ways: by incorporating the complete distribution of ionizing background amplitudes into the standard approach, and by explicitly treating the quasars as discrete -- but isolated -- sources. Our model results in a He II ionization rate that evolves steeply with redshift, increasing by a factor ~2 from z=3.0 to z=2.5. This causes rapid evolution in the mean He II Ly{\alpha} optical depth -- as recently observed -- without appealing to the reionization of He II. The observed behaviour could instead result from rapid evolution in the mean free path of ionizing photons as the helium in higher H I column density absorbers becomes fully ionized.Comment: 14 pages, 9 figures. Accepted by MNRAS; significantly modified from previous versio

The Global 21-cm Signal in the Context of the High-z Galaxy Luminosity Function

Motivated by recent progress in studies of the high-$z$ Universe, we build a new model for the global 21-cm signal that is explicitly calibrated to measurements of the galaxy luminosity function (LF) and further tuned to match the Thomson scattering optical depth of the cosmic microwave background, $\tau_e$. Assuming that the $z \lesssim 8$ galaxy population can be smoothly extrapolated to higher redshifts, the recent decline in best-fit values of $\tau_e$ and the inefficient heating induced by X-ray binaries (HMXBs; the presumptive sources of the X-ray background at high-$z$) imply that the entirety of cosmic reionization and reheating occurs at redshifts $z \lesssim 12$. In contrast to past global 21-cm models, whose $z \sim 20$ ($\nu \sim 70$ MHz) absorption features and strong $\sim 25$ mK emission features were driven largely by the assumption of efficient early star-formation and X-ray heating, our new fiducial model peaks in absorption at $\nu \sim 110$ MHz at a depth of $\sim -160$ mK and has a negligible emission component. As a result, a strong emission signal would provide convincing evidence that HMXBs are not the only drivers of cosmic reheating. Shallow absorption troughs should accompany strong heating scenarios, but could also be caused by a low escape fraction of Lyman-Werner photons. Generating signals with troughs at $\nu \lesssim 95$ MHz requires a floor in the star-formation efficiency in halos below $\sim 10^{9} M_{\odot}$, which is equivalent to steepening the faint-end of the galaxy LF. These findings demonstrate that the global 21-cm signal is a powerful complement to current and future galaxy surveys and efforts to better understand the interstellar medium in high-$z$ galaxies.Comment: 17 pages, 9 figures, in pres

The Fundamentals of the 21-cm Line

We review some of the fundamental physics necessary for computing the highly-redshifted spin-flip background. We first discuss the radiative transfer of the 21-cm line and define the crucial quantities of interest. We then review the processes that set the spin temperature of the transition, with a particular focus on Wouthuysen-Field coupling, which is likely to be the most important process during and after the Cosmic Dawn. Finally, we discuss processes that heat the intergalactic medium during the Cosmic Dawn, including the scattering of Lyman-alpha, cosmic microwave background, and X-ray photons.Comment: To appear as a book chapter in "The Cosmic 21-cm Revolution: Charting the first billion years of our Universe," Ed Andrei Mesinger (Bristol: IOP Publishing Ltd) AAS-IOP ebooks http://www.iopscience.org/books/aas. arXiv admin note: text overlap with arXiv:astro-ph/060803

Quasi-equilibrium models of high-redshift disc galaxy evolution

In recent years, simple models of galaxy formation have been shown to provide reasonably good matches to available data on high-redshift luminosity functions. However, these prescriptions are primarily phenomenological, with only crude connections to the physics of galaxy evolution. Here we introduce a set of galaxy models that are based on a simple physical framework but incorporate more sophisticated models of feedback, star formation, and other processes. We apply these models to the high-redshift regime, showing that most of the generic predictions of the simplest models remain valid. In particular, the stellar mass--halo mass relation depends almost entirely on the physics of feedback (and is thus independent of the details of small-scale star formation) and the specific star formation rate is a simple multiple of the cosmological accretion rate. We also show that, in contrast, the galaxy's gas mass is sensitive to the physics of star formation, although the inclusion of feedback-driven star formation laws significantly changes the naive expectations. While these models are far from detailed enough to describe every aspect of galaxy formation, they inform our understanding of galaxy formation by illustrating several generic aspects of that process, and they provide a physically-grounded basis for extrapolating predictions to faint galaxies and high redshifts currently out of reach of observations. If observations show violations from these simple trends, they would indicate new physics occurring inside the earliest generations of galaxies.Comment: 20 pages, 13 figures, in press at MNRA

The Persistence of Population III Star Formation

We present a semi-analytic model of star formation in the early universe, beginning with the first metal-free stars. By employing a completely feedback-limited star formation prescription, stars form at maximum efficiency until the self-consistently calculated feedback processes halt formation. We account for a number of feedback processes including a meta-galactic Lyman-Werner background, supernovae, photoionization, and chemical feedback. Halos are evolved combining mass accretion rates found through abundance matching with our feedback-limited star formation prescription, allowing for a variety of Population III (Pop III) initial mass functions (IMFs). We find that, for a number of models, massive Pop III star formation can continue on until at least $z \sim 20$ and potentially past $z \sim 6$ at rates of around $10^{-4}$ to $10^{-5}$ M$_\odot$ yr$^{-1}$ Mpc$^{-3}$, assuming these stars form in isolation. At this point Lyman-Werner feedback pushes the minimum halo mass for star formation above the atomic cooling threshold, cutting off the formation of massive Pop III stars. We find that, in most models, Pop II and Pop III star formation co-exist over cosmological time-scales, with the total star formation rate density and resulting radiation background strongly dominated by the former before Pop III star formation finally ends. These halos form at most $\sim 10^3$ M$_\odot$ of massive Pop III stars during this phase and typically have absolute magnitudes in the range of $M_\text{AB} = -5$ to $-10$. We also briefly discuss how future observations from telescopes such as JWST or WFIRST and 21-cm experiments may be able to constrain unknown parameters in our model such as the IMF, star formation prescription, or the physics of massive Pop III stars.Comment: 16 pages, 13 figures, submitted to MNRA