Spin Exchange Rates in Electron-Hydrogen Collisions

The spin temperature of neutral hydrogen, which determines the 21 cm optical depth and brightness temperature, is set by the competition between radiative and collisional processes. In the high-redshift intergalactic medium, the dominant collisions are typically those between hydrogen atoms. However, collisions with electrons couple much more efficiently to the spin state of hydrogen than do collisions with other hydrogen atoms and thus become important once the ionized fraction exceeds ~1%. Here we compute the rate at which electron-hydrogen collisions change the hydrogen spin. Previous calculations included only S-wave scattering and ignored resonances near the n=2 threshold. We provide accurate results, including all partial wave terms through the F-wave, for the de-excitation rate at temperatures T_K < 15,000 K; beyond that point, excitation to n>=2 hydrogen levels becomes significant. Accurate electron-hydrogen collision rates at higher temperatures are not necessary, because collisional excitation in this regime inevitably produces Lyman-alpha photons, which in turn dominate spin exchange when T_K > 6200 K even in the absence of radiative sources. Our rates differ from previous calculations by several percent over the temperature range of interest. We also consider some simple astrophysical examples where our spin de-excitation rates are useful.Comment: submitted to MNRAS, 9 pages, 5 figure

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

The 21 Centimeter Forest

We examine the prospects for studying the pre-reionization intergalactic medium (IGM) through the so-called 21 cm forest in spectra of bright high-redshift radio sources. We first compute the evolution of the mean optical depth for models that include X-ray heating of the IGM gas, Wouthuysen-Field coupling, and reionization. Under most circumstances, the spin temperature T_S grows large well before reionization begins in earnest. As a result, the optical depth is less than 0.001 throughout most of reionization, and background sources must sit well beyond the reionization surface in order to experience measurable absorption. HII regions produce relatively large "transmission gaps" and may therefore still be observable during the early stages of reionization. Absorption from sheets and filaments in the cosmic web fades once T_S becomes large and should be rare during reionization. Minihalos can produce strong (albeit narrow) absorption features. Measuring their abundance would yield useful limits on the strength of feedback processes in the IGM as well as their effect on reionization.Comment: 9 pages, 5 figures, submitted to MNRA

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

Spin Exchange Rates in Proton-Hydrogen Collisions

The spin temperature of neutral hydrogen, which determines the optical depth and brightness of the 21 cm line, is determined by the competition between radiative and collisional processes. Here we examine the role of proton-hydrogen collisions in setting the spin temperature. We use recent fully quantum mechanical calculations of the relevant cross sections, which allow us to present accurate results over the entire physically relevant temperature range 1-10,000 K. For kinetic temperatures T_K>100 K, the proton-hydrogen rate coefficient exceeds that for hydrogen-hydrogen collisions by about a factor of two. However, at low temperatures (T_K < 5 K) H-p collisions become several thousand times more efficient than H-H and even more important than H-e^- collisions.Comment: submitted to MNRAS, 5 pages, 2 figures, typos correcte