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

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

Photo-heating and the fate of hard photons during the reionisation of HeII by quasars

We use a combination of analytic and numerical arguments to consider the impact of quasar photo-heating during HeII reionisation on the thermal evolution of the intergalactic medium (IGM). We demonstrate that rapid (\Delta z 10^4 K) photo-heating is difficult to achieve across the entire IGM unless quasar spectra are significantly harder than implied by current observational constraints. Although filtering of intrinsic quasar radiation through dense regions in the IGM does increase the mean excess energy per HeII photo-ionisation, it also weakens the radiation intensity and lowers the photo-ionisation rate, preventing rapid heating over time intervals shorter than the local photo-ionisation timescale. Moreover, the hard photons responsible for the strongest heating are more likely to deposit their energy inside dense clumps. The abundance of such clumps is, however, uncertain and model-dependent, leading to a fairly large uncertainty in the photo-heating rates. Nevertheless, although some of the IGM may be exposed to a hardened and weakened ionising background for long periods, most of the IGM must instead be reionised by the more abundant, softer photons and with accordingly modest heating rates (\Delta T < 10^4 K). The repeated ionisation of fossil quasar HeIII regions does not increase the net heating because the recombination times in these regions typically exceed the IGM cooling times and the average time lag between successive rounds of quasar activity. Detailed line-of-sight radiative transfer simulations confirm these expectations and predict a rich thermal structure in the IGM during HeII reionisation. [Abridged]Comment: 20 pages, 6 figures, accepted by MNRA

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

Descending from on high: Lyman series cascades and spin-kinetic temperature coupling in the 21 cm line

We examine the effect of Lyman continuum photons on the 21 cm background in the high-redshift universe. The brightness temperature of this transition is determined by the spin temperature T_s, which describes the relative populations of the singlet and triplet hyperfine states. Once the first luminous sources appear, T_s is set by the Wouthuysen-Field effect, in which Lyman-series photons mix the hyperfine levels. Here we consider coupling through n>2 Lyman photons. We first show that coupling (and heating) from scattering of Lyman-n photons is negligible, because they rapidly cascade to lower-energy photons. These cascades can result in either a Lyman-alpha photon -- which will then affect T_s according to the usual Wouthuysen-Field mechanism -- or photons from the 2s -> 1s continuum, which escape without scattering. We show that a proper treatment of the cascades delays the onset of strong Wouthuysen-Field coupling and affects the power spectrum of brightness fluctuations when the overall coupling is still relatively weak (i.e., around the time of the first stars). Cascades damp fluctuations on small scales because only ~ 1/3 of Lyn photons cascade through Lyman-alpha, but they do not affect the large-scale power because that arises from those photons that redshift directly into the Lyman-alpha transition. We also comment on the utility of Lyman-n transitions in providing "standard rulers" with which to study the high-redshift universe.Comment: Accepted by MNRAS. 10 pages, 8 figures. Minor revisions + corrected normalisation of figure

The Effects of Dark Matter Decay and Annihilation on the High-Redshift 21 cm Background

The radiation background produced by the 21 cm spin-flip transition of neutral hydrogen at high redshifts can be a pristine probe of fundamental physics and cosmology. At z~30-300, the intergalactic medium (IGM) is visible in 21 cm absorption against the cosmic microwave background (CMB), with a strength that depends on the thermal (and ionization) history of the IGM. Here we examine the constraints this background can place on dark matter decay and annihilation, which could heat and ionize the IGM through the production of high-energy particles. Using a simple model for dark matter decay, we show that, if the decay energy is immediately injected into the IGM, the 21 cm background can detect energy injection rates >10^{-24} eV cm^{-3} sec^{-1}. If all the dark matter is subject to decay, this allows us to constrain dark matter lifetimes <10^{27} sec. Such energy injection rates are much smaller than those typically probed by the CMB power spectra. The expected brightness temperature fluctuations at z~50 are a fraction of a mK and can vary from the standard calculation by up to an order of magnitude, although the difference can be significantly smaller if some of the decay products free stream to lower redshifts. For self-annihilating dark matter, the fluctuation amplitude can differ by a factor <2 from the standard calculation at z~50. Note also that, in contrast to the CMB, the 21 cm probe is sensitive to both the ionization fraction and the IGM temperature, in principle allowing better constraints on the decay process and heating history. We also show that strong IGM heating and ionization can lead to an enhanced H_2 abundance, which may affect the earliest generations of stars and galaxies.Comment: submitted to Phys Rev D, 14 pages, 8 figure

Hubble Diagram of Gamma-Rays Bursts calibrated with Gurzadyan-Xue Cosmology

Gamma-ray bursts (GRBs) being the most luminous among known cosmic objects carry an essential potential for cosmological studies if properly used as standard candles. In this paper we test with GRBs the cosmological predictions of the Gurzadyan-Xue (GX) model of dark energy, a novel theory that predicts, without any free parameters, the current vacuum fluctuation energy density close to the value inferred from the SNIa observations. We also compare the GX results with those predicted by the concordance scenario $\Lambda$-CDM. According to the statistical approach by Schaefer (2007), the use of several empirical relations obtained from GRBs observables, after a consistent calibration for a specific model, enables one to probe current cosmological models. Based on this recently introduced method, we use the 69 GRBs sample collected by Schaefer (2007); and the most recently released SWIFT satellite data (Sakamoto et al. 2007) together with the 41 GRBs sample collected by Rizzuto et al. (2007), which has the more firmly determined redshifts. Both data samples span a distance scale up to redshift about 7. We show that the GX models are compatible with the Hubble diagram of the Schaefer (2007) 69 GRBs sample. Such adjustment is almost identical to the one for the concordance $\Lambda$-CDM.Comment: 9 pages, 17 figures, 11 tables; Astr. & Astrophys. (in press

Intensity Mapping with Carbon Monoxide Emission Lines and the Redshifted 21 cm Line

We quantify the prospects for using emission lines from rotational transitions of the CO molecule to perform an `intensity mapping' observation at high redshift during the Epoch of Reionization (EoR). The aim of CO intensity mapping is to observe the combined CO emission from many unresolved galaxies, to measure the spatial fluctuations in this emission, and use this as a tracer of large scale structure at very early times in the history of our Universe. This measurement would help determine the properties of molecular clouds -- the sites of star formation -- in the very galaxies that reionize the Universe. We further consider the possibility of cross-correlating CO intensity maps with future observations of the redshifted 21 cm line. The cross spectrum is less sensitive to foreground contamination than the auto power spectra, and can therefore help confirm the high redshift origin of each signal. Furthermore, the cross spectrum measurement would help extract key information about the EoR, especially regarding the size distribution of ionized regions. We discuss uncertainties in predicting the CO signal at high redshift, and discuss strategies for improving these predictions. Under favorable assumptions, and feasible specifications for a CO survey mapping the CO(2-1) and CO(1-0) lines, the power spectrum of CO emission fluctuations and its cross spectrum with future 21 cm measurements from the MWA are detectable at high significance.Comment: 19 pages, 8 figures, submitted to Ap

Searching for the earliest galaxies in the 21 cm forest

We use a model developed by Xu et al. (2010) to compute the 21 cm line absorption signatures imprinted by star-forming dwarf galaxies (DGs) and starless minihalos (MHs). The method, based on a statistical comparison of the equivalent width (W_\nu) distribution and flux correlation function, allows us to derive a simple selection criteria for candidate DGs at very high (z >= 8) redshift. We find that ~ 18% of the total number of DGs along a line of sight to a target radio source (GRB or quasar) can be identified by the condition W_\nu < 0; these objects correspond to the high-mass tail of the DG distribution at high redshift, and are embedded in large HII regions. The criterion W_\nu > 0.37 kHz instead selects ~ 11% of MHs. Selected candidate DGs could later be re-observed in the near-IR by the JWST with high efficiency, thus providing a direct probe of the most likely reionization sources.Comment: 8 pages, 3 figures. Accepted for publication in Science in China Series

Redshifted 21 Centimeter Emission from Minihalos Before Reionization

Before reionization, the intergalactic medium (IGM) may have been sufficiently cold for low-mass "minihalos" to condense out of the gas and subsequently affect reionization. Previous work has shown that minihalos generate reasonably large 21 cm fluctuations. Here we consider this signal in its proper cosmological context and show that isolating minihalos from the rest of the IGM is extremely difficult. Using the well-known halo model, we compute the power spectrum of 21 cm fluctuations from minihalos and show that the signal decreases rapidly as feedback increases the Jeans mass. We then show that even a small Lyman-alpha background increases the 21 cm fluctuations of the diffuse IGM well beyond those of the minihalos; because the mass fraction in the IGM is much larger, minihalos will lie buried within the IGM signal. The distinctive signatures of non-linear bias and minihalo structure emerge only at much smaller scales, well beyond the resolution of any upcoming instruments. Using simple, but representative, reionization histories, we then show that the required Lyman-alpha background level is most likely achieved at z>15, while minihalos are still rare, so that they are almost always degenerate with the diffuse IGM.Comment: 8 pages, 6 figures, submitted to Ap