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

The Impact of HI in Galaxies on 21-cm Intensity Fluctuations During the Reionisation Epoch

We investigate the impact of neutral hydrogen (HI) in galaxies on the statistics of 21-cm fluctuations using analytic and semi-numerical modelling. Following the reionisation of hydrogen the HI content of the Universe is dominated by damped absorption systems (DLAs), with a cosmic density in HI that is observed to be constant at a level equal to ~2% of the cosmic baryon density from z~1 to z~5. We show that extrapolation of this constant fraction into the reionisation epoch results in a reduction of 10-20% in the amplitude of 21-cm fluctuations over a range of spatial scales. The assumption of a different percentage during the reionisation era results in a proportional change in the 21-cm fluctuation amplitude. We find that consideration of HI in galaxies/DLAs reduces the prominence of the HII region induced shoulder in the 21-cm power spectrum (PS), and hence modifies the scale dependence of 21-cm fluctuations. We also estimate the 21cm-galaxy cross PS, and show that the cross PS changes sign on scales corresponding to the HII regions. From consideration of the sensitivity for forthcoming low-frequency arrays we find that the effects of HI in galaxies/DLAs on the statistics of 21-cm fluctuations will be significant with respect to the precision of a PS or cross PS measurement. In addition, since overdense regions are reionised first we demonstrate that the cross-correlation between galaxies and 21-cm emission changes sign at the end of the reionisation era, providing an alternative avenue to pinpoint the end of reionisation. The sum of our analysis indicates that the HI content of the galaxies that reionise the universe will need to be considered in detailed modelling of the 21-cm intensity PS in order to correctly interpret measurements from forthcoming low-frequency arrays.Comment: 11 pages, 6 figures. Submitted to MNRA

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