Probing the neutral fraction of the IGM with GRBs during the epoch of reionization

We show that near-infrared observations of the red side of the Lyα line from a single gamma-ray burst (GRB) afterglow cannot be used to constrain the global neutral fraction of the intergalactic medium (IGM),     , at the GRB's redshift to better than     . Some GRB sightlines will encounter more neutral hydrogen than others at fixed     owing to the patchiness of reionization. GRBs during the epoch of reionization will often bear no discernible signature of a neutral IGM in their afterglow spectra. We discuss the constraints on     from the   z = 6.3  burst, GRB050904, and quantify the probability of detecting a neutral IGM using future spectroscopic observations of high-redshift, near-infrared GRB afterglows. Assuming an observation with signal-to-noise ratio similar to the Subaru FOCAS spectrum of GRB050904 and that the column density distribution of damped Lyα absorbers is the same as measured at lower redshifts, a GRB from an epoch when     can be used to detect a partly neutral IGM at 97 per cent confidence level ≈10 per cent of the time (and, for an observation with three times the sensitivity, ≈30 per cent of the time).     

Redshifted 21-cm observations of high-redshift quasar proximity zones

The introduction of low-frequency radio arrays is expected to revolutionize the study of the reionization epoch. Observation of the contrast in redshifted 21-cm emission between a large H  ii region and the surrounding neutral intergalactic medium (IGM) will be the simplest and most easily interpreted signature. However, the highest redshift quasars known are thought to reside in an ionized IGM. Using a semi-analytic model we describe the redshifted 21-cm signal from the IGM surrounding quasars discovered using the i -drop-out technique (i.e. quasars at   z ∼ 6  ). We argue that while quasars at   z < 6.5  seem to reside in the post-overlap IGM, they will still provide valuable probes of the late stages of the overlap era because the light-travel time across a quasar proximity zone should be comparable to the duration of overlap. For redshifted 21-cm observations within a 32-MHz bandpass, we find that the subtraction of a spectrally smooth foreground will not remove spectral features due to the proximity zone. These features could be used to measure the neutral hydrogen content of the IGM during the late stages of reionization. The density of quasars at   z ∼ 6  is now well constrained. We use the measured quasar luminosity function to estimate the prospects for discovery of high-redshift quasars in fields that will be observed by the Murchison Widefield Array.     

The effects of primordial non-Gaussianity on the cosmological reionization

We investigate the effects of non-Gaussianity in the primordial density field on the reionization history. We rely on a semi-analytic method to describe the processes acting on the intergalactic medium (IGM), relating the distribution of the ionizing sources to that of dark matter haloes. Extending previous work in the literature, we consider models in which the primordial non-Gaussianity is measured by the dimensionless non-linearity parameter f _NL, using the constraints recently obtained from cosmic microwave background data. We predict the ionized fraction and the optical depth at different cosmological epochs assuming two different kinds of non-Gaussianity characterized by a scale-independent and a scale-dependent f _NL and comparing the results to those for the standard Gaussian scenario. We find that a positive f _NL enhances the formation of high-mass haloes at early epochs when reionization begins, and, as a consequence, the IGM ionized fraction can grow by a factor of up to 5 with respect to the corresponding Gaussian model. The increase of the filling factor has a small impact on the reionization optical depth and is of the order of ∼10 per cent if a scale-dependent non-Gaussianity is assumed. Our predictions for non-Gaussian models are in agreement with the latest Wilkinson Microwave Anisotropy Probe results within the error bars, but a higher precision is required to constrain the scale dependence of non-Gaussianity.     

The cross-correlation of the CMB polarization and the 21-cm line fluctuations from cosmic reionization

The cosmic microwave background (CMB) polarization and the 21-cm line fluctuations are powerful probes of cosmological reionization. We study how the cross-correlation between the CMB polarization ( E modes) and the 21-cm line fluctuations can be used to gain further understanding of the reionization history, within the framework of inhomogeneous reionization. Since the E -mode polarization reflects the amplitude of the quadrupole component of the CMB temperature fluctuations, the angular power spectrum of the cross-correlation exhibits oscillations at all multipoles. The first peak of the power spectrum appears at the scale corresponding to the quadrupole at the redshift, which is probed by the 21-cm line fluctuations. The peak reaches its maximum value in redshift when the average ionization fraction of the universe is about half. On the other hand, on small scales, there is a damping that depends on the duration of reionization. Thus, the cross-correlation between the CMB polarization and the 21-cm line fluctuations has the potential to accurately constrain the epoch and the duration of reionization.     

Semi-analytic approach to understanding the distribution of neutral hydrogen in the Universe

Analytic derivations of the correlation function and the column density distribution for neutral hydrogen in the intergalactic medium (IGM) are presented, assuming that the non-linear baryonic mass density distribution in the IGM is lognormal. This ansatz was used earlier by Bi & Davidsen to perform one-dimensional simulations of lines of sight and analyse the properties of absorption systems. We have taken a completely analytic approach, which allows us to explore a wide region of the parameter space for our model. The analytic results have been compared with observations to constrain various cosmological and IGM parameters, whenever possible. Two kinds of correlation functions are defined: (i) along the line of sight (LOS); and (ii) across the transverse direction. We find that the effects on the LOS correlation owing to changes in cosmology and the slope of the equation of state of the IGM, γ , are of the same order, which means that we cannot constrain both the parameters simultaneously. However, it is possible to constrain γ and its evolution using the observed LOS correlation function at different epochs provided that one knows the background cosmology. We suggest that the constraints on the evolution of γ obtained using the LOS correlation can be used as an independent tool to probe the reionization history of the Universe. From the transverse correlation function, we obtain the excess probability, over random, of finding two neutral hydrogen overdense regions separated by an angle θ . We find that this excess probability is always less than 1 per cent for redshifts greater than 2. Our models also reproduce the observed column density distribution for neutral hydrogen, and the shape of the distribution depends on γ . Our calculations suggest that one can rule out γ >1.6 for z ≃2.31 using the column density distribution. However, one cannot rule out higher values of γ at higher redshifts.     

Biased reionization and non-Gaussianity in redshifted 21-cm intensity maps of the reionization epoch

Spatial dependence in the statistics of redshifted 21-cm fluctuations promises to provide the most powerful probe of the reionization epoch. In this paper we consider the second and third moments of the redshifted 21-cm intensity distribution using a simple model that accounts for galaxy bias during the reionization process. We demonstrate that skewness in redshifted 21-cm maps should be substantial throughout the reionization epoch and on all angular scales, owing to the effects of galaxy bias which leads to early reionization in overdense regions of the intergalactic medium (IGM). The variance (or power spectrum) of 21-cm fluctuations will exhibit a minimum in redshift part way through the reionization process, when the global ionization fraction is around 50 per cent. This minimum is generic, and is due to the transition from 21-cm intensity being dominated by overdense to underdense regions as reionization progresses. We show that the details of the reionization history, including the presence of radiative feedback are encoded in the evolution of the autocorrelation and skewness functions with redshift and mean IGM neutral fraction. The amplitudes of fluctuations are particularly sensitive to the masses of ionizing sources, and vary by an order of magnitude for astrophysically plausible models. We discuss the detection of skewness by first-generation instruments, and conclude that the Mileura Wide-field Array–Low-Frequency Demonstrator will have sufficient sensitivity to detect skewness on a range of angular scales at redshifts near the end of reionization, while a subsequent instrument of 10 times the collecting area could map out the evolution of skewness in detail. The observation of a minimum in variance during the reionization history, and the detection of skewness would both provide important confirmation of the cosmological origin of redshifted 21-cm intensity fluctuations.     

The 21-cm 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 τ 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; this occurs so long as the X-ray luminosity of high-redshift starbursts (per unit star formation rate) is comparable to that in nearby galaxies. As a result,  τ≲ 10⁻³  throughout most of reionization, and background sources must sit well beyond the reionization surface in order to experience absorption that is measurable by square-kilometre class telescopes. H  ii 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. Minihaloes 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.     

The evolution of the Lyα forest effective optical depth following He ii reionization

Three independent observational studies have now detected a narrow  (Δ z ≃ 0.5)  dip centred at   z = 3.2  in the otherwise smooth redshift evolution of the Lyα forest effective optical depth. This feature has previously been interpreted as an indirect signature of rapid photoheating in the intergalactic medium (IGM) during the epoch of He  ii reionization. We examine this interpretation using a semi-analytic model of inhomogeneous He  ii reionization and high-resolution hydrodynamical simulations of the Lyα forest. We instead find that a rapid  (Δ z ≃ 0.2)  boost to the IGM temperature  (Δ T ≃ 10⁴ K)  beginning at   z = 3.4  produces a well understood and generic evolution in the Lyα effective optical depth, where a sudden reduction in the opacity is followed by a gradual, monotonic recovery driven largely by adiabatic cooling in the low-density IGM. This behaviour is inconsistent with the narrow feature in the observational data. If photoheating during He  ii reionization is instead extended over several redshift units, as recent theoretical studies suggest, then the Lyα opacity will evolve smoothly with redshift. We conclude that the sharp dip observed in the Lyα forest effective optical depth is instead most likely due to a narrow peak in the hydrogen photoionization rate around   z = 3.2  , and suggest that it may arise from the modulation of either reprocessed radiation during He  ii reionization, or the opacity of Lyman limit systems.     

The amplitude of mass density fluctuations at z 3.25 from the Ly forest of Q1422+231

The real-space optical-depth distribution along the line of sight to the QSO Q1422+231 is recovered from two HIRES spectra using a modified version of the inversion method proposed by Nusser & Haehnelt. The first two moments of the truncated optical-depth distribution are used to constrain the density-fluctuation amplitude of the intergalactic medium (IGM) assuming that the IGM is photoionized by a metagalactic UV background and obeys a temperaturedensity relation. The fluctuation amplitude and the power-law index of the relation between gas and neutral hydrogen (H  i ) density are degenerate. The rms of the IGM density at z 3.25 estimated from the first spectrum is with 1.56< <2 for plausible reionization histories. This corresponds to 0.9 2.1 with ( =1.7)=1.44±0.3. The values obtained from the second spectrum are higher by 20 per cent. If the IGM density traces the dark matter (DM) as suggested by numerical simulations we have measured the fluctuation amplitude of the DM density at an effective Jeans scale of a few 100 kpc. For cold dark matter (CDM)-like power spectra the amplitude of dark matter fluctuations on these small scales depends on the cosmological density parameter . For power spectra normalized to reproduce the space density of present-day clusters and with a slope parameter of =0.21 consistent with the observed galaxy power spectrum, the inferred can be expressed as: =0.61( /1.7)^1.3( x _J/0.62)^0.6 for a flat universe, and =0.91( /1.7)^1.3( x _J/0.62)^0.7 for a =0 universe. x _J is the effective Jeans scale in (comoving) h ¹ Mpc. Based on a suite of detailed mock spectra the 1 error is 25 per cent. The estimates increase with increasing . For the second spectrum we obtain 15 per cent lower values.     

Studying the sources of cosmic reionization with 21-cm fluctuations

We explore the ability of measurements of the 21-cm power spectrum during reionization to enable the simultaneous reconstruction of the reionization history and the properties of the ionizing sources. For various sets of simulated 21-cm observations, we perform maximum likelihood fits in order to constrain the reionization and galaxy formation histories. We employ a flexible six-parameter model that parametrizes the uncertainties in the properties of high-redshift galaxies. The computational speed needed is attained through the use of an analytical model that is in reasonable agreement with numerical simulations of reionization. We find that one-year observations, with the Murchison Widefield Array, should measure the cosmic ionized fraction to  ∼1 per cent  accuracy at the very end of reionization, and a few per cent accuracy around the mid-point of reionization. The mean halo mass of the ionizing sources should be measurable to 10 per cent accuracy when reionization is 2/3 of the way through, and to 20 per cent accuracy throughout the central stage of reionization, if this mass is anywhere in the range 1/3 to 100 billion solar masses.     

The effects of radiative transfer on the reionization of an inhomogeneous universe

Assuming simple dynamics for the growth of density fluctuations, we implement six-dimensional (6D) radiative transfer calculations to elucidate the effects of photon propagation during the reionization of an inhomogeneous universe. The ionizing sources are postulated to be AGN-like in this paper. The present simulations reveal that radiative transfer effects are still prominent considerably after the percolation epoch, in which patchy ionized regions connect with each other. In other words, owing to the collective opacity, the Universe does not become perfectly transparent against ionizing radiation even though strongly self-shielded regions disappear. It turns out that the inhomogeneity of the medium enhances the opacity effects and delays the end of reionization. Owing to such radiative transfer effects, the reionization in an inhomogeneous universe proceeds fairly slowly, in contrast to the prompt reionization in a homogeneous universe, and as a result the surface of reionization is not so sharply edged, but highly uneven. As a signature of the uneven surface of reionization, the cosmic IR background (CIB) radiation, which is produced by Ly photons resulting from radiative recombination, could exhibit strong anisotropies, reflecting the amplitude of density fluctuations at the reionization era. The predicted CIB intensity lies on a level of possible detection by forthcoming IR space telescope facilities.     

Probing the dark ages with the Square Kilometer Array

The epoch of reionization (EoR) sets a fundamental benchmark in cosmic structure formation, corresponding to the formation of the first luminous objects that act to ionize the neutral intergalactic medium (IGM). Recent observations at near-IR and radio wavelengths imply that we are finally probing into this key epoch of galaxy formation at z 6. The Square Kilometer Array (SKA) will provide critical insight into the EoR, in a number of ways. First, the ability of the SKA to image the neutral IGM in 21-cm emission is a truly unique probe of the process of reionization, and is recognized as the next necessary and fundamental step in our study of the evolution of large scale structure and cosmic reionization. Second, study of HI 21-cm absorption toward the first radio loud objects probes small to intermediate scale structure in the neutral ‘cosmic web’, as well as HI in the first collapsed structures (proto-disks and mini-halos). And third, the incomparable sensitivity of the SKA allows for the study of the molecular gas, dust, and star formation activity in the first galaxies, as well as the radio continuum emission from the first accreting massive black holes. Such objects will be obscured at optical wavelengths due to absorption by the neutral IGM.     

Inhomogeneous Reionization and the Polarization of the Cosmic Microwave Background

In a universe with inhomogeneous reionization, the ionized patches create a second-order signal in the cosmic microwave background polarization anisotropy. This signal originates in the coupling of the free-electron fluctuation to the quadruple moment of the temperature anisotropy. We examine the contribution from a simple inhomogeneous reionization model and find that the signal from such a process is below the detectable limits of the Planck Surveyor mission. However, the signal is above the fundamental uncertainty limit from cosmic variance, so that a future detection with a high-accuracy experiment on subarcminute scales is possible.     

How is the reionization epoch defined?

We study the effect of a prolonged epoch of reionization on the angular power spectrum of the cosmic microwave background. Typically reionization studies assume a sudden phase transition, with the intergalactic gas moving from a fully neutral to a fully ionized state at a fixed redshift. Such models are at odds, however, with detailed investigations of reionization, which favour a more extended transition. We have modified the code cmbfast to allow the treatment of more realistic reionization histories and applied it to data obtained from numerical simulations of reionization. We show that the prompt reionization assumed by cmbfast in its original form heavily contaminates any constraint derived on the reionization redshift. We find, however, that prompt reionization models give a reasonable estimate of the epoch at which the mean cosmic ionization fraction was ≈50 per cent, and provide a very good measure of the overall Thomson optical depth. The overall differences in the temperature (polarization) angular power spectra between prompt and extended models with equal optical depths are less than 1 per cent (10 per cent).     

Measurement of the baryonic acoustic oscillation scale in 21 cm intensity fluctuations during the reionization era

It has recently been suggested that the power spectrum of redshifted 21 cm fluctuations could be used to measure the scale of baryonic acoustic oscillations (BAOs) during the reionization era. The resulting measurements are potentially as precise as those offered by the next generation of galaxy redshift surveys at lower redshift. However, unlike galaxy redshift surveys, which in the linear regime are subject to a scale-independent galaxy bias, the growth of ionized regions during reionization is thought to introduce a strongly scale-dependent relationship between the 21 cm and mass power spectra. We use a seminumerical model for reionization to assess the impact of ionized regions on the precision and accuracy with which the BAO scale could be measured using redshifted 21 cm observations. For a model in which reionization is completed at   z ∼ 6  , we find that the constraints on the BAO scale are not systematically biased at   z ≳ 6.5  . In this scenario, and assuming the sensitivity attainable with a low-frequency array comprising 10 times the collecting area of the Murchison Widefield Array, the BAO scale could be measured to within 1.5 per cent in the range  6.5 ≲ z ≲ 7.5  .     

Semi-analytic simulations of galactic winds: volume filling factor, ejection of metals and parameter study

We present a semi-analytic treatment of galactic winds within high-resolution, large-scale cosmological N -body simulations of a Λ cold dark matter (ΛCDM) universe. The evolution of winds is investigated by following the expansion of supernova-driven superbubbles around the several hundred thousand galaxies that form in an approximately spherical region of space with diameter 52  h ⁻¹ Mpc and mean density close to the mean density of the universe. We focus our attention on the impact of winds on the diffuse intergalactic medium. Initial conditions for mass loss at the base of winds are taken from Shu, Mo & Mao. Results are presented for the volume filling factor and the mass fraction of the intergalactic medium (IGM) affected by winds, and their dependence on the model parameters is carefully investigated. The mass-loading efficiency of bubbles is a key factor to determine the evolution of winds and their global impact on the IGM: the higher the mass loading, the later the IGM is enriched with metals. Galaxies with 10⁹ < M _★ < 10¹⁰ M_⊙ are responsible for most of the metals ejected into the IGM at   z = 3  , while galaxies with   M _★ < 10⁹ M_⊙   give a non-negligible contribution only at higher redshifts, when larger galaxies have not yet assembled. We find a higher mean IGM metallicity than Lyα forest observations suggest, and we argue that the discrepancy may be explained by the high temperatures of a large fraction of the metals in winds, which may not leave detectable imprints in absorption in the Lyα forest.     

The impact of H i in galaxies on 21-cm intensity fluctuations during the reionization epoch

We investigate the impact of neutral hydrogen (H  i ) in galaxies on the statistics of 21-cm fluctuations using seminumerical modelling. Following the reionization of hydrogen, the H  i content of the Universe is dominated by damped absorption systems (DLAs), with a cosmic density in H  i that is observed to be constant at a level equal to ∼2 per cent of the cosmic baryon density from   z ∼ 1  to   z ∼ 5  . We show that extrapolation of this constant fraction into the reionization epoch results in a reduction in the amplitude of 21-cm fluctuations over a range of spatial scales. We further find that consideration of H  i in galaxies/DLAs reduces the prominence of the H  ii region induced shoulder in the 21-cm power spectrum (PS), and hence modifies the scale dependence of 21-cm fluctuations. We also estimate the 21-cm–galaxy cross PS and show that the cross PS changes sign on scales corresponding to the H  ii regions. From consideration of the sensitivity for forthcoming low-frequency arrays, we find that the effects of H  i 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 reionized first we demonstrate that the cross-correlation between galaxies and 21-cm emission changes sign at the end of the reionization era, providing an alternative avenue to pinpoint the end of reionization. The sum of our analysis indicates that the H  i content of the galaxies that reionize 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.     

Nonequilibrium carbon ionization states and the extragalactic far-UV background with HeII absorption

Using nonequilibrium calculations of the ionic states and the recently calculated extragalactic ultraviolet background radiation with absorption by intergalactic HeII we determine the ratios of CIII to CIV expected at z∼2–3, as functions of metallicity, gas density and temperature. We constrain the spectrum of the extragalactic ultraviolet background radiation by fitting the observed abundance ratios carbon ions at these redshifts with those expected from different models of the background radiation. Our analysis of the observed ratios shows that ‘delayed reionization’ models, which assume a large fraction of HeII at z∼3, is not favored by data. Our results suggest that HeII reionization was inhomogeneous, consistent with the predictions from recent simulations.     

The contribution of the IGM and minihaloes to the 21-cm signal of reionization

We study the statistical properties of the cosmological 21-cm signal from both the intergalactic medium (IGM) and minihaloes, using a reionization simulation that includes a self-consistent treatment of minihalo photoevaporation. We consider two models for minihalo formation and three typical thermal states of the IGM – heating purely by ionization, heating from both ionizing and Lyα photons and a maximal 'strong heating' model. We find that the signal from the IGM is almost always dominant over that from minihaloes. In our calculation, the differential brightness temperature,  δ T _b,  of minihaloes is never larger than 2 mK. Although there are indeed some differences in the signals from the minihaloes and from the IGM, even with the planned generation of radio telescopes it will be unfeasible to detect them. However, minihaloes significantly affect the ionization state of the IGM and the corresponding 21-cm flux.