The epoch of helium reionization

We study the reionization of He  ii by quasars using a numerical approach that combines 3D radiative transfer calculations with cosmological hydrodynamical simulations. Sources producing the ionizing radiation are selected according to an empirical quasar luminosity function, and are assigned luminosities according to their intrinsic masses. The free parameters associated with this procedure are (1) a universal source lifetime, (2) a minimum mass cut-off, (3) a minimum luminosity cut-off, (4) a solid angle specifying the extent to which radiation is beamed, and (5) a tail-end spectral index for the radiative energy distribution of the sources. We present models in which these parameters are varied, and examine characteristics of the resultant reionization process that distinguish the various cases. In addition, we extract artificial spectra from the simulations and quantify statistical properties of the spectral features in each model.
We find that the most important factor affecting the evolution of He  ii reionization is the cumulative number of ionizing photons that are produced by the sources. Comparisons between He  ii opacities measured observationally and those obtained by our analysis reveal that the available ranges in plausible values for the parameters provide enough leeway to provide a satisfactory match. However, one property common to all our calculations is that the epoch of He  ii reionization must have occurred at a redshift in the range  3≲ z ≲4  . If so, future observational programmes will be able to directly trace the details of the ionization history of helium and to probe the low-density phase of the intergalactic medium during this phase of the evolution of the Universe.     

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.     

Zero-metallicity stellar sources and the reionization epoch

We reconsider the problem of the cosmological reionization owing to stellar sources. Using a method similar to that developed by Haiman & Loeb, we investigate the effect of changing the stellar models and the stellar spectra adopted for deriving the ionizing photon production rate. In particular, we study the consequences of adopting zero-metallicity stars, which is the natural choice for the first stellar populations. We construct young isochrones representative of Population III stars from existing sets of evolutionary models (by Forieri and Cassisi & Castellani) and calculate a suitable library of zero-metallicity model atmospheres. The number of ionizing photons emitted by such a zero-metal population is about 40 per cent higher than that produced by standard metal-poor isochrones. We find that adopting suitable zero-metallicity models modifies the reionization epoch. However the latter is still largely affected by current uncertainties in other important physical processes such as the efficiency of the star formation and the fraction of escaping UV photons.     

Cosmological reionization around the first stars: Monte Carlo radiative transfer

We study the evolution of ionization fronts around the first protogalaxies by using high-resolution numerical cosmological (Λ+ cold dark matter, CDM, model) simulations and Monte Carlo radiative transfer methods. We present the numerical scheme in detail and show the results of test runs from which we conclude that the scheme is both fast and accurate. As an example of interesting cosmological application, we study the reionization produced by a stellar source of total mass M =2×10⁸ M_⊙ turning on at z ≈12, located at a node of the cosmic web. The study includes a spectral energy distribution of a zero-metallicity stellar population, and two initial mass functions (IMFs; Salpeter/Larson). The expansion of the ionization front (I-front) is followed as it breaks out from the galaxy and is channelled by the filaments into the voids, assuming (in a 2D representation) a characteristic butterfly shape. The ionization evolution is very well tracked by our scheme, as realized by the correct treatment of the channelling and shadowing effects resulting from overdensities. We confirm previous claims that both the shape of the IMF and the ionizing power metallicity dependence are important to correctly determine the reionization of the Universe.     

The 21-cm power spectrum after reionization

We discuss the 21-cm power spectrum (PS) following the completion of reionization. In contrast to the reionization era, this PS is proportional to the PS of mass density fluctuations, with only a small modulation due to fluctuations in the ionization field on scales larger than the mean-free-path of ionizing photons. We derive the form of this modulation, and demonstrate that its effect on the 21-cm PS will be smaller than 1 per cent for physically plausible models of damped Lyα systems. In contrast to the 21-cm PS observed prior to reionization, in which H  ii regions dominate the ionization structure, the simplicity of the 21-cm PS after reionization will enhance its utility as a cosmological probe by removing the need to separate the PS into physical and astrophysical components. As a demonstration, we consider the Alcock–Paczynski test and show that the next generation of low-frequency arrays could measure the angular distortion of the PS at the per cent level for   z ∼ 3–5  .     

The ionizing background at the end of reionization

One of the most sought-after signatures of reionization is a rapid increase in the ionizing background (usually measured through the Lyα optical depth towards distant quasars). Conventional wisdom associates this with the 'overlap' phase when ionized bubbles merge, allowing each source to affect a much larger volume. We argue that this picture fails to describe the transition to the post-overlap Universe, where Lyman-limit systems (LLSs) absorb ionizing photons over moderate length-scales  (≲20–100   Mpc)  . Using an analytic model, we compute the probability distribution of the amplitude of the ionizing background throughout reionization, including both discrete ionized bubbles and LLSs (parametrized by an attenuation length, which we impose rather than attempt to model self-consistently). We show that the overlap does not by itself cause a rapid increase in the ionizing background or a rapid decrease in the mean Lyα transmission towards distant quasars. More detailed seminumeric models support these conclusions. We argue that the rapid changes should instead be interpreted as evolution in the attenuation length itself, which may or may not be directly related to overlap.     

Ionization state of cosmic hydrogen by early stars and quasars

Cosmic hydrogen is reionized and maintained in its highly ionized state by the ultraviolet emission attributed to an early generation of stars and quasars. The Lyα opacity observed in absorption spectra of high-redshift quasars permits more stringent constraints on the ionization state of cosmic hydrogen. Based on density perturbation and structure formation theory, we develop an analytic model to trace the evolution of the ionization state in the post-overlap epoch of reionization, in which the bias factor is taken into account. For quasars, we represent an improved luminosity function by utilizing a hybrid approach for the halo formation rate that is in reasonable agreement with the published measurements at 2 ≤ z ≤ 6. Comparison with the classic Press-Schechter mass function of dark matter halos, we demonstrate that the biased mass distribution indeed enhances star formation efficiency in the overdense environment by more than 25 per cent following the overlap of ionized bubbles. In addition, an alternative way is introduced to derive robust estimates of the mean free path for ionizing photons. In our model, star-forming galaxies are likely to dominate the ionizing background radiation beyond z = 3, and quasars contribute equally above a redshift of z ～ 2.5. From 5 ≤ z ≤ 6, the lack of evolution in photoionization rate can thus be explained by the relatively flat evolution in star formation efficiency, although the mean free path of ionizing photons increases rapidly. Moreover, in the redshift interval z ～ 2 - 6, the expected mean free path and Gunn-Peterson optical depth obviously evolve by a factor of ～ 500 and ～50 respectively. We find that the relative values of critical overdensities for hydrogen ionization and collapse could be 430% at z ≈2 and 2% at z ≈6, suggesting a rapid overlap process in the overdense regions around instant quasars following reionization. We further illustrate that the absolute estimates of the fraction of neutral hydrogen computed from theoretical models may n     

21-cm fluctuations from inhomogeneous X-ray heating before reionization

Many models of early structure formation predict a period of heating immediately preceding reionization, when X-rays raise the gas temperature above that of the cosmic microwave background. These X-rays are often assumed to heat the intergalactic medium (IGM) uniformly, but in reality will heat the gas more strongly closer to the sources. We develop a framework for calculating fluctuations in the 21-cm brightness temperature that originate from this spatial variation in the heating rate. High-redshift sources are highly clustered, leading to significant gas temperature fluctuations (with fractional variations ∼40 per cent, peaking on   k ∼ 0.1 Mpc⁻¹  scales). This induces a distinctive peak-trough structure in the angle-averaged 21-cm power spectrum, which may be accessible to the proposed Square Kilometre Array. This signal reaches the ∼10 mK level, and is stronger than that induced by Lyα flux fluctuations. As well as probing the thermal evolution of the IGM before reionization, this 21-cm signal contains information about the spectra of the first X-ray sources. Finally, we consider disentangling temperature, density and Lyα flux fluctuations as functions of redshift.     

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.     

Spatial fluctuations in the spectral shape of the ultraviolet background at 2 < z < 3 and the reionization of helium

The low-density hydrogen and helium in the intergalactic medium (IGM) probed by quasi-stellar object (QSO) absorption lines is sensitive to the amplitude and spectral shape of the metagalactic ultraviolet (UV) background. We use realistic H  i and He  ii Lyα forest spectra, constructed from state-of-the-art hydrodynamical simulations of a Λ cold dark matter (ΛCDM) universe to confirm the reliability of using line profile fitting techniques to infer the ratio of the metagalactic H  i and He  ii ionization rates. We further show that the large spatial variations and the anticorrelation with H  i absorber density observed in the ratio of the measured He  ii to H  i column densities can be explained in a model where the H  i ionization rate is dominated by the combined UV emission from young star-forming galaxies and QSOs and the He  ii ionization rate is dominated by emission from QSOs only. In such a model the large fluctuations in the column density ratio are due to the small number of QSOs expected to contribute at any given point to the He  ii ionization rate. A significant contribution to UV emission at the He  ii photoelectric edge from hot gas in galaxies and galaxy groups would decrease the expected fluctuations in the column density ratio. Consequently, this model appears difficult to reconcile with the large increase in He  ii opacity fluctuations towards higher redshift. Our results further strengthen previous suggestions that observed He  ii Lyα forest spectra at z ∼ 2–3.5 probe the tail end of the reionization of He  ii by QSOs.