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 ac-count. 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 galax-ies 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 rel-ative 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 esti-mates of the fraction of neutral hydrogen computed from theoretical models may not be important because of comparable uncertainties in the computation.     

Modification of the 21-cm power spectrum by quasars during the epoch of reionization

We assess the effect of a population of high-redshift quasars on the 21-cm power spectrum during the epoch of reionization. Our approach is to implement a seminumerical scheme to calculate the three-dimensional structure of ionized regions surrounding massive haloes at high redshift. We include the ionizing influence of luminous quasars by populating a simulated overdensity field with quasars using a Monte Carlo Markov Chain algorithm. We find that quasars modify both the amplitude and shape of the power spectrum at a level which is of the same order as the fractional contribution to reionization. The modification is found both at constant redshift and at constant global neutral fraction, and arises because ionizing photons produced by quasars are biased relative to the density field at a level that is higher than stellar ionizing photons. The modification of the power spectrum is likely to be small, rendering the effect of quasars difficult to isolate. However, we find the modification of the power spectrum by quasars to be at a level that is comparable to the precision expected for future low-frequency telescopes. Correct interpretation of observations will therefore require the effect of quasars to be considered, and our results imply that quasar ionization will need to be included in detailed modelling of observed 21-cm power spectra.     

Radiation from early black holes – I. Effects on the neutral intergalactic medium

In the pre-reionization Universe, the regions of the intergalactic medium (IGM) which are far from luminous sources are the last to undergo reionization. Until then, they should be scarcely affected by stellar radiation; instead, the X-ray emission from an early black hole (BH) population can have much larger influence. We investigate the effects of such emission, looking at a number of BH model populations (differing for the cosmological density evolution of BHs, the BH properties, and the spectral energy distribution of the BH emission). We find that BH radiation can easily heat the IGM to  10³–10⁴ K  , while achieving partial ionization. The most interesting consequence of this heating is that BHs are expected to induce a 21-cm signal (  δ T _b∼ 20–30 mK  at   z ≲ 12  ) which should be observable with forthcoming experiments (e.g. LOFAR). We also find that at   z ≲ 10  BH emission strongly increases the critical mass separating star-forming and non-star-forming haloes.     

The imprint of cosmic reionization on galaxy clustering

We consider the effect of reionization on the clustering properties of galaxy samples at intermediate redshifts ( z ∼ 0.3–5.5). Current models for the reionization of intergalactic hydrogen predict that overdense regions will be reionized early, thus delaying the build-up of stellar mass in the progenitors of massive lower redshift galaxies. As a result, the stellar populations observed in intermediate-redshift galaxies are somewhat younger and hence brighter in overdense regions of the Universe. Galaxy surveys would therefore be sensitive to galaxies with a somewhat lower dark matter mass in overdense regions. The corresponding increase in the observed number density of galaxies can be parametrized as a galaxy bias due to reionization. We model this process using merger trees combined with a stellar synthesis code. Our model demonstrates that reionization has a significant effect on the clustering properties of galaxy samples that are selected based on their star formation properties. The bias correction in Lyman-break galaxies (including those in proposed baryonic oscillation surveys at z < 1) is at the level of 10–20 per cent for a halo mass of  10¹² M_⊙  , leading to corrections factors of 1.5–2 in the halo mass inferred from measurements of clustering length. The reionization of helium could also lead to a sharp increase in the amplitude of the galaxy correlation function at z ∼ 3. We find that the reionization bias is approximately independent of scale and halo mass. However, since the traditional galaxy bias is mass dependent, the reionization bias becomes relatively more important for lower mass systems. The correction to the bias due to reionization is very small in surveys of luminous red galaxies at z < 1.     

Population III stars: hidden or disappeared?

A Population III/Population II transition from massive to normal stars is predicted to occur when the metallicity of the star-forming gas crosses the critical range   Z _cr= 10^−5±1 Z_⊙  . To investigate the cosmic implications of such a process, we use numerical simulations which follow the evolution, metal enrichment and energy deposition of both Population II and Population III stars. We find that: (i) due to inefficient heavy element transport by outflows and slow 'genetic' transmission during hierarchical growth, large fluctuations around the average metallicity arise; as a result, Population III star formation continues down to   z = 2.5  , but at a low peak rate of  10⁻⁵ M_⊙ yr⁻¹ Mpc⁻³  occurring at   z ≈ 6  (about 10⁻⁴ of the Population II one); and (ii) Population III star formation proceeds in an 'inside–out' mode in which formation sites are progressively confined to the periphery of collapsed structures, where the low gas density and correspondingly long free-fall time-scales result in a very inefficient astration. These conclusions strongly encourage deep searches for pristine star formation sites at moderate  (2 < z < 5)  redshifts where metal-free stars are likely to be hidden.     

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.