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.     

The correlation between star formation and 21-cm emission during the reionization epoch

Reionization is thought to be dominated by low-mass galaxies, while direct observations of resolved galaxies probe only the most massive, rarest objects. The cross-correlation between fluctuations in the surface brightness of the cumulative Lyα emission (which serves as a proxy for the star formation rate) and the redshifted 21-cm signal from neutral hydrogen in the intergalactic medium (IGM) will directly probe the causal link between the production of ionizing photons in galaxies and the reionization of the IGM. We discuss the prospects for detecting this cross-correlation for unresolved galaxies. We find that on angular scales ≲10 arcmin detection will be practical using wide-field near-infrared (near-IR) imaging from space in combination with the forthcoming Mileura Wide-field Array – Low Frequency Demonstrator. When redshifted 21-cm observations of the neutral IGM are combined with space-based near-IR imaging of Lyα emission, the detection on angular scales ≲3 arcmin will be limited by the sensitivity of the 21-cm signal, even when a small-aperture optical telescope (∼2 m) and a moderate field of view (∼10 deg²) are used. On scales ≳3 arcmin, the measurement of cross-correlation will be limited by the accuracy of the foreground sky subtraction.     

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.     

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.     

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 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  .     

Baryonic acoustic oscillations in 21-cm emission: a probe of dark energy out to high redshifts

Low-frequency observatories are currently being constructed with the goal of detecting redshifted 21-cm emission from the epoch of reionization. These observatories will also be able to detect intensity fluctuations in the cumulative 21-cm emission after reionization, from hydrogen in unresolved damped Lyα absorbers (such as gas-rich galaxies) down to a redshift z ∼ 3.5. The inferred power spectrum of 21-cm fluctuations at all redshifts will show acoustic oscillations, whose comoving scale can be used as a standard ruler to infer the evolution of the equation of state for the dark energy. We find that the first generation of low-frequency experiments (such as MWA or LOFAR) will be able to constrain the acoustic scale to within a few per cent in a redshift window just prior to the end of the reionization era, provided that foregrounds can be removed over frequency bandpasses of ≳8 MHz. This sensitivity to the acoustic scale is comparable to the best current measurements from galaxy redshift surveys, but at much higher redshifts. Future extensions of the first-generation experiments (involving an order of magnitude increase in the antennae number of the MWA) could reach sensitivities below 1 per cent in several redshift windows and could be used to study the dark energy in the unexplored redshift regime of 3.5 ≲ z ≲ 12. Moreover, new experiments with antennae designed to operate at higher frequencies would allow precision measurements (≲1 per cent) of the acoustic peak to be made at more moderate redshifts (1.5 ≲ z ≲ 3.5), where they would be competitive with ambitious spectroscopic galaxy surveys covering more than 1000 deg². Together with other data sets, observations of 21-cm fluctuations will allow full coverage of the acoustic scale from the present time out to z ∼ 12.     

A method to measure the mass of damped Lyα absorber host galaxies using fluctuations in 21-cm emission

Observations of damped Lyα absorbers (DLAs) indicate that the fraction of hydrogen in its neutral form (H  i ) is significant by mass at all redshifts. This gas represents the reservoir of material that is available for star formation at late times. As a result, observational identification of the systems in which this neutral hydrogen resides is an important missing ingredient in models of galaxy formation. Precise identification of DLA host mass via traditional clustering studies is not practical owing to the small numbers of known systems being spread across sparsely distributed sightlines. However, following the completion of re-ionization, 21-cm surface brightness fluctuations will be dominated by neutral hydrogen in DLAs. No individual DLAs could be detected in 21-cm emission. Rather, observations of these fluctuations will measure the combined clustering signal from all DLAs within a large volume. We show that measurement of the spherically averaged power spectrum of 21-cm intensity fluctuations due to DLAs could be used to measure the galaxy bias for DLA host galaxies when combined with an independent measurement of the cosmological H  i mass density from quasar absorption studies. Utilizing this technique, the low-frequency arrays now under construction could measure the characteristic DLA host mass with a statistical precision as low as 0.3 dex at z ≳ 4. In addition, high signal-to-noise ratio observations of the peculiar-motion-induced anisotropy of the power spectrum would facilitate measurement of both the DLA host mass and the cosmic H  i density directly from 21-cm fluctuations. By exploiting this anisotropy, a second generation of low-frequency arrays with an order of magnitude increase in collecting area could measure the values of cosmic H  i density and DLA host mass, with uncertainties of a few per cent and a few tens of per cent, respectively.     

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.     

Large-scale non-Gaussianities in the 21-cm background anisotropies from the era of reionization

The brightness temperature fluctuations in the 21-cm background related to the neutral hydrogen distribution provide a probe of the physics related to the era of reionization, when the intergalactic medium changed from being completely neutral to partially ionized. We formulate statistics of 21-cm brightness temperature anisotropies in terms of the angular power spectrum, the bispectrum, and the trispectrum. Using the trispectrum, we estimate the covariance related to the power spectrum measurements and show that correlations resulting from non-Gaussianities are below a per cent, at most. While all-sky observations of the 21-cm background at arcminute-scale resolution can be used to measure the bispectrum with a cumulative signal-to-noise ratio of the order of a few tens, in the presence of foregrounds and instrumental noise related to first-generation interferometers, the measurement is unlikely to be feasible. For most purposes, non-Gaussianities in 21-cm fluctuations can be ignored and the distribution can be described with Gaussian statistics. Because 21-cm fluctuations are significantly contaminated by foregrounds, such as galactic synchrotron or low-frequency radio point sources, the lack of significant non-Gaussianity in the signal suggests that any significant detection of non-Gaussianity could be the result of foregrounds. Similarly, in addition to the frequency information that is now proposed to separate 21-cm fluctuations from foregrounds, if the non-Gaussian structure of foregrounds is known a priori, this additional information could potentially be used to reduce the confusion further.