Gravitational wave background from neutrino-driven gamma-ray bursts

We study cosmic microwave background (CMB) secondary anisotropies produced by inhomogeneous reionization by means of cosmological simulations coupled with the radiative transfer code crash . The reionization history is consistent with the Wilkinson Microwave Anisotropy Probe Thomson optical depth determination. We find that the signal arising from this process dominates over the primary CMB component for   l ≳ 4000  and reaches a maximum amplitude of   l ( l + 1) C_l /2π≃ 1.6 × 10⁻¹³  on arcmin scales (i.e. l as large as several thousands). We then cross-correlate secondary CMB anisotropy maps with neutral hydrogen 21-cm line emission fluctuations obtained from the same simulations. The two signals are highly anticorrelated on angular scales corresponding to the typical size of H  ii regions (including overlapping) at the 21-cm map redshift. We show how the CMB/21-cm cross-correlation can be used: (i) to study the nature of the reionization sources; (ii) to reconstruct the cosmic reionization history; (iii) to infer the mean cosmic ionization level at any redshift. We discuss the feasibility of the proposed experiment with forthcoming facilities.     

Reionization and the large-scale 21-cm cosmic microwave background cross-correlation

Of the many probes of reionization, the 21-cm line and the cosmic microwave background (CMB) are among the most effective. We examine how the cross-correlation of the 21-cm brightness and the CMB Doppler fluctuations on large angular scales can be used to study this epoch. We employ a new model of the growth of large-scale fluctuations of the ionized fraction as reionization proceeds. We take into account the peculiar velocity field of baryons and show that its effect on the cross-correlation can be interpreted as a mixing of Fourier modes. We find that the cross-correlation signal is strongly peaked towards the end of reionization and that the sign of the correlation should be positive because of the inhomogeneity inherent to reionization. The signal peaks at degree scales (ℓ∼ 100) and comes almost entirely from large physical scales ( k ∼ 10⁻² Mpc). Since many of the foregrounds and noise that plague low-frequency radio observations will not correlate with CMB measurements, the cross-correlation might appear to provide a robust diagnostic of the cosmological origin of the 21-cm radiation around the epoch of reionization. Unfortunately, we show that these signals are actually only weakly correlated and that cosmic variance dominates the error budget of any attempted detection. We conclude that the detection of a cross-correlation peak at degree-size angular scales is unlikely even with ideal experiments.     

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.     

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.     

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.     

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.     

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.     

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  .     

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  .     

Thermal and kinematic corrections to the microwave background polarization induced by galaxy clusters along the line of sight

We derive analytic expressions for the leading-order corrections to the polarization induced in the cosmic microwave background (CMB) owing to scattering of photons off hot electrons in galaxy clusters along the line of sight. For a thermal distribution of electrons with kinetic temperature k _B T _e∼10 keV and bulk peculiar velocity V ∼1000 km s⁻¹, the dominant corrections to the polarization induced by the primordial CMB quadrupole and the cluster peculiar velocity arise from electron thermal motion and are at the level of ∼10 per cent in each case, near the peak of the polarization signal. When more sensitive measurements become feasible, these effects will be significant for the determination of transverse peculiar velocities, and the value of the CMB quadrupole at the cluster redshift, via the cluster polarization route.     

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).     

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.     

The difference PDF of 21-cm fluctuations: a powerful statistical tool for probing cosmic reionization

A new generation of radio telescopes are currently being built with the goal of tracing the cosmic distribution of atomic hydrogen at redshifts 6–15 through its 21-cm line. The observations will probe the large-scale brightness fluctuations sourced by ionization fluctuations during cosmic reionization. Since detailed maps will be difficult to extract due to noise and foreground emission, efforts have focused on a statistical detection of the 21-cm fluctuations. During cosmic reionization, these fluctuations are highly non-Gaussian and thus more information can be extracted than just the one-dimensional function that is usually considered, i.e. the correlation function. We calculate a two-dimensional function that if measured observationally would allow a more thorough investigation of the properties of the underlying ionizing sources. This function is the probability distribution function (PDF) of the difference in the 21-cm brightness temperature between two points, as a function of the separation between the points. While the standard correlation function is determined by a complicated mixture of contributions from density and ionization fluctuations, we show that the difference PDF holds the key to separately measuring the statistical properties of the ionized regions.     

Absorption in the 21-cm Line in Primordial Matter Density Fluctuations at the Stage of Their Nonlinear Compression

The mechanisms of absorption formation in the cosmic microwave background (CMB) spectrum at the frequency of the 21-cm line of the transition between the ground-state hyperfine sublevels of the hydrogen atom are analyzed. We show that a strong nonlinearity at the compression stage of primordial matter density fluctuations can give rise to a significant (in depth) absorption even before the explosions of the first stars. In this case, the main effect is due to the heating of matter in a certain narrow range of temperatures under cloud compression. We consider a steady-state radiative transfer in the 21-cm line in a medium that represents a contracting primordial matter density fluctuation at a given redshift z modeled by a homogeneous spherically symmetric cloud in the state of collapse with an adiabatic change in the gas temperature. For a sequence of cloud states with different degrees of compression we have calculated the frequency profiles of the line in the flux of radiation emerging from the cloud. In the initial state we specify the cloud radius r₀, while the gas density is assumed to be equal to the mean cosmological density for a given redshift. We show that for a separate cloud at z = 20, r₀ = 1 kpc, and a degree of radius compression of 1.9 the absorption depth in the line center can reach 0.9 K. When averaged over an ensemble of clouds, the central frequency of the line and its width are determined by the details of the fluctuation evolution dynamics.

     

Current models of the observable consequences of cosmic reionization and their detectability

A number of large current experiments aim to detect the signatures of the cosmic reionization at redshifts z > 6. Their success depends crucially on understanding the character of the reionization process and its observable consequences and designing the best strategies to use. We use large-scale simulations of cosmic reionization to evaluate the reionization signatures at redshifted 21-cm and small-scale cosmic microwave background (CMB) anisotropies in the best current model for the background universe, with fundamental cosmological parameters given by Wilkinson Microwave Anisotropy Probe three-year results. We find that the optimal frequency range for observing the 'global step' of the 21-cm emission is 120–150 MHz, while statistical studies should aim at 140–160 MHz, observable by GMRT. Some strongly non-Gaussian brightness features should be detectable at frequencies up to ∼190 MHz. In terms of sensitivity-signal trade-off relatively low resolutions, corresponding to beams of at least a few arcminutes, are preferable. The CMB anisotropy signal from the kinetic Sunyaev–Zel'dovich effect from reionized patches peaks at tens of μK at arcminute scales and has an rms of ∼1 μK, and should be observable by the Atacama Cosmology Telescope and the South Pole Telescope. We discuss the various observational issues and the uncertainties involved, mostly related to the poorly known reionization parameters and, to a lesser extend, to the uncertainties in the background cosmology.     

A primordial feature at the scale of superclusters of galaxies

We investigate a spatially flat cold dark matter model (with the matter density parameter     with a primordial feature in the initial power spectrum. We assume that there is a bump in the power spectrum of density fluctuations at wavelengths     , which corresponds to the scale of superclusters of galaxies . There are indications for such a feature in the power spectra derived from redshift surveys and also in the power spectra derived from peculiar velocities of galaxies. We study the mass function of clusters of galaxies, the power spectrum of the cosmic microwave background (CMB) temperature fluctuations, the rms bulk velocity and the rms peculiar velocity of clusters of galaxies. The baryon density is assumed to be consistent with the big bang nucleosynthesis value. We show that with an appropriately chosen feature in the power spectrum of density fluctuations at the scale of superclusters, the mass function of clusters, the CMB power spectrum, the rms bulk velocity and the rms peculiar velocity of clusters are in good agreement with the observed data.     

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.     

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.     

Constraining the nature of dark energy using the Square Kilometer Array Telescope

We investigate the potential of the Square Kilometer Array Telescope (SKA) to constrain the sound speed of dark energy. The Integrated Sachs Wolfe (ISW) effect results in a significant power spectrum signal when Cosmic Microwave Background (CMB) temperature anisotropies are cross-correlated with galaxies detectable with the SKA in H  i . We consider using this measurement, the autocorrelation of H  i galaxies and the CMB temperature power spectrum to derive constraints on the sound speed. We study the contributions to the cross-correlation signal made by galaxies at different redshifts and use redshift tomography to improve the signal-to-noise. We use a  χ²  analysis to estimate the significance of detecting a sound speed different from that expected in quintessence models, finding that there is potential to distinguish very low sound speeds from the quintessence value.     

Shine the dark ages

Recent WMAP results indicate quite early reionization of the universe. Here we discuss possible implications on CMB anisotropies and CMB polarization of the early reionization.