We study constraints on allowed reionization histories by comparing predictions of a physical semi-numerical model with secondary temperature and polarization anisotropies of the cosmic microwave background (CMB). Our model has four free parameters characterizing the evolution of ionizing efficiency $ζ$ and the minimum mass $M_{\mathrm{min}}$ of haloes that can produce ionizing radiation. Comparing the model predictions with the presently available data of the optical depth $τ$ and kinematic Sunyaev-Zeldovich signal, we find that we can already rule out a significant region of the parameter space. We limit the duration of reionization $Δz=1.30^{+0.19}_{-0.60}$ ($Δz < 2.9$ at $99\%$ C.L.), one of the tightest constraints on the parameter. The constraints mildly favour $M_{\mathrm{min}} \gtrsim 10^9 \mathrm{M}_{\odot}$ (at $68\%$ C.L.) at $z \sim 8$, thus indicating the presence of reionization feedback. Our analysis provides an upper bound on the secondary $B$-mode amplitude $D_{l=200}^{BB}<18$ nK$^2$ at $99\%$ C.L. We also study how the constraints can be further tightened with upcoming space and ground-based CMB missions. Our study, which relies solely on CMB data, has implications not only for upcoming CMB surveys for detecting primordial gravitational waves but also redshifted 21 cm studies.
We present constraints on the patchy reionization by measuring the trispectrum of the Planck 2015 cosmic microwave background (CMB) temperature anisotropies. The patchy reionization leads to anisotropies in the CMB optical depth, and the statistics of the observed CMB anisotropies is altered. We estimate the trispectrum of the CMB temperature anisotropies to constrain spatial variation of the optical depth. We show that the measured trispectrum is consistent with that from the standard lensed CMB simulation at $2σ$. While no evidence of the patchy reionization is found in the Planck 2015 tempe…
Current cosmic microwave background (CMB) bounds on the sum of the neutrino masses assume a sudden reionization scenario described by a single parameter that determines the onset of reionization. We investigate the bounds on the neutrino mass in a more general reionization scenario based on a principal component approach. We found the constraint on the sum of the neutrino masses from CMB data can be relaxed by a $\sim$40% in a generalized reionization scenario. Moreover, the amplitude of the r.m.s. mass fluctuations $σ_8$ is also considerably lower providing a better consistency with a low amp…
Inhomogeneous reionization gives rise to angular fluctuations in the Cosmic Microwave Background (CMB) optical depth tau(n) to the last scattering surface, correlating different spherical harmonic modes and imprinting characteristic non-Gaussianity on CMB maps. Recently the minimum variance quadratic estimator has been derived using this mode-coupling signal, and found that the optical depth fluctuations could be detected with (S/N)^2 ~ 100 in futuristic experiments like CMBPol. We first demonstrate that the non-Gaussian signal from gravitational lensing of CMB is the dominant source of contam…
Upcoming cosmic microwave background (CMB) experiments will measure temperature fluctuations on small angular scales with unprecedented precision. Small-scale CMB fluctuations are a mixture of late-time effects: gravitational lensing, Doppler shifting of CMB photons by moving electrons (the kSZ effect), and residual foregrounds. We propose a new statistic which separates the kSZ signal from the others, and also allows the kSZ signal to be decomposed in redshift bins. The decomposition extends to high redshift, and does not require external datasets such as galaxy surveys. In particular, the hi…
We study the signal from patchy reionization in view of the future high accuracy polarization measurements of the Cosmic Microwave Background (CMB). We implement an extraction procedure of the patchy reionization signal analogous to CMB lensing. We evaluate the signal to noise ratio (SNR) for the future Stage IV (S4) CMB experiment. The signal has a broad peak centered on the degree angular scales, with a long tail at higher multipoles. The CMB S4 experiment can effectively constrain the properties of reionization by measuring the signal on degree scales. The signal amplitude depends on the pr…
We study how uncertainty in the reionization history of the universe affects estimates of other cosmological parameters from the Cosmic Microwave Background. We analyze WMAP7 data and synthetic Planck-quality data generated using a realistic scenario for the reionization history of the universe obtained from high-resolution numerical simulation. We perform parameter estimation using a simple sudden reionization approximation, and using the Principal Component Analysis (PCA) technique proposed by Mortonson and Hu. We reach two main conclusions: (1) Adopting a simple sudden reionization model do…
Patchy reionization leaves a number of imprints on the small-scale cosmic microwave background (CMB) temperature fluctuations, the largest of which is the kinematic Sunyaev-Zel'dovich (kSZ), the Doppler shift of CMB photons scattering off moving electrons in ionized bubbles. It has long been known that in the CMB power spectrum, this imprint of reionization is largely degenerate with the kSZ signal produced by late-time galaxies and clusters, thus limiting our ability to constrain reionization. Following Smith & Ferraro (2017), it is possible to isolate the reionization contribution in a model…
The measurement of the optical depth to free electrons, tau_r, in the cosmic microwave background (CMB) provides an important constraint on reionization, but is degenerate to more complex reionization models. Small angular-scale CMB measurements of the kinetic Sunyaev-Zeldovich (kSZ) and Ostriker-Vishniac (OV) effects have the potential to break this degeneracy. We calculate the OV signal for various extended reionization histories described by a simple analytic form. These models are parametrized by dz, the duration of the reionization event. For reionization histories with identical values o…
The search for primordial gravitational waves through the $B$-mode polarization pattern in the CMB is one of the major goals of current and future CMB experiments. Besides foregrounds, a potential hurdle in this search is the anisotropic secondary $B$-mode polarization generated by the scattering of CMB photons off free electrons produced during patchy cosmological reionization. Robust predictions of these secondary anisotropies are challenging because of uncertainties in the reionization history. In this paper, we revise estimates of the reionization-induced $B$-mode signal by incorporating r…
We investigate how much the ratio of cosmic microwave background (CMB) polarization power spectra $C^{BB}_\ell/C^{EE}_\ell$ at low-$\ell$ ($\ell \lesssim 10$) depends on the process of reionization. Both such low-$\ell$ B-mode and E-mode polarization powers are dominantly produced by Thomson scattering of CMB photons off the free electrons which are produced in the process of reionization. Since the reionization should be finished until at least the redshift $z \simeq 6$ and the low-$\ell$ polarization powers are produced at late time, the ratio is rather insensitive by the ionization process …
B-modes in CMB polarization from patchy reionization arise from two effects: generation of polarization from scattering of quadrupole moments by reionization bubbles, and fluctuations in the screening of E-modes from recombination. The scattering contribution has been studied previously, but the screening contribution has not yet been calculated. We show that on scales smaller than the acoustic scale (l>300), the B-mode power from screening is larger than the B-mode power from scattering. The ratio approaches a constant ~2.5 below the damping scale (l>2000). On degree scales relevant for gravi…
The accurate understanding of the ionization history of the Universe plays a fundamental role in modern cosmology. It includes a phase of cosmological reionization after the standard recombination epoch, possibly associated to the early stages of structure and star formation. While the simple "τ-parametrization" of the reionization process and, in particular, of its imprints on the CMB anisotropy likely represents a sufficiently accurate modelling for the interpretation of current CMB data, a great attention has been recently posed on the accurate computation of the reionization signatures in …
Into the Gompverse: A robust Gompertzian reionization model for CMB analyses
Pengcheng Laboratory（鹏城实验室）；Universidad de Costa Rica（哥斯达黎加大学）；Institute of Space Sciences (ICE, CSIC)（空间科学研究所（ICE，CSIC））；Institut d’Estudis Espacials de Catalunya (IEEC)（加泰罗尼亚太空研究学院（IEEC））；Sun Yat-Sen University（中山大学）
Cosmic Reionization imprints its signature on the temperature and polarization anisotropies of the cosmic microwave background (CMB). Advances in CMB telescopes have already placed a significant constraint on the history of reionization. As near-future CMB telescopes target the maximum sensitivity, or observations limited only by the cosmic variance (CV), we hereby forecast the potential of future CMB observations in constraining the history of reionization. In this study, we perform Markov Chain Monte Carlo analysis for CV-limited E-mode polarization observations such as the LiteBIRD (Light s…
We propose a hybrid quadratic estimator to measure cross correlations between gravitational lensing of the cosmic microwave background (CMB) and differential screening effects arising from fluctuations in the electron column density, such as could arise from patchy reionization. The hybrid quadratic estimators are validated by simulated data sets with both Planck and CMB-Stage 4 (CMB-S4) instrumental properties and found to be able to recover the cross-power spectra with almost no biases. We apply this technique to Planck 2015 temperature data and obtain cross-power spectra between gravitation…
In this paper, we explore the constraints on the reionization history that are provided by current observations of the Lyman-alpha forest and the CMB. Rather than using a particular semi-analytic model, we take the novel approach of parametrizing the ionizing sources with arbitrary functions, and perform likelihood analyses to constrain possible reionization histories. We find model independent conclusions that reionization is likely to be mostly complete by z=8 and that the IGM was 50% ionized at z=9-10. Upcoming low-frequency observations of the redshifted 21 cm line of neutral hydrogen are …
We show how cross-correlating a high redshift external tracer field, such as the 21cm neutral hydrogen distribution and product maps involving Cosmic Microwave Background (CMB) temperature and polarisation fields, that probe mixed bispectrum involving these fields, can help to determine the reionization history of the Universe, beyond what can be achieved from cross-spectrum analysis. Taking clues from recent studies for the detection of primordial non-Gaussianity (Munshi & Heavens 2010), we develop a set of estimators that can study reionization using a power spectrum associated with the bisp…
We investigate the constraints on the reionization history of the Universe from a joint analysis of the cosmic microwave background and neutral hydrogen fraction data. The $\tanh$ parametrization and principal component analysis methods are applied to the reionization history respectively. The commonly used $\tanh$ parametrization is oversimplistic when the neutral hydrogen fraction data are taken into account. Using the principal component analysis method, the reconstructed reionization history is consistent with the neutral hydrogen fraction data. With the principal component analysis method…
Based on the work by Mitra, Choudhury & Ferrara (2010), we obtain model-independent constraints on reionization from cosmic microwave background (CMB) and QSO absorption line data by decomposing the function N_{ion}(z) (the number of photons entering the IGM per baryon in collapsed objects) into its principal components. The main addition in this work is that for the CMB data set, we explicitly include the angular power spectra C_l for TT, TE and EE modes in our analysis which seem to contain somewhat more information than taking the electron scattering optical depth tau_{el} as a single data …
We present an observational search for the possible correlation between cosmic microwave background (CMB) polarization map and soft X-ray background (SXRB) based on the ROSAT All-sky Survey (RASS) archive and WMAP five-year observations. This is motivated by the fact that some of the CMB polarization may arise from the scattering of CMB photons due to the free electrons generated by X-ray heating sources in the epoch of reionization. Detection of such a correlation allows one to study the role of X-ray heating in the process of reionization. However, the cross angular power spectrum of the CMB…
We explore the constraints on the history of reionization from Planck 2015 Cosmic Microwave Background (CMB) data and we derive the forecasts for future CMB observations. We consider a class of monotonic histories of reionization as parametrized by two additional extra parameters with respect to the average optical depth used in the instantaneous reionization modeling. We investigate the degeneracies between the history of reionization and selected extensions of the standard cosmological model. In particular, we consider the degeneracies with the total mass of the neutrino sector and we discus…
The global history of reionization was shaped by the relative amounts of starlight released by three halo mass groups: atomic-cooling halos (ACHs) with virial temperatures Tvir > 10^4 K, either (1) massive enough to form stars even after reionization (HMACHs, >~ 10^9 Msun) or (2) less-massive (LMACHs), subject to star formation suppression when overtaken by reionization, and (3) H2-cooling minihalos (MHs) with Tvir < 10^4 K, whose star formation is predominantly suppressed by the H2-dissociating Lyman-Werner (LW) background. Our previous work showed that including MHs caused two-stage reioniza…
The epoch of reionization is one of the major phase transitions in the history of the universe, and is a focus of ongoing and upcoming cosmic microwave background (CMB) experiments with improved sensitivity to small-scale fluctuations. Reionization also represents a significant contaminant to CMB-derived cosmological parameter constraints, due to the degeneracy between the Thomson-scattering optical depth, $τ$, and the amplitude of scalar perturbations, $A_s$. This degeneracy subsequently hinders the ability of large-scale structure data to constrain the sum of the neutrino masses, a major tar…
It has been several years since the first detection of Gunn-Peterson troughs in the z > 6 Ly-alpha forest and since the first measurement of the Thomson scattering optical depth through reionization from the cosmic microwave background (CMB). Present day CMB measurements provide a significant constraint on the mean redshift of reionization, and the Ly-alpha forest provides a lower bound on the redshift at which reionization ended. However, no observation has provided definitive information on the duration and morphology of this process. This article is intended as a short review on the most pr…
Cross-correlating the patchy screening and kinetic Sunyaev-Zel'dovich effects as a new probe of reionization
School of Earth and Space Exploration, Arizona State University（亚利桑那州立大学地球与空间探索学院）；Department of Applied Mathematics and Theoretical Astrophysics, University of Cambridge（剑桥大学应用数学与理论天体物理系）；Department of Physics, Carnegie Mellon University（卡内基梅隆大学物理系）；McWilliams Center for Cosmology and Astrophysics, Carnegie Mellon University（卡内基梅隆大学麦克威廉斯宇宙学与天体物理学中心）
We review the observable consequences of the epoch of reionization (EoR) on the cosmic microwave background (CMB), and the resulting constraints on the EoR. We discuss how Thomson scattering with the free electrons produced during EoR equates to an optical depth for CMB photons. The optical depth measurements from the WMAP and Planck satellites, using large-scale CMB polarization power spectra, is one of the few current constraints on the timing of cosmic reionization. We also present forecasts for the precision with which the optical depth will be measured by future satellite missions. Second…
High-redshift QSO spectra show large spatial fluctuations in the Ly-alpha opacity of the intergalactic medium on surprisingly large scales at z>~5.5. We present a radiative transfer simulation of cosmic reionization driven by galaxies that reproduces this large scatter and the rapid evolution of the Ly-alpha opacity distribution at 5<z<6. The simulation also reproduces the low Thomson scattering optical depth reported by the latest CMB measurement and is consistent with the observed short near-zones and strong red damping wings in the highest-redshift QSOs. It also matches the rapid disappeara…
The Epoch of Reionization (EoR) depends on the complex astrophysics governing the birth and evolution of the first galaxies and structures in the intergalactic medium. EoR models rely on cosmic microwave background (CMB) observations, and in particular the large-scale E-mode polarization power spectra (EE PS), to help constrain their highly uncertain parameters. However, rather than directly forward-modelling the EE PS, most EoR models are constrained using a summary statistic -- the Thompson scattering optical depth, $τ_e$. Compressing CMB observations to $τ_e$ requires adopting a basis set f…
Cosmic baryon evolution during the Cosmic Dawn and Reionization results in redshifted 21-cm spectral distortions in the cosmic microwave background (CMB). These encode information about the nature and timing of first sources over redshifts 30-6 and appear at meter wavelengths as a tiny CMB distortion along with the Galactic and extragalactic radio sky, which is orders of magnitude brighter. Therefore, detection requires precise methods to model foregrounds. We present a method of foreground fitting using maximally smooth (MS) functions. We demonstrate the usefulness of MS functions over tradit…
The power spectrum of reconstructed cosmic microwave background (CMB) lensing maps is a powerful tool for constraints on cosmological parameters like the sum of the neutrino masses and the dark energy equation of state. One possible complication is the kinematic Sunyaev-Zel'dovich (kSZ) effect, due to the scattering of CMB photons by moving electrons, which can bias the reconstruction of the CMB lensing power spectrum through both kSZ-lensing correlations and the non-Gaussianity of the kSZ temperature anisotropies. We investigate for the first time the bias to CMB lensing reconstruction from t…
The Thomson optical depth from reionization is a limiting factor in measuring the amplitude of primordial fluctuations, and hence in measuring physics that affects the low-redshift amplitude, such as the neutrino masses. Current constraints on the optical depth, based on directly measuring large-scale cosmic microwave background (CMB) polarization, are challenging due to foregrounds and systematic effects. Here, we consider an indirect measurement of large-scale polarization, using observed maps of small-scale polarization together with maps of fields that distort the CMB, such as CMB lensing …
We consider the prospects of probing features in the primordial power spectrum with future Cosmic Microwave Background (CMB) polarization measurements. In the scope of the inflationary scenario, such features in the spectrum can be produced by local non-smooth pieces in an inflaton potential (smooth and quasi-flat in general) which in turn may originate from fast phase transitions during inflation in other quantum fields interacting with the inflaton. They can fit some outliers in the CMB temperature power spectrum which are unaddressed within the standard inflationary ${\mathrmΛ}$CDM model. W…
We explore a new approach for extracting reionization-era contributions to the kinetic Sunyaev-Zel'dovich (kSZ) effect. Our method utilizes the cross-power spectrum between filtered and squared maps of the cosmic microwave background (CMB) and photometric galaxy surveys during the Epoch of Reionization (EoR). This kSZ$^2$-galaxy cross-power spectrum statistic has been successfully detected at lower redshifts ($z \lesssim 1.5$). Here we extend this method to $z \gtrsim 6$ as a potential means to extract signatures of patchy reionization. We model the expected signal across multiple photometric …
The Challenge of Observing Patchy Reionization with CMB Optical-Depth Fluctuations
The University of Chicago（芝加哥大学）；Institute for Advanced Study（高等研究院）；Fermi National Accelerator Laboratory（费米国家加速器实验室）；Kavli Institute for Cosmological Physics（卡弗里宇宙物理学研究所）
We investigate the effect of primordial non-Gaussianity on the cross-correlation between the CMB anisotropies and the 21 cm fluctuations from the epoch of reionization. We assume an analytic reionization model and an ionization fraction with $f_{\rm NL}$ induced scale dependent bias. We estimate the angular power spectrum of the cross-correlation of the CMB and 21 cm. In order to evaluate the detectability, the signal-to-noise (S/N) ratio for only a single redshift slice is also calculated for current and future observations, such as CMB observations by Planck satellite and 21 cm observations …
Reionization of the cosmic neutral hydrogen by the first stars in the Universe is an inhomogeneous process which produces spatial fluctuations in free electron density. These fluctuations lead to observable signatures in cosmological probes like the cosmic microwave background (CMB). We explore the effect of the electron density fluctuations on CMB using photon-conserving semi-numerical simulations of reionization named \texttt{SCRIPT}. We show that the amplitude of the kinematic Sunyaev-Zeldovich (kSZ) and $B$-mode polarization signal depends on the patchiness in the spatial distribution of e…
It has recently been shown that supersonic relative velocities between dark matter and baryonic matter can have a significant effect on formation of the first structures in the universe. If this effect is still non-negligible during the epoch of hydrogen reionization, it generates large-scale anisotropy in the free electron density, which gives rise to a CMB B-mode. We compute the B-mode power spectrum and find a characteristic shape with acoustic peaks at l ~ 200, 400, ... The amplitude of this signal is a free parameter which is related to the dependence of the ionization fraction on the rel…
We present an approximate, analytical calculation of the reionized spectra $C_l^{XX}$ of cosmic microwave background radiation (CMB) anisotropies and polarizations generated by relic gravitational waves (RGWs). Three simple models of reionization are explored, whose visibility functions are fitted by gaussian type of functions as approximations. We have derived the analytical polarization $β_l$ and temperature anisotropies $α_l$, both consisting of two terms proportional to RGWs at the decoupling and at the reionization as well. The explicit dependence of $β_l$ and $α_l$ upon the reionization …
We explore the fundamental limits to which reionization histories can be constrained using only large-scale cosmic microwave background (CMB) anisotropy measurements. The redshift distribution of the fractional ionization $x_e(z)$ affects the angular distribution of CMB polarization. We project constraints on the reionization history of the universe using low-noise full-sky temperature and E-mode measurements of the CMB. We show that the measured TE power spectrum, $\hat C_\ell^\mathrm{TE}$, has roughly one quarter of the constraining power of $\hat C_\ell^\mathrm{EE}$ on the reionization opti…
Amongst standard model parameters that are constrained by cosmic microwave background (CMB) observations, the optical depth $τ$ stands out as a nuisance parameter. While $τ$ provides some crude limits on reionization, it also degrades constraints on other cosmological parameters. Here we explore how 21 cm cosmology---as a direct probe of reionization---can be used to independently predict $τ$ in an effort to improve CMB parameter constraints. We develop two complementary schemes for doing so. The first uses 21 cm power spectrum observations in conjunction with semi-analytic simulations to pred…
Future arcminute resolution polarization data from ground-based Cosmic Microwave Background (CMB) observations can be used to estimate the contribution to the temperature power spectrum from the primary anisotropies and to uncover the signature of reionization near $\ell=1500$ in the small angular-scale temperature measurements. Our projections are based on combining expected small-scale E-mode polarization measurements from Advanced ACTPol in the range $300<\ell<3000$ with simulated temperature data from the full Planck mission in the low and intermediate $\ell$ region, $2<\ell<2000$. We show…
The Impact of Population III.1 Flash Reionization for CMB Polarization and Thomson Scattering Optical Depth
Chalmers University of Technology（查尔姆斯理工大学）；University of Virginia（弗吉尼亚大学）；Max-Planck-Institut für Astrophysik（马克斯·普朗克天体物理学研究所）；Ludwig-Maximilians-Universität München（慕尼黑大学）；The University of Tokyo（东京大学）
The density contrast of the Universe, parametrized in terms of the matter power spectrum and its variance, can amplify the signal of the free-free process in the plasma. The damping of fluctuations on scales smaller than the DM particle free streaming scale corresponds to a suppression of the total matter power spectrum on large wave numbers k. We derive the time evolution of the variance of the matter power spectrum for various cosmological models and parameters by numerically computing the power spectrum with a modified version of the Boltzmann code CAMB, for different values of the cut-off …
We propose a new reionization probe that uses cosmic microwave background (CMB) observations; the cross-correlation between fluctuations in the CMB optical depth which probes the integrated electron density, $δτ$, and the Compton $y$-map which probes the integrated electron pressure. This cross-correlation is much less contaminated than the $y$-map power spectrum by late-time cluster contributions. In addition, this cross-correlation can constrain the temperature of ionized bubbles while the optical-depth fluctuations and kinetic SZ effect can not. We measure this new observable using a Planck…
The first generation (Pop-III) stars can ionize 1-10% of the universe by $z=15$, when the metal-enriched (Pop-II) stars may contribute negligibly to the ionization. This low ionization tail might leave detectable imprints on the large-scale CMB E-mode polarization. However, we show that physical models for reionization are unlikely to be sufficiently extended to detect any parameter beyond the total optical depth through reionization. This result is driven in part by the total optical depth inferred by Planck, indicating a reionization midpoint around $z=8$, which in combination with the requi…
Raising the Optical Depth to Reionization with Dark Matter Decay
Key Laboratory of Dark Matter and Space Astronomy, Purple Mountain Observatory, Chinese Academy of Sciences（中国科学院紫金山天文台暗物质与空间天文重点实验室）；School of Astronomy and Space Science, University of Science and Technology of China（中国科学技术大学天文与空间科学学院）；Department of Strategic and Advanced Interdisciplinary Research, Peng Cheng Laboratory（鹏城实验室战略与先进交叉研究部）
We discuss the secondary cosmic microwave background (CMB) anisotropy due to kinetic Sunyaev-Zel'dovich (kSZ) effect from ionized bubbles around individual quasars prior to the reionization of the Universe. The bubbles create local ionization modulations which move with the large scale structure linear bulk flow and act as sources for kSZ. We improve upon previous calculations of this effect, using a halo model based description of quasar abundance, and find that the kSZ distortion power spectrum, $C_\ell$, from the bubbles to be sub-dominant to kSZ from patchy reionization driven by galaxies.…
