Rapid and Late Cosmic Reionization Driven by Massive Galaxies: a Joint Analysis of Constraints from 21-cm, Lyman Line & CMB Data Sets

TL;DR

This work demonstrates that a neural density estimation–accelerated Bayesian joint analysis of CMB, Lyman-line, and 21-cm data can tightly constrain the Epoch of Reionization within a semi-numerical framework. The results indicate that reionization was driven predominantly by massive galaxies in atomic-cooling halos with $M_{ m min}(z) \,\gtrsim\,2.6\times10^{9} M_{igodot}$ (equivalently $V_c\,\gtrsim\,50{\rm\ km\,s^{-1}}$) and occurred rapidly over $\Delta z_{\rm re} < 1.8$, with the midpoint at $z_{50}=7.16^{+0.15}_{-0.12}$. The joint analysis shifts the predicted 21-cm signal toward lower amplitudes and later times, and constrains the high-redshift global signal to be shallower than deep absorption troughs (e.g., $A<62$ mK at $z=17.2$). The conclusions are model-dependent, yet they align with simulations that massive halos dominate late reionization and highlight the value of combining 21-cm upper limits, Ly$\alpha$/Ly$\beta$ constraints, and CMB measurements to obtain a coherent picture of cosmic reionization; future work incorporating mass-dependent star formation efficiencies and JWST constraints is expected to further sharpen these inferences.

Abstract

Observations of the Epoch of Reionization (EoR) have the potential to answer long-standing questions of astrophysical interest regarding the nature of the first luminous sources and their effects on the intergalactic medium (IGM). We present astrophysical constraints from a Neural Density Estimation-Accelerated Bayesian joint analysis of constraints deriving from Cosmic Microwave Background power spectrum measurements from Planck and SPT, IGM neutral fraction measurements from Lyman-line-based data sets and 21-cm power spectrum upper limits from HERA, LOFAR and the MWA. In the context of the model employed, the data is found to be consistent with galaxies forming from predominantly atomic-cooled hydrogen gas in dark matter halos, with masses $M_\mathrm{min} \gtrsim 2.6 \times 10^{9}~M_{\odot} ((1+z)/10)^{\frac{1}{2}}$ at 95% credibility ($V_\mathrm{c} \gtrsim 50~\mathrm{km~s^{-1}}$) being the dominant galactic population driving reionization. These galaxies reionize the neutral hydrogen in the IGM over a narrow redshift interval ($Δz_\mathrm{re} < 1.8$ at 95% credibility), with the midpoint of reionization (when the sky-averaged IGM neutral fraction is 50%) constrained to $z_{50} = 7.16^{+0.15}_{-0.12}$. Given the parameter posteriors from our joint analysis, we find that the posterior predictive distribution of the global 21-cm signal is reduced in amplitude and shifted to lower redshifts relative to the model prior. We caution, however, that our inferences are model-dependent. Future work incorporating updated, mass-dependent star formation efficiencies in atomic cooling halos, informed by the latest UV luminosity function constraints from the James Webb Space Telescope, promises to refine these inferences further and enhance our understanding of cosmic reionization.

Figures (10)

• Figure 1: Probability distributions of astrophysical parameters derived with analyses of high-redshift data sets and which form the inputs to the joint analysis carried out in this work. \ref{['Fig:B24Posteriors2']} shows the one- and two-dimensional posterior probability distributions of the astrophysical parameters derived from the combination of HERA+MWA+LOFAR analysis in B24. The colorbar displays the peak-normalised binned probability of histogram bins within the 2D joint posterior distributions, where dark green denotes bins that have maximum posterior probability and white bins those with negligible probability. The sparsely and densely hatched regions of the 1D posteriors and areas enclosed by solid and dashed black lines in the 2D posteriors contain 68% and 95% of the probability, respectively, in each case. \ref{['Fig:LymanLineConstraints2']} shows one-dimensional posterior distributions on $\overline{x}_\mathrm{H_{I}}$ using Lyman line constraints deriving from measurements of the Ly$\alpha$ and Ly$\beta$ forest dark pixel fraction (orange), the clustering of Ly$\alpha$ emitters (red), the analysis of the damping wings of bright quasar (green), and the evolution of the Ly$\alpha$ equivalent width (cyan). The redshifts of the objects from which the individual PDFs are derived are labelled in the figure legend. The mapping between legend labels and the papers in which the original analyses were carried out is given in \ref{['Tab:DataSets']}. \ref{['Fig:Plancktauposterior2']} shows the Planck TT,TE,EE+low$l$+lowE+lensing one-dimensional marginal posterior on the total CMB optical depth, $\tau_\mathrm{CMB}$. \ref{['Fig:SPTdzrePosterior2']} shows the one-dimensional marginal posterior distribution on $\Delta z_\mathrm{re}$ from 2021ApJ...908..199R, using SPT measurements of the kSZ effect imprinted on the CMB power spectrum, in combination with a prior on the tSZ bispectrum from 2014ApJ...784..143C and assuming the 2014JCAP...08..010C model for the homogeneous kSZ power.
• Figure 3: EoR information content provided by the data sets included in our analysis, as measured by the marginal KL divergence ($\mathcal{D}_\mathrm{KL}(\bm{\upTheta} \vert \bm{D})$) between the priors and posteriors of the one- and two-dimensional probability densities of the astrophysical parameters of the model. \ref{['Fig:InformationContent2DSummaryCMB']} shows $\mathcal{D}_\mathrm{KL}(\bm{\upTheta} \vert \bm{D}_\mathrm{CMB})$, where $\bm{D}_\mathrm{CMB}$ are the Planck 2018 constraints on $\tau_\mathrm{CMB}$ and R21 constraints on $\Delta z_\mathrm{re}$ from SPT data. \ref{['Fig:InformationContent2DSummaryLl']} shows $\mathcal{D}_\mathrm{KL}(\bm{\upTheta} \vert \bm{D}_\mathrm{Ll})$, where $\bm{D}_\mathrm{Ll}$ are the Lyman line constraints on the high-redshift IGM neutral fraction illustrated in \ref{['Fig:LymanLineConstraints2']}. \ref{['Fig:InformationContent2DSummary21cm']} shows $\mathcal{D}_\mathrm{KL}(\bm{\upTheta} \vert \bm{D}_\mathrm{21-cm})$, where $\bm{D}_\mathrm{21-cm}$ are the HERA+MWA+LOFAR power spectrum upper limits analysed in B24. \ref{['Fig:InformationContent2DSummaryJoint']} shows $\mathcal{D}_\mathrm{KL}(\bm{\upTheta} \vert \bm{D}_\mathrm{Joint})$, where $\bm{D}_\mathrm{Joint}$ is the combination of the aforementioned constraints. Squares that are black indicate that the corresponding data set contains no information about those parameters (or, equivalently, there is not a statistically significant difference between their prior and posterior distributions). Conversely, the light squares indicate that the data set contains a greater quantity of information that constrains those parameters, as quantified by a significant difference in the posterior distribution of the parameters relative to their priors.
• Figure 4: One- and two-dimensional posterior probability densities of the circular velocity, $\log_{10}(V_\mathrm{c})$, and the CMB optical depth, $\tau_\mathrm{CMB}$. Posteriors in purple derive from CMB power spectrum constraints (Planck TT,TE,EE+low$l$+lowE+lensing constraint on $\tau_\mathrm{CMB}$ and R21 constraint on $\Delta z_\mathrm{re}$ from SPT data). Those in red derive from Lyman line constraints on the sky averaged IGM neutral fraction (see \ref{['Tab:DataSets']}). Those in blue derive from our full joint analysis. The solid and transparent shaded contours plotted in the 2D posteriors contain 68% and 95% of the probability, respectively.
• Figure 5: The percentage ($100f_\mathrm{c}$; see \ref{['Eq:KLDivergenceFractionalConsistency']}) of the five dimensional prior probability density of the astrophysical parameters of our model that is consistent with each data set individually and in combination, as well as their associated $1 \sigma$ uncertainties accounting for sampling and model error. The smaller the percentage of the astrophysical prior consistent with the data, the more constraining that data set is. The corresponding KL divergences between the five dimensional prior and posterior probability densities, from which the percentile constraints are calculated, can be read from the twin y-axis.
• Figure 6: One- and two-dimensional marginal posterior probability densities of the astrophysical parameters derived from the combination of upper limits on the power spectrum of redshifted 21-cm emission from the EoR with HERA, the MWA and LOFAR, high-redshift IGM neutral fraction measurements inferred from Lyman line data, and CMB power spectrum constraints on $\tau_\mathrm{CMB}$ from Planck and on $\Delta z_\mathrm{re}$ from SPT. The colorbar displays the peak-normalised, binned probability of histogram bins within the 2D joint posterior densities, where dark blue denotes bins that have maximum posterior probability and white bins those with negligible probability. The sparsely and densely hatched regions of the 1D posteriors and areas enclosed by solid and dashed black lines in the 2D posteriors contain 68% and 95% of the probability, respectively, in each case.