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Observations of the cosmic 21-cm power spectrum (PS) are starting to enable precision Bayesian inference of galaxy properties and physical cosmology, during the first billion years of our Universe. Here we investigate the impact of common approximations about the likelihood used in such inferences, including: (i) assuming a Gaussian functional form; (ii) estimating the mean from a single realization; and (iii) estimating the (co)variance at a single point in parameter space. We compare ‘classical’ inference that uses an explicit likelihood with simulation-based inference (SBI) that estimates the likelihood from a training set. Our forward models include: (i) realizations of the cosmic 21-cm signal computed with 21cmFAST by varying ultraviolet (UV) and X-ray galaxy parameters together with the initial conditions; (ii) realizations of the telescope noise corresponding to a $1000 \, \mathrm{h}$ integration with the low-frequency component of the Square Kilometre Array (SKA1-Low); and (iii) the excision of Fourier modes corresponding to a foreground-dominated horizon ‘wedge’. We find that the 1D PS likelihood is well described by a Gaussian accounting for covariances between wave modes and redshift bins (higher order correlations are small). However, common approaches of estimating the forward-modelled mean and (co)variance from a random realization or at a single point in parameter space result in biased and overconstrained posteriors. Our best results come from using SBI to fit a non-Gaussian likelihood with a Gaussian mixture neural density estimator. Such SBI can be performed with up to an order of magnitude fewer simulations than classical, explicit likelihood inference. Thus SBI provides accurate posteriors at a comparably low computational cost.

 

Upper limits from the current generation of interferometers targeting the 21-cm signal from high redshifts have recently begun to rule out physically realistic, though still extreme, models of the Epoch of Reionization (EoR). While inferring the detailed properties of the first galaxies is one of the most important motivations for measuring the high-z 21-cm signal, they can also provide useful constraints on the properties of the intergalactic medium (IGM). Motivated by this, we build a simple, phenomenological model for the 21-cm power spectrum that works directly in terms of IGM properties, which bypasses the computationally expensive 3D semi-numerical modeling generally employed in inference pipelines and avoids explicit assumptions about galaxy properties. The key simplifying assumptions are that (i) the ionization field is binary, and composed of spherical bubbles with an abundance described well by a parametric bubble size distribution, and (ii) that the spin temperature of the ‘bulk’ IGM outside bubbles is uniform. Despite the simplicity of the model, the mean ionized fraction and spin temperature of the IGM recovered from mock 21-cm power spectra generated with 21cm fast are generally in good agreement with the true input values. This suggests that it is possible to obtain comparable constraints on the IGM using models with very different assumptions, parameters, and priors. Our approach will thus be complementary to semi-numerical models as upper limits continue to improve in the coming years.

 

The mean free path of ionizing photons,λ_mfp, is a critical parameter for modeling the intergalactic medium (IGM) both during and after reionization. We present direct measurements ofλ_mfpfrom QSO spectra over the redshift range 5 <z< 6, including the first measurements atz≃ 5.3 and 5.6. Our sample includes data from the XQR-30 VLT large program, as well as new Keck/ESI observations of QSOs nearz∼ 5.5, for which we also acquire new [Cii] 158μm redshifts with ALMA. By measuring the Lyman continuum transmission profile in stacked QSO spectra, we find${\lambda }_{\mathrm{mfp}}={9.33}_{-1.80}^{+2.06}$,${5.40}_{-1.40}^{+1.47}$,${3.31}_{-1.34}^{+2.74}$, and${0.81}_{-0.48}^{+0.73}$pMpc atz= 5.08, 5.31, 5.65, and 5.93, respectively. Our results demonstrate thatλ_mfpincreases steadily and rapidly with time over 5 <z< 6. Notably, we find thatλ_mfpdeviates significantly from predictions based on a fully ionized and relaxed IGM as late asz= 5.3. By comparing our results to model predictions and indirectλ_mfpconstraints based on IGM Lyαopacity, we find that the evolution ofλ_mfpis consistent with scenarios wherein the IGM is still undergoing reionization and/or retains large fluctuations in the ionizing UV background well below redshift 6.

 

Abstract Measuring the density of the intergalactic medium using quasar sight lines in the epoch of reionization is challenging due to the saturation of Ly α absorption. Near a luminous quasar, however, the enhanced radiation creates a proximity zone observable in the quasar spectra where the Ly α absorption is not saturated. In this study, we use 10 high-resolution ( R ≳ 10,000) z ∼ 6 quasar spectra from the extended XQR-30 sample to measure the density field in the quasar proximity zones. We find a variety of environments within 3 pMpc distance from the quasars. We compare the observed density cumulative distribution function (CDF) with models from the Cosmic Reionization on Computers simulation and find a good agreement between 1.5 and 3 pMpc from the quasar. This region is far away from the quasar hosts and hence approaching the mean density of the universe, which allows us to use the CDF to set constraints on the cosmological parameter σ 8 = 0.6 ± 0.3. The uncertainty is mainly due to the limited number of high-quality quasar sight lines currently available. Utilizing the more than 200 known quasars at z ≳ 6, this method will allow us to tighten the constraint on σ 8 to the percent level in the future. In the region closer to the quasar within 1.5 pMpc, we find that the density is higher than predicted in the simulation by 1.23 ± 0.17, suggesting that the typical host dark matter halo mass of a bright quasar ( M 1450 < −26.5) at z ∼ 6 is log 10 ( M h / M ⊙ ) = 12.5 − 0.7 + 0.4 . 

This paper presents the design and deployment of the Hydrogen Epoch of Reionization Array (HERA) phase II system. HERA is designed as a staged experiment targeting 21 cm emission measurements of the Epoch of Reionization. First results from the phase I array are published as of early 2022, and deployment of the phase II system is nearing completion. We describe the design of the phase II system and discuss progress on commissioning and future upgrades. As HERA is a designated Square Kilometre Array pathfinder instrument, we also show a number of “case studies” that investigate systematics seen while commissioning the phase II system, which may be of use in the design and operation of future arrays. Common pathologies are likely to manifest in similar ways across instruments, and many of these sources of contamination can be mitigated once the source is identified.

 

The formation of the first galaxies during cosmic dawn and reionization (at redshifts z = 5–30), triggered the last major phase transition of our universe, as hydrogen evolved from cold and neutral to hot and ionized. The 21-cm line of neutral hydrogen will soon allow us to map these cosmic milestones and study the galaxies that drove them. To aid in interpreting these observations, we upgrade the publicly available code 21cmFAST. We introduce a new, flexible parametrization of the additive feedback from: an inhomogeneous, H2-dissociating (Lyman–Werner; LW) background; and dark matter – baryon relative velocities; which recovers results from recent, small-scale hydrodynamical simulations with both effects. We perform a large, ‘best-guess’ simulation as the 2021 installment of the Evolution of 21-cm Structure (EOS) project. This improves the previous release with a galaxy model that reproduces the observed UV luminosity functions (UVLFs), and by including a population of molecular-cooling galaxies. The resulting 21-cm global signal and power spectrum are significantly weaker, primarily due to a more rapid evolution of the star formation rate density required to match the UVLFs. Nevertheless, we forecast high signal-to-noise detections for both HERA and the SKA. We demonstrate how the stellar-to-halo mass relation of the unseen, first galaxies can be inferred from the 21-cm evolution. Finally, we show that the spatial modulation of X-ray heating due to relative velocities provides a unique acoustic signature that is detectable at z ≈ 10–15 in our fiducial model. Ours are the first public simulations with joint inhomogeneous LW and relative-velocity feedback across the entire cosmic dawn and reionization, and we make them available at this link https://scholar.harvard.edu/julianbmunoz/eos-21.

 

ABSTRACT The presence of excess scatter in the Ly-α forest at z ∼ 5.5, together with the existence of sporadic extended opaque Gunn-Peterson troughs, has started to provide robust evidence for a late end of hydrogen reionization. However, low data quality and systematic uncertainties complicate the use of Ly-α transmission as a precision probe of reionization’s end stages. In this paper, we assemble a sample of 67 quasar sightlines at z > 5.5 with high signal-to-noise ratios of >10 per ≤15 km s−1 spectral pixel, relying largely on the new XQR-30 quasar sample. XQR-30 is a large program on VLT/X-Shooter which obtained deep (SNR > 20 per pixel) spectra of 30 quasars at z > 5.7. We carefully account for systematics in continuum reconstruction, instrumentation, and contamination by damped Ly-α systems. We present improved measurements of the mean Ly-α transmission over 4.9 < z < 6.1. Using all known systematics in a forward modelling analysis, we find excellent agreement between the observed Ly-α transmission distributions and the homogeneous-UVB simulations Sherwood and Nyx up to z ≤ 5.2 (<1σ), and mild tension (∼2.5σ) at z = 5.3. Homogeneous UVB models are ruled out by excess Ly-α transmission scatter at z ≥ 5.4 with high confidence (>3.5σ). Our results indicate that reionization-related fluctuations, whether in the UVB, residual neutral hydrogen fraction, and/or IGM temperature, persist in the intergalactic medium until at least z = 5.3 (t = 1.1 Gyr after the big bang). This is further evidence for a late end to reionization. 

ABSTRACT The reionization of hydrogen is closely linked to the first structures in the Universe, so understanding the timeline of reionization promises to shed light on the nature of these early objects. In particular, transmission of Lyman alpha (Ly α) from galaxies through the intergalactic medium (IGM) is sensitive to neutral hydrogen in the IGM, so can be used to probe the reionization timeline. In this work, we implement an improved model of the galaxy UV luminosity to dark matter halo mass relation to infer the volume-averaged fraction of neutral hydrogen in the IGM from Ly α observations. Many models assume that UV-bright galaxies are hosted by massive dark matter haloes in overdense regions of the IGM, so reside in relatively large ionized regions. However, observations and N-body simulations indicate that scatter in the UV luminosity–halo mass relation is expected. Here, we model the scatter (though we assume the IGM topology is unaffected) and assess the impact on Ly α visibility during reionization. We show that UV luminosity–halo mass scatter reduces Ly α visibility compared to models without scatter, and that this is most significant for UV-bright galaxies. We then use our model with scatter to infer the neutral fraction, $\overline{x}_{\mathrm{ H}\,{\small I}}$, at z ∼ 7 using a sample of Lyman-break galaxies in legacy fields. We infer $\overline{x}_{\mathrm{ H}\,{\small I}} = 0.55_{-0.13}^{+0.11}$ with scatter, compared to $\overline{x}_{\mathrm{ H}\,{\small I}} = 0.59_{-0.14}^{+0.12}$ without scatter, a very slight decrease and consistent within the uncertainties. Finally, we place our results in the context of other constraints on the reionization timeline and discuss implications for future high-redshift galaxy studies. 

To mitigate the effects of Radio Frequency Interference (RFI) on the data analysis pipelines of 21 cm interferometric instruments, numerous inpaint techniques have been developed. In this paper, we examine the qualitative and quantitative errors introduced into the visibilities and power spectrum due to inpainting. We perform our analysis on simulated data as well as real data from the Hydrogen Epoch of Reionization Array (HERA) Phase 1 upper limits. We also introduce a convolutional neural network that is capable of inpainting RFI corrupted data. We train our network on simulated data and show that our network is capable of inpainting real data without requiring to be retrained. We find that techniques that incorporate high wavenumbers in delay space in their modelling are best suited for inpainting over narrowband RFI. We show that with our fiducial parameters discrete prolate spheroidal sequences (dpss) and clean provide the best performance for intermittent RFI while Gaussian progress regression (gpr) and least squares spectral analysis (lssa) provide the best performance for larger RFI gaps. However, we caution that these qualitative conclusions are sensitive to the chosen hyperparameters of each inpainting technique. We show that all inpainting techniques reliably reproduce foreground dominated modes in the power spectrum. Since the inpainting techniques should not be capable of reproducing noise realizations, we find that the largest errors occur in the noise dominated delay modes. We show that as the noise level of the data comes down, clean and dpss are most capable of reproducing the fine frequency structure in the visibilities.

 

Combining the visibilities measured by an interferometer to form a cosmological power spectrum is a complicated process. In a delay-based analysis, the mapping between instrumental and cosmological space is not a one-to-one relation. Instead, neighbouring modes contribute to the power measured at one point, with their respective contributions encoded in the window functions. To better understand the power measured by an interferometer, we assess the impact of instrument characteristics and analysis choices on these window functions. Focusing on the Hydrogen Epoch of Reionization Array (HERA) as a case study, we find that long-baseline observations correspond to enhanced low-k tails of the window functions, which facilitate foreground leakage, whilst an informed choice of bandwidth and frequency taper can reduce said tails. With simple test cases and realistic simulations, we show that, apart from tracing mode mixing, the window functions help accurately reconstruct the power spectrum estimator of simulated visibilities. The window functions depend strongly on the beam chromaticity and less on its spatial structure – a Gaussian approximation, ignoring side lobes, is sufficient. Finally, we investigate the potential of asymmetric window functions, down-weighting the contribution of low-k power to avoid foreground leakage. The window functions presented here correspond to the latest HERA upper limits for the full Phase I data. They allow an accurate reconstruction of the power spectrum measured by the instrument and will be used in future analyses to confront theoretical models and data directly in cylindrical space.