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The James Webb Space Telescope (JWST) is discovering an increasing number of galaxies well into the early stages of the Epoch of Reionization (EoR). Many of these galaxies are clustered with strong Lyman alpha (Ly$\alpha$) emission, motivating the presence of surrounding cosmic HII regions that would facilitate Ly$\alpha$ transmission through the intergalactic medium (IGM). Detecting these HII "bubbles" would allow us to connect their growth to the properties of the galaxies inside them. Here we develop a new forward-modeling framework to estimate the local HII region size and location from Ly$\alpha$ spectra of galaxy groups in the early stages of the EoR. Our model takes advantage of the complementary information provided by neighboring sightlines through the IGM. Our forward models sample the main sources of uncertainty, including: (i) the global neutral fraction; (ii) EoR morphology; (iii) emergent Ly$\alpha$ emission; and (iv) NIRSpec instrument noise. Depending on the availability of complementary nebular lines, $\sim$ 0.006 $\unicode{x2013}$ 0.01 galaxies per cMpc$^3$, are required to be $\gtrsim$95\% confident that the HII bubble location and size recovered by our method is accurate to within $\sim$ 1 comoving Mpc. This corresponds roughly to tens of galaxies at $z\sim7\unicode{x2013}8$ in $\sim$2x2 tiled pointing with JWST NIRSpec. Such a sample is achievable with a targeted survey with completeness down to $M_{\rm UV}^{\rm min}\lesssim$ -19 $\unicode{x2013}$ -17, depending on the over-density of the field. We test our method on 3D EoR simulations as well as misspecified equivalent width distributions, in both cases accurately recovering the HII region surrounding targeted galaxy groups., Comment: 14 pages, 15 figures, submitted to A&A

Inflationary models that involve bursts of particle production generate bump-like features in the primordial power spectrum of density perturbations. These features influence the evolution of density fluctuations, leaving their unique signatures in cosmological observations. A detailed investigation of such signatures would help constrain physical processes during inflation. With this motivation, the goal of this paper is two-fold. First, we conduct a detailed analysis of the effects of bump-like primordial features on the sky-averaged 21 cm signal. Using semi-numerical simulations, we demonstrate that the primordial features can significantly alter the ionization history and the global 21 cm profile, making them a promising probe of inflationary models. We found a special scale (namely, the turnover wavenumber, $k^{\rm turn}$) at which the effect of primordial bump-like features on the global 21 cm profile vanishes. Also, we found that the behaviour of the primordial features on the global profile and ionization history are quite opposite for $k > k^{\rm turn}$ and $k < k^{\rm turn}$. We trace the root cause of these behaviours to the effects of primordial features on the halo mass function at high redshifts. Furthermore, we discuss the degeneracy between the astrophysical parameters and the primordial features in detail. Secondly, for a fixed set of astrophysical parameters, we derive upper limits on the amplitude of bump-like features in the range $10^{-1} < k\,[{\rm Mpc}^{-1}] < 10^2$ using current limits on optical depth to reionization from CMB data by Planck., Comment: 30 pages

The Lyman alpha (Lya) forest in the spectra of z>5 quasars provides a powerful probe of the late stages of the Epoch of Reionization (EoR). With the recent advent of exquisite datasets such as XQR-30, many models have struggled to reproduce the observed large-scale fluctuations in the Lya opacity. Here we introduce a Bayesian analysis framework that forward-models large-scale lightcones of IGM properties, and accounts for unresolved sub-structure in the Lya opacity by calibrating to higher-resolution hydrodynamic simulations. Our models directly connect physically-intuitive galaxy properties with the corresponding IGM evolution, without having to tune "effective" parameters or calibrate out the mean transmission. The forest data, in combination with UV luminosity functions and the CMB optical depth, are able to constrain global IGM properties at percent level precision in our fiducial model. Unlike many other works, we recover the forest observations without evoking a rapid drop in the ionizing emissivity from z~7 to 5.5, which we attribute to our sub-grid model for recombinations. In this fiducial model, reionization ends at $z=5.44\pm0.02$ and the EoR mid-point is at $z=7.7\pm0.1$. The ionizing escape fraction increases towards faint galaxies, showing a mild redshift evolution at fixed UV magnitude, Muv. Half of the ionizing photons are provided by galaxies fainter than Muv~-12, well below direct detection limits of optical/NIR instruments including JWST. We also show results from an alternative galaxy model that does not allow for a redshift evolution in the ionizing escape fraction. Despite being decisively disfavored by the Bayesian evidence, the posterior of this model is in qualitative agreement with that from our fiducial model. We caution however that our conclusions regarding the early stages of the EoR and which sources reionized the Universe are more model-dependent., Comment: 21 pages, 12 figures, 3 tables (submitted to PASA)

The precise characterization and mitigation of systematic effects is one of the biggest roadblocks impeding the detection of the fluctuations of cosmological 21cm signals. Missing data in radio cosmological experiments, often due to radio frequency interference (RFI), poses a particular challenge to power spectrum analysis as it could lead to the ringing of bright foreground modes in Fourier space, heavily contaminating the cosmological signals. Here we show that the problem of missing data becomes even more arduous in the presence of systematic effects. Using a realistic numerical simulation, we demonstrate that partially flagged data combined with systematic effects can introduce significant foreground ringing. We show that such an effect can be mitigated through inpainting the missing data. We present a rigorous statistical framework that incorporates the process of inpainting missing data into a quadratic estimator of the 21cm power spectrum. Under this framework, the uncertainties associated with our inpainting method and its impact on power spectrum statistics can be understood. These results are applied to the latest Phase II observations taken by the Hydrogen Epoch of Reionization Array, forming a crucial component in power spectrum analyses as we move toward detecting 21cm signals in the ever more noisy RFI environment., Comment: 25 pages, 11 figures; Replaced to match accepted ApJ version. New version contains small editorial changes throughout in response to referee comments, no changes to results

In 2018 the EDGES experiment claimed the first detection of the global cosmic 21cm signal, which featured an absorption trough centered around $z \sim 17$ with a depth of approximately -500mK. This amplitude is deeper than the standard prediction (in which the radio background is determined by the cosmic microwave background) by a factor of two and potentially hints at the existence of a radio background excess. While this result was obtained by fitting the data with a phenomenological flattened-Gaussian shape for the cosmological signal, here we develop a physical model for the inhomogeneous radio background sourced by the first galaxies hosting population III stars. Star formation in these galaxies is quenched at lower redshifts due to various feedback mechanisms, so they serve as a natural candidate for the excess radio background hinted by EDGES, without violating present day measurements by ARCADE2. We forward-model the EDGES sky temperature data, jointly sampling our physical model for the cosmic signal, a foreground model, and residual calibration errors. We compare the Bayesian evidences obtained by varying the complexity and prior ranges for the systematics. We find that the data is best explained by a model with seven log-polynomial foreground terms, and that it requires calibration residuals. Interestingly, the presence of a cosmic 21cm signal with a non-standard depth is decisively disfavored. This is contrary to previous EDGES analysis in the context of extra radio background models, serving as a caution against using a ''pseudo-likelihood'' built on a model (flattened Gaussian) that is different from the one being used for inference. We make our simulation code and associated emulator publicly-available., Comment: 17 pages, 9 figures, 1 table, version submitted to A&A

Ionized bubble sizes during reionization trace physical properties of the first galaxies. JWST's ability to spectroscopically confirm and measure Lyman-alpha (Ly$\alpha$) emission in sub-L* galaxies opens the door to mapping ionized bubbles in 3D. However, existing Lya-based bubble measurement strategies rely on constraints from single galaxies, which are limited by the large variability in intrinsic Ly$\alpha$ emission. As a first step, we present two bubble size estimation methods using Lya spectroscopy of ensembles of galaxies, enabling us to map ionized structures and marginalize over Ly$\alpha$ emission variability. We test our methods using Gpc-scale reionization simulations of the intergalactic medium (IGM). To map bubbles in the plane of the sky, we develop an edge detection method based on the asymmetry of Ly$\alpha$ transmission as a function of spatial position. To map bubbles along the line-of-sight, we develop an algorithm using the tight relation between Ly$\alpha$ transmission and the line-of-sight distance from galaxies to the nearest neutral IGM patch. Both methods can robustly recover bubbles with radius $\gtrsim$10 comoving Mpc, sufficient for mapping bubbles even in the early phases of reionization, when the IGM is $\sim70-90\%$ neutral. These methods require $\gtrsim$0.002-0.004 galaxies/cMpc$^3$, a $5\sigma$ Ly$\alpha$ equivalent width upper limit of $\lesssim$30\r{A} for the faintest targets, and redshift precision $\Delta z \lesssim 0.015$, feasible with JWST spectroscopy. Shallower observations will provide robust lower limits on bubble sizes. Additional constraints on IGM transmission from Ly$\alpha$ escape fractions and line profiles will further refine these methods, paving the way to our first direct understanding of ionized bubble growth., Comment: 15 pages (+ 3 pages in Appendix), 17 figures, submitted to A&A

A precise measurement of photometric redshifts (photo-z) is key for the success of modern photometric galaxy surveys. Machine learning (ML) methods show great promise in this context, but suffer from covariate shift (CS) in training sets due to selection bias where interesting sources are underrepresented, and the corresponding ML models show poor generalisation properties. We present an application of the StratLearn method to the estimation of photo-z, validating against simulations where we enforce the presence of CS to different degrees. StratLearn is a statistically principled approach that relies on splitting the source and target datasets into strata based on estimated propensity scores (i.e. the probability for an object to be in the source set given its observed covariates). After stratification, two conditional density estimators are fit separately to each stratum, then combined via a weighted average. We benchmark our results against the GPz algorithm, quantifying the performance of the two codes with a set of metrics. Our results show that the StratLearn-z metrics are only marginally affected by the presence of CS, while GPz shows a significant degradation of performance in the photo-z prediction for fainter objects. For the strongest CS scenario, StratLearn-z yields a reduced fraction of catastrophic errors, a factor of 2 improvement for the RMSE and one order of magnitude improvement on the bias. We also assess the quality of the conditional redshift estimates with the probability integral transform (PIT). The PIT distribution obtained from StratLearn-z features fat fewer outliers and is symmetric, i.e. the predictions appear to be centered around the true redshift value, despite showing a conservative estimation of the spread of the conditional redshift distributions. Our julia implementation of the method is available at \url{https://github.com/chiaramoretti/StratLearn-z}., Comment: Prepared for submission to the Open Journal of Astrophysics; comments welcome

The 21 cm transition from neutral Hydrogen promises to be the best observational probe of the Epoch of Reionisation (EoR). This has led to the construction of low-frequency radio interferometric arrays, such as the Hydrogen Epoch of Reionization Array (HERA), aimed at systematically mapping this emission for the first time. Precision calibration, however, is a requirement in 21 cm radio observations. Due to the spatial compactness of HERA, the array is prone to the effects of mutual coupling, which inevitably lead to non-smooth calibration errors that contaminate the data. When unsmooth gains are used in calibration, intrinsically spectrally-smooth foreground emission begins to contaminate the data in a way that can prohibit a clean detection of the cosmological EoR signal. In this paper, we show that the effects of mutual coupling on calibration quality can be reduced by applying custom time-domain filters to the data prior to calibration. We find that more robust calibration solutions are derived when filtering in this way, which reduces the observed foreground power leakage. Specifically, we find a reduction of foreground power leakage by 2 orders of magnitude at k=0.5.

The stochastic nature of star formation and photon propagation in high-redshift galaxies can result in sizable galaxy-to-galaxy scatter in their properties. Ignoring this scatter by assuming mean quantities can bias estimates of their emissivity and corresponding observables. We construct a flexible, semi-empirical model, sampling scatter around the following mean relations: (i) the conditional halo mass function (CHMF); (ii) the stellar-to-halo mass relation (SHMR); (iii) galaxy star formation main sequence (SFMS); (iv) fundamental metallicity relation (FMR); (v) conditional intrinsic luminosity; and (vi) photon escape fraction. In our fiducial model, ignoring scatter in these galaxy properties overestimates the duration of the EoR, delaying its completion by up to $\Delta z$ ~ 2. We quantify the relative importance of each of the above sources of scatter in determining the ionizing, soft-band X-ray and Lyman Werner (LW) emissivities as a function of scale and redshift. We find that scatter around the SFMS is important for all bands, especially at the highest redshifts where the emissivity is dominated by the faintest, most "bursty" galaxies. Ignoring this scatter would underestimate the mean emissivity and its standard deviation computed over 5 cMpc regions by factors of up to $\sim$2-10 at $5< z < 15$. Scatter around the X-ray luminosity to star formation rate relation is important for determining X-ray emissivity, accounting for roughly half of its mean and standard deviation. The importance of scatter in the ionizing escape fraction depends on its functional form, while scatter around the SHMR contributes at the level of ~10-20%. Although scatter does flatten the UV luminosity functions, shifting the bright end by 1-2 magnitudes, the level of scatter in our fiducial model is insufficient to fully explain recent estimates from JWST photometry (consistent with previous studies)., Comment: 17 pages, 13 figures, accepted to A&A

Interferometric experiments designed to detect the highly redshifted 21-cm signal from neutral hydrogen are producing increasingly stringent constraints on the 21-cm power spectrum, but some k-modes remain systematics-dominated. Mutual coupling is a major systematic that must be overcome in order to detect the 21-cm signal, and simulations that reproduce effects seen in the data can guide strategies for mitigating mutual coupling. In this paper, we analyse 12 nights of data from the Hydrogen Epoch of Reionization Array and compare the data against simulations that include a computationally efficient and physically motivated semi-analytic treatment of mutual coupling. We find that simulated coupling features qualitatively agree with coupling features in the data; however, coupling features in the data are brighter than the simulated features, indicating the presence of additional coupling mechanisms not captured by our model. We explore the use of fringe-rate filters as mutual coupling mitigation tools and use our simulations to investigate the effects of mutual coupling on a simulated cosmological 21-cm power spectrum in a "worst case" scenario where the foregrounds are particularly bright. We find that mutual coupling contaminates a large portion of the "EoR Window", and the contamination is several orders-of-magnitude larger than our simulated cosmic signal across a wide range of cosmological Fourier modes. While our fiducial fringe-rate filtering strategy reduces mutual coupling by roughly a factor of 100 in power, a non-negligible amount of coupling cannot be excised with fringe-rate filters, so more sophisticated mitigation strategies are required., Comment: 19 pages, 12 figures, submitted to MNRAS

The attenuation of Ly$\alpha$ photons by neutral hydrogen in the intergalactic medium (IGM) at $z\gtrsim5$ continues to be a powerful probe for studying the epoch of reionisation. Given a framework to estimate the intrinsic (true) Ly$\alpha$ emission of high-$z$ sources, one can infer the ionisation state of the IGM during reionisation. In this work, we use the enlarged XQR-30 sample of 42 high-resolution and high-SNR QSO spectra between $5.8\lesssim\,z\lesssim\,6.6$ obtained with VLT/X-Shooter to place constraints on the IGM neutral fraction. This is achieved using our existing Bayesian QSO reconstruction framework which accounts for uncertainties such as the: (i) posterior distribution of predicted intrinsic Ly$\alpha$ emission profiles (obtained via covariance matrix reconstruction of the Ly$\alpha$ and N V emission lines from unattenuated high-ionisation emission line profiles; C IV, Si IV + O IV] and C III]) and (ii) distribution of ionised regions within the IGM using synthetic damping wing profiles drawn from a $1.6^3$ Gpc$^3$ reionisation simulation. Following careful quality control, we used 23 of the 42 available QSOs to obtain constraints/limits on the IGM neutral fraction during the tail-end of reionisation. Our median and 68th percentile constraints on the IGM neutral fraction are: $0.20\substack{+0.14\\-0.12}$ and $0.29\substack{+0.14\\-0.13}$ at $z = 6.15$~and 6.35. Further, we also report 68th percentile upper-limits of $\bar{x}_{\mathrm{H\,{\scriptscriptstyle I}}} < 0.21$, 0.20, 0.21 and 0.18 at $z = 5.8, 5.95, 6.05$~and 6.55. These results imply reionisation is still ongoing at $5.8\lesssim\,z\lesssim\,6.55$, consistent with previous results from XQR-30 (dark fraction and Ly$\alpha$ forest) along with other observational probes considered in the literature., Comment: 21 pages, 9 figures and 2 tables. Accepted for publication in MNRAS

Reconstructing the intrinsic Ly$\alpha$ line flux from high-$z$ QSOs can place constraints on the neutral hydrogen content of the intergalactic medium during reionisation. There are now $\gtrsim10$ different Ly$\alpha$ reconstruction pipelines using different methodologies to predict the Ly$\alpha$ line flux from correlations with the spectral information redward of Ly$\alpha$. However, there have been few attempts to directly compare the performance of these pipelines. Therefore, we devised a blind QSO challenge to compare these reconstruction pipelines on a uniform set of objects. Each author was provided de-identified, observed rest-frame QSO spectra with spectral information only redward of 1260\AA\ rest-frame to ensure unbiased reconstruction. We constructed two samples of 30 QSOs, from X-Shooter and SDSS both spanning $3.5

The detection of the 21-cm signal at $z\gtrsim6$ will reveal insights into the properties of the first galaxies responsible for driving reionisation. To extract this information, we perform parameter inference which requires embedding 3D simulations of the 21-cm signal within a Bayesian inference pipeline. Presently, when performing inference we must choose which sources of uncertainty to sample and which to hold fixed. Since the astrophysics of galaxies are much more uncertain than those of the underlying halo-mass function (HMF), we usually parameterise and model the former while fixing the latter. However, in doing so we may bias our inference of the properties of these first galaxies. In this work, we explore the consequences of assuming an incorrect choice of HMF and quantify the relative biases in our inferred astrophysical model parameters when considering the wrong HMF. We then relax this assumption by constructing a generalised five parameter model for the HMF and simultaneously recover these parameters along with our underlying astrophysical model. For this analysis, we use 21cmFAST and perform Simulation-Based Inference by applying marginal neural ratio estimation to learn the likelihood-to-evidence ratio using Swyft. Using a mock 1000 hour observation of the 21-cm power spectrum from the forthcoming Square Kilometre Array, conservatively assuming foreground wedge avoidance, we find assuming the incorrect HMF can bias the recovered astrophysical parameters by up to $\sim3-4\sigma$ even when including independent information from observed luminosity functions. When considering our generalised HMF model, we recover constraints on our astrophysical parameters with a factor of $\sim2-4$ larger marginalised uncertainties. Importantly, these constraints are unbiased, agnostic to the underlying HMF and therefore more conservative., Comment: 27 pages, 14 figures, 3 tables and 3 appendices. Submitted to MNRAS, comments welcome

Enlightening our understanding of the first galaxies responsible for driving reionisation requires detecting the 21-cm signal from neutral hydrogen. Interpreting the wealth of information embedded in this signal requires Bayesian inference. Parameter inference from the 21-cm signal is primarily restricted to the spherically averaged power spectrum (1D PS) owing to its relatively straightforward derivation of an analytic likelihood function enabling traditional Monte-Carlo Markov-Chain (MCMC) approaches. However, in recent years, simulation-based inference (SBI) has become feasible which removes the necessity of having an analytic likelihood, enabling more complex summary statistics of the 21-cm signal to be used for Bayesian inference. In this work, we use SBI, specifically marginal neural ratio estimation to learn the likelihood-to-evidence ratio with Swyft, to explore parameter inference using the cylindrically averaged 2D PS. Since the 21-cm signal is anisotropic, the 2D PS should yield more constraining information compared to the 1D PS which isotropically averages the signal. For this, we consider a mock 1000 hr observation of the 21-cm signal using the SKA and compare the performance of the 2D PS relative to the 1D PS. Additionally, we explore two separate foreground mitigation strategies, perfect foreground removal and wedge avoidance. We find the 2D PS outperforms the 1D PS by improving the marginalised uncertainties on individual astrophysical parameters by up to $\sim30-40$ per cent irrespective of the foreground mitigation strategy. Primarily, these improvements stem from how the 2D PS distinguishes between the transverse, $k_{\perp}$, and redshift dependent, $k_{\parallel}$ information which enables greater sensitivity to the complex reionisation morphology., Comment: 16 pages, 6 figures and 1 table. Submitted to MNRAS, comments welcome

Radio interferometers targeting the 21cm brightness temperature fluctuations at high redshift are subject to systematic effects that operate over a range of different timescales. These can be isolated by designing appropriate Fourier filters that operate in fringe-rate (FR) space, the Fourier pair of local sidereal time (LST). Applications of FR filtering include separating effects that are correlated with the rotating sky vs. those relative to the ground, down-weighting emission in the primary beam sidelobes, and suppressing noise. FR filtering causes the noise contributions to the visibility data to become correlated in time however, making interpretation of subsequent averaging and error estimation steps more subtle. In this paper, we describe fringe rate filters that are implemented using discrete prolate spheroidal sequences, and designed for two different purposes -- beam sidelobe/horizon suppression (the `mainlobe' filter), and ground-locked systematics removal (the `notch' filter). We apply these to simulated data, and study how their properties affect visibilities and power spectra generated from the simulations. Included is an introduction to fringe-rate filtering and a demonstration of fringe-rate filters applied to simple situations to aid understanding., Comment: 21 pages, 18 figures, submitted to Monthly Notices of the Royal Astronomical Society

The cosmic 21-cm signal will bring data-driven advances to studies of the Cosmic Dawn (CD) and Epoch of Reionization (EoR). Radio telescopes such as the SKA will eventually map the HI fluctuations over the first billion years - the majority of our observable Universe. With such large data volumes, it becomes increasingly important to develop "optimal" summary statistics, allowing us to learn as much as possible about the CD and EoR. In this work we compare the constraining power of several 21-cm summary statistics, using the determinant of the Fisher information matrix, $\det F$. Since we do not have an established "fiducial" model for the astrophysics of the first galaxies, we compute the distribution of $\det F$ across the prior volume. Using a large database of cosmic 21-cm lightcones that include realizations of telescope noise, we compare the following summaries: (i) the spherically-averaged power spectrum (1DPS), (ii) the cylindrically-averaged power spectrum (2DPS), (iii) the 2D Wavelet scattering transform (WST), (iv) a recurrent neural network (RNN), (v) an information-maximizing neural network (IMNN), and (vi) the combination of 2DPS and IMNN. Our best performing individual summary is the 2DPS, having relatively high Fisher information throughout parameter space. Although capable of achieving the highest Fisher information for some parameter choices, the IMNN does not generalize well, resulting in a broad distribution. Our best results are achieved with the concatenation of the 2DPS and IMNN. The combination of only these two complimentary summaries reduces the recovered parameter variances on average by factors of $\sim$6.5 - 9.5, compared with using each summary independently. Finally, we point out that that the common assumption of a constant covariance matrix when doing Fisher forecasts using 21-cm summaries can significantly underestimate parameter constraints., Comment: 11 pages, 9 figures, updated to match the version published in A&A

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 Kilometer Array (SKA) 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.

Detection of the faint 21 cm line emission from the Cosmic Dawn and Epoch of Reionisation will require not only exquisite control over instrumental calibration and systematics to achieve the necessary dynamic range of observations but also validation of analysis techniques to demonstrate their statistical properties and signal loss characteristics. A key ingredient in achieving this is the ability to perform high-fidelity simulations of the kinds of data that are produced by the large, many-element, radio interferometric arrays that have been purpose-built for these studies. The large scale of these arrays presents a computational challenge, as one must simulate a detailed sky and instrumental model across many hundreds of frequency channels, thousands of time samples, and tens of thousands of baselines for arrays with hundreds of antennas. In this paper, we present a fast matrix-based method for simulating radio interferometric measurements (visibilities) at the necessary scale. We achieve this through judicious use of primary beam interpolation, fast approximations for coordinate transforms, and a vectorised outer product to expand per-antenna quantities to per-baseline visibilities, coupled with standard parallelisation techniques. We validate the results of this method, implemented in the publicly-available matvis code, against a high-precision reference simulator, and explore its computational scaling on a variety of problems., Comment: 24 pages, 10 figures, accepted to RAS Techniques and Instruments, matvis is publicly available at https://github.com/HERA-Team/matvis

Observations with radio arrays that target the 21-cm signal originating from the early Universe suffer from a variety of systematic effects. An important class of these are reflections and spurious couplings between antennas. We apply a Hamiltonian Monte Carlo sampler to the modelling and mitigation of these systematics in simulated Hydrogen Epoch of Reionisation Array (HERA) data. This method allows us to form statistical uncertainty estimates for both our models and the recovered visibilities, which is an important ingredient in establishing robust upper limits on the Epoch of Reionisation (EoR) power spectrum. In cases where the noise is large compared to the EoR signal, this approach can constrain the systematics well enough to mitigate them down to the noise level for both systematics studied. Where the noise is smaller than the EoR, our modelling can mitigate the majority of the reflections with there being only a minor level of residual systematics, while cross-coupling sees essentially complete mitigation. Our approach performs similarly to existing filtering/fitting techniques used in the HERA pipeline, but with the added benefit of rigorously propagating uncertainties. In all cases it does not significantly attenuate the underlying signal., Comment: 19 pages, 14 figures, submitted to MNRAS

The key to detecting neutral hydrogen during the epoch of reionization (EoR) is to separate the cosmological signal from the dominating foreground radiation. We developed direct optimal mapping (DOM) to map interferometric visibilities; it contains only linear operations, with full knowledge of point spread functions from visibilities to images. Here, we demonstrate a fast Fourier transform-based image power spectrum and its window functions computed from the DOM images. We use noiseless simulation, based on the Hydrogen Epoch of Reionization Array Phase I configuration, to study the image power spectrum properties. The window functions show $<10^{-11}$ of the integrated power leaks from the foreground-dominated region into the EoR window; the 2D and 1D power spectra also verify the separation between the foregrounds and the EoR., Comment: Published in ApJ

Recent years have witnessed rapid progress in observations of the Epoch of Reionization (EoR). These have enabled high-dimensional inference of galaxy and intergalactic medium (IGM) properties during the first billion years of our Universe. However, even using efficient, semi-numerical simulations, traditional inference approaches that compute 3D lightcones on-the-fly can take $10^5$ core hours. Here we present 21cmEMU: an emulator of several summary observables from the popular 21cmFAST simulation code. 21cmEMU takes as input nine parameters characterizing EoR galaxies, and outputs the following summary statistics: (i) the IGM mean neutral fraction; (ii) the 21-cm power spectrum; (iii) the mean 21-cm spin temperature; (iv) the sky-averaged (global) 21-cm signal; (v) the ultraviolet (UV) luminosity functions (LFs); and (vi) the Thomson scattering optical depth to the cosmic microwave background (CMB). All observables are predicted with sub-percent median accuracy, with a reduction of the computational cost by a factor of over 10$^4$. After validating inference results, we showcase a few applications, including: (i) quantifying the relative constraining power of different observational datasets; (ii) seeing how recent claims of a late EoR impact previous inferences; and (iii) forecasting upcoming constraints from the sixth observing season of the Hydrogen Epoch of Reionization Array (HERA) telescope. 21cmEMU is publicly-available, and is included as an alternative simulator in the public 21CMMC sampler., Comment: 21 pages, 13 figures, submitted to MNRAS

Recently, the Lyman-$\alpha$ (Ly$\alpha$) forest flux auto-correlation function has been shown to be sensitive to the mean free path of hydrogen-ionizing photons, $\lambda_{\text{mfp}}$, for simulations at $z \geq 5.4$. Measuring $\lambda_{\text{mfp}}$ at these redshifts will give vital information on the ending of reionization. Here we present the first observational measurements of the Ly$\alpha$ forest flux auto-correlation functions in ten redshift bins from $5.1 \leq z \leq 6.0$. We use a sample of 35 quasar sightlines at $z > 5.7$ from the extended XQR-30 data set, this data has signal-to-noise ratios of $> 20$ per spectral pixel. We carefully account for systematic errors in continuum reconstruction, instrumentation, and contamination by damped Ly$\alpha$ systems. With these measurements, we introduce software tools to generate auto-correlation function measurements from any simulation. For an initial comparison, we show our auto-correlation measurements with simulation models for recently measured $\lambda_{\text{mfp}}$ values and find good agreements. Further work in modeling and understanding the covariance matrices of the data is necessary to get robust measurements of $\lambda_{\text{mfp}}$ from this data., Comment: 17 pages, 13 figures, submitted to MNRAS

The redshifted 21cm signal from the Cosmic Dawn is expected to provide unprecedented insights into early Universe astrophysics and cosmology. Here we explore how dark matter can heat the intergalactic medium before the first galaxies, leaving a distinctive imprint in the 21cm power spectrum. We provide the first dedicated Fisher matrix forecasts on the sensitivity of the Hydrogen Epoch of Reionization Array (HERA) telescope to dark matter decays. We show that with 1000 hours of observation, HERA has the potential to improve current cosmological constraints on the dark matter decay lifetime by up to three orders of magnitude. Even in extreme scenarios with strong X-ray emission from early-forming, metal-free galaxies, the bounds on the decay lifetime would be improved by up to two orders of magnitude. Overall, HERA shall improve on existing limits for dark matter masses below $2$ GeV$/c^2$ for decays into $e^+e^-$ and below few MeV$/c^2$ for decays into photons., Comment: 34 pages, 12 figures. v2: published version with additional references and improved figures

The mean free path of ionizing photons, $\lambda_{\rm mfp}$, is a critical parameter for modeling the intergalactic medium (IGM) both during and after reionization. We present direct measurements of $\lambda_{\rm mfp}$ from QSO spectra over the redshift range $5

The patchy kinetic Sunyaev-Zel'dovich (kSZ) signal is an integral probe of the timing and morphology of the epoch of reionization (EoR). Recent observations have claimed a low signal-to-noise (S/N) measurement, with a dramatic increase in S/N expected in the near future. In this work, we quantify what we can learn about the EoR from the kSZ signal. We perform Bayesian inference by sampling galaxy properties and using forward-models of the kSZ as well as other EoR and galaxy observations in the likelihood. Including the recent kSZ measurement obtained by the South Pole Telescope ($\mathcal{D}_{3000}^{\rm{pkSZ}} = 1.1_{-0.7}^{+1.1} \mu$K$^2$) shifts the posterior distribution in favor of faster and later reionization models, resulting in lower values of the optical depth to the CMB: $\tau_e = 0.052_{-0.008}^{+0.009}$ with a 68$\%$ confidence interval (C.I.). The combined EoR and UV luminosity function observations also imply a typical ionizing escape fraction of $0.04_{-0.03}^{+0.05}$ (95$\%$ C.I.), without a strong dependence on halo mass. We show how the patchy kSZ power from our posterior depends on the commonly-used parameters of reionization. For a given midpoint and duration, the EoR morphology only has a few percent impact on the patchy kSZ power in our posterior. However, a physical model is needed to obtain tight constraints from the current low S/N patchy kSZ measurement, as it allows us to take advantage of complimentary high-$z$ observations. Future high S/N detections of the patchy kSZ should decrease the current uncertainties on the timing of the EoR by factors of $\sim$2 - 3., Comment: 14 pages, 6 figures, accepted to MNRAS (MNRAS, 526, 3170)

We explore how the characteristics of the cross-correlation functions between the 21cm emission from the spin-flip transition of neutral hydrogen (HI) and early Lyman-$\alpha$ (Ly$\alpha$) radiation emitting galaxies (Ly$\alpha$ emitters, LAEs) depend on the reionisation history and topology and the simulated volume. For this purpose, we develop an analytic expression for the 21cm-LAE cross-correlation function and compare it to results derived from different Astraeus and 21cmFAST reionisation simulations covering a physically plausible range of scenarios where either low-mass ($<10^{9.5}M_\odot$) or massive ($>10^{9.5}M_\odot$) galaxies drive reionisation. Our key findings are: (i) the negative small-scale ($<2$ cMpc) cross-correlation amplitude scales with the intergalactic medium's (IGM) average HI fraction ($\langle\chi_\mathrm{HI}\rangle$) and spin-temperature weighted overdensity in neutral regions ($\langle1+\delta\rangle_\mathrm{HI}$); (ii) the inversion point of the cross-correlation function traces the peak of the size distribution of ionised regions around LAEs; (iii) the cross-correlation amplitude at small scales is sensitive to the reionisation topology, with its anti-correlation or correlation decreasing the stronger the ionising emissivity of the underlying galaxy population is correlated to the cosmic web gas distribution (i.e. the more low-mass galaxies drive reionisation); (iv) the required simulation volume to not underpredict the 21cm-LAE anti-correlation amplitude when the cross-correlation is derived via the cross-power spectrum rises as the size of ionised regions and their variance increases. Our analytic expression can serve two purposes: to test whether simulation volumes are sufficiently large, and to act as a fitting function when cross-correlating future 21cm signal Square Kilometre Array and LAE galaxy observations., Comment: 13 pages, 5 figures; accepted for publication in MNRAS

The final phase of the reionization process can be probed by rest-frame UV absorption spectra of quasars at z>6, shedding light on the properties of the diffuse intergalactic medium within the first Gyr of the Universe. The ESO Large Programme "XQR-30: the ultimate XSHOOTER legacy survey of quasars at z~5.8-6.6" dedicated ~250 hours of observations at the VLT to create a homogeneous and high-quality sample of spectra of 30 luminous quasars at z~6, covering the rest wavelength range from the Lyman limit to beyond the MgII emission. Twelve quasar spectra of similar quality from the XSHOOTER archive were added to form the enlarged XQR-30 sample, corresponding to a total of ~350 hours of on-source exposure time. The median effective resolving power of the 42 spectra is R~11400 and 9800 in the VIS and NIR arm, respectively. The signal-to-noise ratio per 10 km/s pixel ranges from ~11 to 114 at $\lambda \simeq 1285$ \AA rest frame, with a median value of ~29. We describe the observations, data reduction and analysis of the spectra, together with some first results based on the E-XQR-30 sample. New photometry in the H and K bands are provided for the XQR-30 quasars, together with composite spectra whose characteristics reflect the large absolute magnitudes of the sample. The composite and the reduced spectra are released to the community through a public repository, and will enable a range of studies addressing outstanding questions regarding the first Gyr of the Universe., Comment: 21 pages, 10 figures. Final version accepted by MNRAS

We investigate the impact of field-to-field variation, deriving from cosmic variance, in measured Lyman-$\alpha$ emitter (LAE) luminosity functions (LFs) and this variation's impact on inferences of the neutral fraction of the intergalactic medium (IGM) during reionization. We post-process a z=7 IGM simulation to populate the dark matter halos with LAEs. These LAEs have realistic UV magnitudes, Ly$\alpha$ fluxes, and Ly$\alpha$ line profiles. We calculate the attenuation of Ly$\alpha$ emission in universes with varying IGM neutral fraction, $\bar{\rm{x}}_{\rm{HI}}$. In a $\bar{\rm{x}}_{\rm{HI}}=0.3$ simulation, we perform 100 realizations of a mock 2 square degree survey with a redshift window $\Delta z = 0.5$ and flux limit $\rm{f}_{Ly\alpha}>1\times10^{-17}\:\rm{ergs}\:\: \rm{s}^{-1} \: \rm{cm}^{-2}$; such a survey is typical in depth and volume of the largest LAE surveys conducted today. For each realization, we compute the LAE LF and use it to recover the input $\bar{\rm{x}}_{\rm{HI}}$. Comparing the inferred values of $\bar{\rm{x}}_{\rm{HI}}$ across the ensemble of the surveys, we find that cosmic variance, deriving from large-scale structure and variation in the neutral gas along the sightline, imposes a floor in the uncertainty of $\Delta \bar{\rm{x}}_{\rm{HI}} \sim 0.2$ when $\bar{\rm{x}}_{\rm{HI}}$ $=0.3$. We explore mitigation strategies to decrease this uncertainty, such as increasing the volume, decreasing the flux limit, or probing the volume with many independent fields. Increasing the area and/or depth of the survey does not mitigate the uncertainty, but composing a survey with many independent fields is effective. This finding highlights the best strategy for LAE surveys aiming at constraining $\bar{\rm{x}}_{\rm{HI}}$ of the universe during reionization., Comment: 17 pages, 13 figures

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 UV and X-ray galaxy parameters together with the initial conditions; (ii) realizations of the telescope noise corresponding to a 1000 h integration with SKA1-Low; (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 wavemodes and redshift bins (higher order correlations are small). However, common approaches of estimating the forward-modeled mean and (co)variance from a random realization or at a single point in parameter space result in biased and over-constrained 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., Comment: 16 pages, 12 figures, updated to match the version accepted for publication in MNRAS

Constraining when and how reionisation began is pivotal for understanding when the first galaxies formed. Lyman-alpha (Ly$\alpha$) emission from galaxies is currently our most promising probe of these early stages. At z>7 the majority of galaxies detected with Ly$\alpha$ are in candidate overdensities. Here we quantify the probability of these galaxies residing in large ionised bubbles. We create (1.6 Gpc)$^3$ reionising intergalactic medium (IGM) simulations, providing sufficient volume to robustly measure bubble size distributions around UV-bright galaxies and rare overdensities. We find $M_{\rm UV} \lesssim -16$ galaxies and overdensities are $\gtrsim$10-1000x more likely to trace ionised bubbles compared to randomly selected positions. The brightest galaxies and strongest overdensities have bubble size distributions with highest characteristic size and least scatter. We compare two models: gradual reionisation driven by numerous UV-faint galaxies versus more rapid reionisation by rarer brighter galaxies, producing larger bubbles at fixed neutral fraction. We demonstrate that recently observed z~7 overdensities are highly likely to trace large ionised bubbles, corroborated by their high Ly$\alpha$ detection rates. However, the z~8.7 association of Ly$\alpha$ emitters in EGS and GN-z11, with Ly$\alpha$ at z=10.6, are unlikely to trace large bubbles in our fiducial model -- 11% and 7% probability of >1 proper Mpc bubbles, respectively. Ly$\alpha$ detections at such high redshifts could be explained by: a less neutral IGM than previously expected; larger ionised regions at fixed neutral fraction; or if intrinsic Ly$\alpha$ flux is unusually strong in these galaxies. We discuss how to test these scenarios with JWST and the prospects for using upcoming wide-area surveys to distinguish between reionisation models., Comment: 15 pages (+ 3 pages in Appendix), 13 figures, submitted to MNRAS

The upcoming Square Kilometre Array Observatory (SKAO) will produce images of neutral hydrogen distribution during the epoch of reionization by observing the corresponding 21-cm signal. However, the 21-cm signal will be subject to instrumental limitations such as noise and galactic foreground contamination which pose a challenge for accurate detection. In this study, we present the SegU-Net v2 framework, an enhanced version of our convolutional neural network, built to identify neutral and ionized regions in the 21-cm signal contaminated with foreground emission. We trained our neural network on 21-cm image data processed by a foreground removal method based on Principal Component Analysis achieving an average classification accuracy of 71 per cent between redshift $z=7$ to $11$. We tested SegU-Net v2 against various foreground removal methods, including Gaussian Process Regression, Polynomial Fitting, and Foreground-Wedge Removal. Results show comparable performance, highlighting SegU-Net v2's independence on these pre-processing methods. Statistical analysis shows that a perfect classification score with $AUC=95\%$ is possible for $8(10\, {\rm cMpc})^3$ at $z>9$, for follow-up studies with infrared/optical telescopes to detect these sources., Comment: 19 pages, 10 figures, 3 tables, 2 appendixes

Radio interferometers aiming to measure the power spectrum of the redshifted 21 cm line during the Epoch of Reionisation (EoR) need to achieve an unprecedented dynamic range to separate the weak signal from overwhelming foreground emissions. Calibration inaccuracies can compromise the sensitivity of these measurements to the effect that a detection of the EoR is precluded. An alternative to standard analysis techniques makes use of the closure phase, which allows one to bypass antenna-based direction-independent calibration. Similarly to standard approaches, we use a delay spectrum technique to search for the EoR signal. Using 94 nights of data observed with Phase I of the Hydrogen Epoch of Reionization Array (HERA), we place approximate constraints on the 21 cm power spectrum at $z=7.7$. We find at 95% confidence that the 21 cm EoR brightness temperature is $\le$(372)$^2$ "pseudo" mK$^2$ at 1.14 "pseudo" $h$ Mpc$^{-1}$, where the "pseudo" emphasises that these limits are to be interpreted as approximations to the actual distance scales and brightness temperatures. Using a fiducial EoR model, we demonstrate the feasibility of detecting the EoR with the full array. Compared to standard methods, the closure phase processing is relatively simple, thereby providing an important independent check on results derived using visibility intensities, or related., Comment: 16 pages, 14 figures, accepted for publication by MNRAS

The 21-cm signal from neutral hydrogen in the early universe will provide unprecedented information about the first stars and galaxies. Extracting this information, however, requires accounting for many unknown astrophysical processes. Semi-numerical simulations are key for exploring the vast parameter space of said processes. These simulations use approximate techniques such as excursion-set and perturbation theory to model the 3D evolution of the intergalactic medium, at a fraction of the computational cost of hydrodynamic and/or radiative transfer simulations. However, exploring the enormous parameter space of the first galaxies can still be computationally expensive. Here we introduce 21cmfish, a Fisher-matrix wrapper for the semi-numerical simulation 21cmFAST. 21cmfish facilitates efficient parameter forecasts, scaling to significantly higher dimensionalities than MCMC approaches, assuming a multi-variate Gaussian posterior. Our method produces comparable parameter uncertainty forecasts to previous MCMC analyses but requires ~10$^4$x fewer simulations. This enables a rapid way to prototype analyses adding new physics and/or additional parameters. We carry out a forecast for HERA using the largest astrophysical parameter space to-date, with 10 free parameters, spanning both population II and III star formation. We find X-ray parameters for the first galaxies could be measured to sub-percent precision, and, though they are highly degenerate, the stellar-to-halo mass relation and ionizing photon escape fraction for population II and III galaxies can be constrained to ~10% precision (logarithmic quantities). Using a principal component analysis we find HERA is most sensitive to the product of the ionizing escape fraction and the stellar-to-halo mass fraction for population II galaxies., Comment: 18 pages, accepted for publication in MNRAS. Fisher-matrix wrapper for 21cmFAST available here: https://github.com/charlottenosam/21cmfish

Radio Frequency Interference (RFI) is one of the systematic challenges preventing 21cm interferometric instruments from detecting the Epoch of Reionization. To mitigate the effects of RFI on data analysis pipelines, numerous inpaint techniques have been developed to restore RFI corrupted data. 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 capable of inpainting RFI corrupted data in interferometric instruments. We train our network on simulated data and show that our network is capable at inpainting real data without requiring to be retrained. We find that techniques that incorporate high wavenumbers in delay space in their modeling are best suited for inpainting over narrowband RFI. We also show that with our fiducial parameters Discrete Prolate Spheroidal Sequences (DPSS) and CLEAN provide the best performance for intermittent ``narrowband'' 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 find these results to be consistent in both simulated and real visibilities. 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 in the future, as the noise level of the data comes down, CLEAN and DPSS are most capable of reproducing the fine frequency structure in the visibilities of HERA data., Comment: 21 pages, 13 figures

We report the most sensitive upper limits to date on the 21 cm epoch of reionization power spectrum using 94 nights of observing with Phase I of the Hydrogen Epoch of Reionization Array (HERA). Using similar analysis techniques as in previously reported limits (HERA Collaboration 2022a), we find at 95% confidence that $\Delta^2(k = 0.34$ $h$ Mpc$^{-1}$) $\leq 457$ mK$^2$ at $z = 7.9$ and that $\Delta^2 (k = 0.36$ $h$ Mpc$^{-1}) \leq 3,496$ mK$^2$ at $z = 10.4$, an improvement by a factor of 2.1 and 2.6 respectively. These limits are mostly consistent with thermal noise over a wide range of $k$ after our data quality cuts, despite performing a relatively conservative analysis designed to minimize signal loss. Our results are validated with both statistical tests on the data and end-to-end pipeline simulations. We also report updated constraints on the astrophysics of reionization and the cosmic dawn. Using multiple independent modeling and inference techniques previously employed by HERA Collaboration (2022b), we find that the intergalactic medium must have been heated above the adiabatic cooling limit at least as early as $z = 10.4$, ruling out a broad set of so-called "cold reionization" scenarios. If this heating is due to high-mass X-ray binaries during the cosmic dawn, as is generally believed, our result's 99% credible interval excludes the local relationship between soft X-ray luminosity and star formation and thus requires heating driven by evolved low-metallicity stars., Comment: 57 pages, 37 figures. Updated to match the accepted ApJ version. Corresponding author: Joshua S. Dillon

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., Comment: 18 pages, 19 figures, accepted for publication in MNRAS

While there is now a consensus that X-ray binaries (XRBs) are the dominant X-ray sources in the early Universe and play a significant role during the epoch of heating of the intergalactic medium (IGM), recent studies report contradicting results regarding their contribution in the nebular emission of local Universe galaxies. Ultraluminous X-ray sources (ULXs), which dominate the X-ray budget of normal galaxies, may be important interstellar-medium (ISM) ionizing sources. However, their output in the extreme UV (EUV) and soft--X-ray part of the spectrum remains observationally unconstrained. In this paper, we predict the ionizing and heating power from ULX populations under the geometrical beaming scenario, and three models describing the emission from super-critical accretion disks. We find that our theoretical spectra for ULX populations cannot (can) explain the HeII (NeV) emission observed in some galaxies, with their contribution being less (more) important than the underlying stellar population. Stochastic fluctuations in the number of ULXs may allow for equal contributions in the HeII emission, in a fraction of galaxies. We provide average spectra of ULX populations as an input to local, and early-Universe studies. We find that the soft--X-ray emission arising from super-critical accretion is significant for the heating of the IGM, and consistent with recent constraints from the 21-cm cosmic signal. Based on the dependence on the adopted compact-object (CO) mass and accretion model, we encourage efforts in modeling ULX spectra via simulations, and their combination with detailed binary population synthesis models., Comment: 8 pages. 6 figures, 1 table. This article has been accepted for publication in the Astronomy & Astrophysics journal. The full Table 1 will be made available via CDS

Luminous quasars powered by accretion onto billion solar mass black holes already exist at the epoch of Reionisation, when the Universe was 0.5-1 Gyr old. These objects likely reside in over-dense regions of the Universe, and will grow to form today's giant galaxies. How their huge black holes formed in such short times is debated, particularly as they lie above the local black hole mass-galaxy dynamical mass correlation, thus following the black hole-dominance growth path. It is unknown what slowed down the black hole growth, leading towards the symbiotic growth observed in the local Universe, and when this process started, although black hole feedback is a likely driver. This deadlock is due to the lack of large, homogeneous samples of high-redshift quasars with high-quality, broad-band spectroscopic information. Here we report results from a VLT/X-shooter survey of 30 quasars at redshift 5.8$\le$z$\le$6.6 (XQR-30). About 50% of their spectra reveal broad blue-shifted absorption line (BAL) throughs, tracing powerful ionised winds. The BAL fraction in z$\gtrsim$6 quasars is 2-3 times higher than in quasars at z~2-4.5. XQR-30 BAL quasars exhibit extreme outflow velocities, up to 17% of the light speed, rarely observed at lower redshift. These outflows inject large amounts of energy into the galaxy interstellar medium, which can contrast nuclear gas accretion, slowing down the black-hole growth. The star-formation rate in high-z quasar hosts is generally $>$100 M$_\odot$/yr, so these galaxies are growing at a fast rate. The BAL phase may then mark the beginning of significant feedback, acting first on black hole growth and possibly later on galaxy growth. The red optical colors of BAL quasars at z$\gtrsim$6 indeed suggest that these systems are dusty and may be caught during an initial quenching phase of obscured accretion., Comment: This preprint has not undergone peer review or any post-submission improvements or corrections. The Version of Record of this article is published in Nature, and is available online at https://doi.org/10.1038/s41586-022-04608-1

Motivated by the desire for wide-field images with well-defined statistical properties for 21cm cosmology, we implement an optimal mapping pipeline that computes a maximum likelihood estimator for the sky using the interferometric measurement equation. We demonstrate this direct optimal mapping with data from the Hydrogen Epoch of Reionization (HERA) Phase I observations. After validating the pipeline with simulated data, we develop a maximum likelihood figure-of-merit for comparing four sky models at 166MHz with a bandwidth of 100kHz. The HERA data agree with the GLEAM catalogs to <10%. After subtracting the GLEAM point sources, the HERA data discriminate between the different continuum sky models, providing most support for the model of Byrne et al. 2021. We report the computation cost for mapping the HERA Phase I data and project the computation for the HERA 320-antenna data; both are feasible with a modern server. The algorithm is broadly applicable to other interferometers and is valid for wide-field and non-coplanar arrays., Comment: 16 pages, 10 figures, 2 tables, published on ApJ

High-energy emission associated with star formation has been proposed as a significant source of interstellar medium (ISM) ionization in low-metallicity starbursts and an important contributor to the heating of the intergalactic medium (IGM) in the high-redshift ($z > 8$) Universe. Using Chandra observations of a sample of 30 galaxies at $D \approx$~200--450 Mpc that have high specific star-formation rates of 3--9 Gyr$^{-1}$ and metallicities near $Z \approx 0.3 Z_\odot$, we provide new measurements of the average 0.5--8 keV spectral shape and normalization per unit star-formation rate (SFR). We model the sample-combined X-ray spectrum as a combination of hot gas and high-mass X-ray binary (HMXB) populations and constrain their relative contributions. We derive scaling relations of $\log L_{\rm 0.5-8 keV}^{\rm HMXB}$/SFR $= 40.19 \pm 0.06$ and $\log L_{\rm 0.5-2 keV}^{\rm gas}$/SFR $= 39.58^{+0.17}_{-0.28}$; significantly elevated compared to local relations. The HMXB scaling is also somewhat higher than $L_{\rm 0.5-8 keV}^{\rm HMXB}$-SFR-$Z$ relations presented in the literature, potentially due to our galaxies having relatively low HMXB obscuration and young and X-ray luminous stellar populations. The elevation of the hot gas scaling relation is at the level expected for diminished attenuation due to a reduction of metals; however, we cannot conclude that an $L_{\rm 0.5-2 keV}^{\rm gas}$-SFR-$Z$ relation is driven solely by changes in ISM metal content. Finally, we present SFR-scaled spectral models (both emergent and intrinsic) that span the X-ray--to--IR band, providing new benchmarks for studies of the impact of ISM ionization and IGM heating in the early Universe., Comment: Accepted for publication in ApJ (25 pages, 9 figures, and 4 tables)

X-rays from High-Mass X-ray Binaries (HMXBs) are likely the main source of heating of the intergalactic medium (IGM) during Cosmic Dawn (CD), before the completion of reionization. This Epoch of Heating (EoH; $z\sim 10-15$) should soon be detected via the redshifted 21-cm line from neutral hydrogen, allowing us to indirectly study the properties of HMXBs in the unseen, first galaxies. Low-redshift observations, as well as theoretical models, imply that the integrated X-ray luminosity to star formation rate of HMXBs ($L_{\rm X}/{\rm SFR}$) should increase in metal-poor environments, typical of early galaxies. Here we study the impact of the metallicity ($Z$) dependence of $L_{\rm X}/{\rm SFR}$ during the EoH. For our fiducial models, galaxies with star formation rates of order $10^{-3} - 10^{-1}$ $M_\odot$ yr$^{-1}$ and metallicities of order $10^{-3} - 10^{-2}$ $Z_\odot$ are the dominant contributors to the X-ray background (XRB) during this period. Different $L_{\rm X}/{\rm SFR}$-$Z$ relations result in factors of $\sim$ 3 differences in these ranges, as well as in the mean IGM temperature and the large-scale 21-cm power, at a given redshift. We compute mock 21-cm observations adopting as a baseline a 1000h integration with the upcoming Square Kilometer Array (SKA), for two different $L_{\rm X}/{\rm SFR}$-$Z$ relations. We perform inference on these mock observations using the common simplification of a constant $L_{\rm X}/{\rm SFR}$, finding that constant $L_{\rm X}/{\rm SFR}$ models can recover the IGM evolution of the more complicated $L_{\rm X}/{\rm SFR}$-$Z$ simulations only during the EoH. At $z<10$, where the typical galaxies are more polluted, constant $L_{\rm X}/{\rm SFR}$ models over-predict the XRB and its relative contribution to the early stages of the reionization.

A limiting systematic effect in 21-cm interferometric experiments is the chromaticity due to the coupling between the sky and the instrument. This coupling is sourced by the instrument primary beam; therefore it is important to know the beam to extremely high precision. Here we demonstrate how known beam uncertainties can be characterized using databases of beam models. In this introductory work, we focus on beam errors arising from physically offset and/or broken antennas within a station. We use the public code OSKAR to generate an "ideal" SKA beam formed from 256 antennas regularly-spaced in a 35-m circle, as well as a large database of "perturbed" beams sampling distributions of broken/offset antennas. We decompose the beam errors ("ideal" minus "perturbed") using Principal Component Analysis (PCA) and Kernel PCA (KPCA). Using 20 components, we find that PCA/KPCA can reduce the residual of the beam in our datasets by 60-90% compared with the assumption of an ideal beam. Using a simulated observation of the cosmic signal plus foregrounds, we find that assuming the ideal beam can result in 1% error in the EoR window and 10% in the wedge of the 2D power spectrum. When PCA/KPCA is used to characterize the beam uncertainties, the error in the power spectrum shrinks to below 0.01% in the EoR window and <1% in the wedge. Our framework can be used to characterize and then marginalize over uncertainties in the beam for robust next-generation 21-cm parameter estimation., Comment: 12 pages, 9 main figures

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 3-D 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 \textsc{21cmfast} 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., Comment: 23 pages, 14 figures, accepted for publication in MNRAS, code publicly available at https://github.com/mirochaj/micro21cm

The excursion set reionization framework is widely used, due to its speed and accuracy in reproducing the 3D topology of reionization. However, it is known that it does not conserve photon number. Here, we introduce an efficient, on-the-fly recipe to approximately account for photon conservation. Using a flexible galaxy model shown to reproduce current high-$z$ observables, we quantify the bias in the inferred reionization history and galaxy properties resulting from the non-conservation of ionizing photons. Using a mock 21-cm observation, we perform inference with and without correcting for ionizing photon conservation. We find that ignoring photon conservation results in very modest biases in the inferred galaxy properties, for our fiducial model. The notable exception is in the power-law scaling of the ionizing escape fraction with halo mass, which can be biased from the true value by $\sim2.4\sigma$ (corresponding to $\sim0.2$ in the power-law index). Our scheme is implemented in the public code ${\tt 21cmFAST}$., Comment: 9 pages, 4 figures, 1 table, accepted for publication in MNRAS

Bright, high redshift ($z>6$) QSOs are powerful probes of the ionisation state of the intervening intergalactic medium (IGM). The detection of Ly$\alpha$ damping wing absorption imprinted in the spectrum of high-z QSOs can provide strong constraints on the epoch of reionisation (EoR). In this work, we perform an independent Ly$\alpha$ damping wing analysis of two known $z>7$ QSOs; DESJ0252-0503 at $z=7.00$ (Wang et al.) and J1007+2115 at $z=7.51$ (Yang et al.). For this, we utilise our existing Bayesian framework which simultaneously accounts for uncertainties in: (i) the intrinsic Ly$\alpha$ emission profile (reconstructed from a covariance matrix of measured emission lines; extended in this work to include NV) and (ii) the distribution of ionised (H\,{\scriptsize II}) regions within the IGM using a $1.6^3$ Gpc$^3$ reionisation simulation. This approach is complementary to that used in the aforementioned works as it focuses solely redward of Ly$\alpha$ ($1218 < \lambda < 1230$\AA) making it more robust to modelling uncertainties while also using a different methodology for (i) and (ii). We find, for a fiducial EoR morphology, $\bar{x}_{\rm HI} = 0.64\substack{+0.19 \\ -0.23}$ (68 per cent) at $z=7$ and $\bar{x}_{\rm HI} = 0.27\substack{+0.21 \\ -0.17}$ at $z=7.51$ consistent within $1\sigma$ to the previous works above, though both are slightly lower in amplitude. Following the inclusion of NV into our reconstruction pipeline, we perform a reanalysis of ULASJ1120+0641 at $z=7.09$ (Mortlock et al.) and ULASJ1342+0928 at $z=7.54$ (Ba\~nados et al.) finding $\bar{x}_{\rm HI} = 0.44\substack{+0.23 \\ -0.24}$ at $z=7.09$ and $\bar{x}_{\rm HI} = 0.31\substack{+0.18 \\ -0.19}$ at $z=7.54$. Finally, we combine the QSO damping wing constraints for all four $z\gtrsim7$ QSOs to obtain a single, unified constraint of $\bar{x}_{\rm HI} = 0.49\substack{+0.11 \\ -0.11}$ at $z=7.29$., Comment: 15 pages, 9 figures. Submitted to MNRAS, comments welcome

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 {\tt 21cmFAST}. We introduce a new, flexible parametrization of the additive feedback from: an inhomogeneous, $H_2$-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 $z \approx 10-15$ 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., Comment: 23+3 pages, 23+3 figures. Matches accepted version. Simulation output available at https://www.dropbox.com/sh/dqh9r6wb0s68jfo/AACc9ZCqsN0SQ_JJN7GRVuqDa?dl=0

Measuring the density of the intergalactic medium using quasar sightlines in the epoch of reionization is challenging due to the saturation of Lyman-$\alpha$ absorption. Near a luminous quasar, however, the enhanced radiation creates a proximity zone observable in the quasar spectra where the Lyman-$\alpha$ absorption is not saturated. In this study, we use $10$ high-resolution ($R\gtrsim 10,000$) $z\sim 6$ 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 $\textit{Cosmic Reionization on Computers}$ simulation, and find a good agreement between $1.5$ to $3$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 $\sigma_8=0.6\pm0.3$. The uncertainty is mainly due to the limited number of high-quality quasar sightlines currently available. Utilizing the more than $>200$ known quasars at $z\gtrsim 6$, this method will allow us in the future to tighten the constraint on $\sigma_8$ to the percent level. In the region closer to the quasar within $1.5$ pMpc, we find the density is higher than predicted in the simulation by $1.23 \pm 0.17$, suggesting the typical host dark matter halo mass of a bright quasar ($M_{\rm 1450}<-26.5$) at $z\sim 6$ is $\log_{\rm 10} (M/M_\odot)=12.5^{+0.4}_{-0.7}$., Comment: 16 pages, 11 figures, submitted to ApJ, comments are welcome

We present a framework for identifying and flagging malfunctioning antennas in large radio interferometers. We outline two distinct categories of metrics designed to detect outliers along known failure modes of large arrays: cross-correlation metrics, based on all antenna pairs, and auto-correlation metrics, based solely on individual antennas. We define and motivate the statistical framework for all metrics used, and present tailored visualizations that aid us in clearly identifying new and existing systematics. We implement these techniques using data from 105 antennas in the Hydrogen Epoch of Reionization Array (HERA) as a case study. Finally, we provide a detailed algorithm for implementing these metrics as flagging tools on real data sets., Comment: 31 pages, 17 figures