arXiv subjects

Bradley Greig

Publications and source records attributed to Bradley Greig.

At least 19 recordsLinked to original sources

arXiv2025

Exploring One-point Statistics in HERA Phase I Data: Effects of Foregrounds and Systematics on Measuring One-Point Statistics

Measuring one-point statistics in redshifted 21 cm intensity maps offers an opportunity to explore non-Gaussian features of the early universe. We assess the impact of instrumental effects on measurements made with the Hydrogen Epoch of Reionization Array (HERA) by forward modeling observational and simulation data. Using HERA Phase I observations over 94 nights, we examine the second (m2, variance) and third (m3) moments of images. We employ the DAYENU-filtering method for foreground removal and reduce simulated foreground residuals to 10% of the 21 cm signal residuals. In noiseless cosmological simulations, the amplitudes of one-point statistics measurements are significantly reduced by the instrument response and further reduced by wedge-filtering. Analyses with wedge-filtered observational data, along with expected noise simulations, show that systematics alter the probability distribution of the map pixels. Likelihood analysis based on the observational data shows m2 measurements disfavor the cold reionization model characterized by inefficient X-ray heating, in line with other power spectra measurements. Small signals in m3 due to the instrument response of the Phase I observation and wedge-filtering make it challenging to use these non-Gaussian statistics to explore model parameters. Forecasts with the full HERA array predict high signal-to-noise ratios for m2, m3, and S3 assuming no foregrounds, but wedge-filtering drastically reduces these ratios. This work demonstrates conclusively that a comprehensive understanding of instrumental effects on m2 and m3 is essential for their use as a cosmological probe, given their dependence on the underlying model.

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arXiv2024

Damping Wing-Like Features in the Stacked Ly$\alpha$ Forest: Potential Neutral Hydrogen Islands at $z<6$

Recent quasar absorption line observations suggest that reionization may end as late as $z \approx 5.3$. As a means to search for large neutral hydrogen islands at $z<6$, we revisit long dark gaps in the Ly$\beta$ forest in VLT/X-Shooter and Keck/ESI quasar spectra. We stack the Ly$\alpha$ forest corresponding to both edges of these Ly$\beta$ dark gaps and identify a damping wing-like extended absorption profile. The average redshift of the stacked forest is $z=5.8$. By comparing these observations with reionization simulations, we infer that such a damping wing-like feature can be naturally explained if these gaps are at least partially created by neutral islands. Conversely, simulated dark gaps lacking neutral hydrogen struggle to replicate the observed damping wing features. Furthermore, this damping wing-like profile implies that the volume-averaged neutral hydrogen fraction must be $\langle x_{\rm HI} \rangle \geq 6.1 \pm 3.9\%$ at $z = 5.8$. Our results offer robust evidence that reionization extends below $z=6$.

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arXiv2024

IGM damping wing constraints on the tail end of reionisation from the enlarged XQR-30 sample

The attenuation of Ly$α$ 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$α$ 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$α$ emission profiles (obtained via covariance matrix reconstruction of the Ly$α$ 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$α$ forest) along with other observational probes considered in the literature.

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arXiv2024

Blind QSO reconstruction challenge: Exploring methods to reconstruct the Ly$α$ emission line of QSOs

Reconstructing the intrinsic Ly$α$ 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$α$ reconstruction pipelines using different methodologies to predict the Ly$α$ line flux from correlations with the spectral information redward of Ly$α$. 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 1260Å rest-frame to ensure unbiased reconstruction. We constructed two samples of 30 QSOs, from X-Shooter and SDSS both spanning $3.5<z<4.5$. Importantly, the purpose of this comparison study was not to champion a single, best performing reconstruction pipeline but rather to explore the relative performance of these pipelines over a range of QSOs with broad observational characteristics to infer general trends. In summary, we find machine learning approaches in general provide the strongest ``best guesses" but underestimate the accompanying statistical uncertainty, although these can be recalibrated, whilst pipelines that decompose the spectral information, for example principal component or factor analysis generally perform better at predicting the Ly$α$ profile. Further, we found that reconstruction pipelines trained on SDSS QSOs performed similarly on average for both the X-Shooter and SDSS samples indicating no discernible biases owing to differences in the observational characteristics of the training set or QSO being reconstructed, although the recovered distributions of reconstructions for X-Shooter were broader likely due to an increased fraction of outliers.

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arXiv2024

Inferring astrophysical parameters using the 2D cylindrical power spectrum from reionisation

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.

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arXiv2024

Exploring the role of the halo mass function for inferring astrophysical parameters during reionisation

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 $\sim3-4σ$ 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.

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arXiv2024

A demonstration of the effect of fringe-rate filtering in the Hydrogen Epoch of Reionization Array delay power spectrum pipeline

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.

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arXiv2024

Hydrogen Epoch of Reionization Array (HERA) Phase II Deployment and Commissioning

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.

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arXiv2023

matvis: A matrix-based visibility simulator for fast forward modelling of many-element 21 cm arrays

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.

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arXiv2023

Dark-ages reionization and galaxy formation simulation -- XXI. Constraining the evolution of the ionizing escape fraction

The fraction of ionizing photons that escape their host galaxies to ionize hydrogen in the inter-galactic medium (IGM) is a critical parameter in analyses of the reionization era. In this paper we use the Meraxes semi-analytic galaxy formation model to infer the mean ionizing photon escape fraction and its dependence on galaxy properties through joint modelling of the observed high redshift galaxy population and existing constraints on the reionization history. Using a Bayesian framework, and under the assumption that escape fraction is primarily related to halo mass, we find that the joint constraints of the UV luminosity function, CMB optical depth, and the Ly$α$ forest require an escape fraction of $(18\pm5)\%$ for galaxies within haloes of $M\lesssim10^{9}$M$_\odot$ and $(5\pm2)\%$ for more massive haloes. In terms of galaxy properties, this transition in escape fraction occurs at stellar masses of $M_\star\sim10^7$M$_\odot$, nearly independent of redshift. As a function of redshift, reionization is dominated by the smaller $M_\star\lesssim10^7$M$_\odot$ galaxies with high escape fractions at $z\gtrsim6$ and by the larger $M_\star\gtrsim10^7$M$_\odot$ galaxies with lower escape fractions at $z\lesssim6$. Galaxies with star formation rates of $10^{-2.5}$M$_\odot$yr$^{-1}$ to $10^{-1.5}$M$_\odot$yr$^{-1}$ provide the dominant source of ionizing photons throughout reionization. Our results are consistent with recent direct measurements of a $\sim5\%$ escape fraction from massive galaxies at the end of reionization and support the picture of low mass galaxies being the dominant sources of ionizing photons during reionization.

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arXiv2023

Bayesian estimation of cross-coupling and reflection systematics in 21cm array visibility data

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. Incoherently averaging the recovered power spectra can further reduce the noise and improve recovery. Where the noise level is lower than the EoR, our modelling can mitigate the majority of the reflections and coupling with there being only a minor level of residual systematics. 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.

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arXiv2023

Direct Optimal Mapping Image Power Spectrum and its Window Functions

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.

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arXiv2023

Fisher matrix forecasts on the astrophysics of galaxies during the epoch of reionisation from the 21-cm power spectra

The hyperfine 21-cm transition of neutral hydrogen from the early Universe ($z>5$) is a sensitive probe of the formation and evolution of the first luminous sources. Using the Fisher matrix formalism we explore the complex and degenerate high-dimensional parameter space associated with the high-$z$ sources of this era and forecast quantitative constraints from a future 21-cm power spectrum (21-cm PS) detection. This is achieved using MERAXES, a coupled semi-analytic galaxy formation model and reionisation simulation, applied to an $N$-body halo merger tree with a statistically complete population of all atomically cooled galaxies out to $z\sim20$. Our mock observation assumes a 21-cm detection spanning $z \in [5, 24]$ from a 1000 h mock observation with the forthcoming Square Kilometre Array and is calibrated with respect to ultraviolet luminosity functions (UV LFs) at $z\in[5, 10]$, the optical depth of CMB photons to Thompson scattering from Planck, and various constraints on the IGM neutral fraction at $z > 5$. In this work, we focus on the X-ray luminosity, ionising UV photon escape fraction, star formation and supernova feedback of the first galaxies. We demonstrate that it is possible to recover 5 of the 8 parameters describing these properties with better than $50$ per cent precision using just the 21-cm PS. By combining with UV LFs, we are able to improve our forecast, with 5 of the 8 parameters constrained to better than 10 per cent (and all below 50 per cent).

astro-ph.CO↗

arXiv2023

21cmfish: Fisher-matrix framework for fast parameter forecasts from the cosmic 21-cm signal

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.

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arXiv2023

New quasar proximity zone size measurements at $z\sim 6$ using the enlarged XQR-30 sample

Proximity zones of high-redshift quasars are unique probes of their central supermassive black holes as well as the intergalactic medium in the last stages of reionization. We present 22 new measurements of proximity zones of quasars with redshifts between 5.8 and 6.6, using the enlarged XQR-30 sample of high-resolution, high-SNR quasar spectra. The quasars in our sample have UV magnitudes of $M_{1450}\sim -27$ and black hole masses of $10^9$$\unicode{x2013}$$10^{10}$ M$_\odot$. Our inferred proximity zone sizes are 2$\unicode{x2013}$7 physical Mpc, with a typical uncertainty of less than 0.5 physical Mpc, which, for the first time, also includes uncertainty in the quasar continuum. We find that the correlation between proximity zone sizes and the quasar redshift, luminosity, or black hole mass, indicates a large diversity of quasar lifetimes. Two of our proximity zone sizes are exceptionally small. The spectrum of one of these quasars, with $z=6.02$, displays, unusually for this redshift, damping wing absorption without any detectable metal lines, which could potentially originate from the IGM. The other quasar has a high-ionization absorber $\sim$0.5 pMpc from the edge of the proximity zone. This work increases the number of proximity zone measurements available in the last stages of cosmic reionization to 87. This data will lead to better constraints on quasar lifetimes and obscuration fractions at high redshift, which in turn will help probe the seed mass and formation redshift of supermassive black holes.

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arXiv2023

Characterization Of Inpaint Residuals In Interferometric Measurements of the Epoch Of Reionization

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.

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arXiv2023

Thermal and Reionisation History within a Large-Volume Semi-Analytic Galaxy Formation Simulation

We predict the 21-cm global signal and power spectra during the Epoch of Reionisation using the MERAXES semi-analytic galaxy formation and reionisation model, updated to include X-ray heating and thermal evolution of the intergalactic medium. Studying the formation and evolution of galaxies together with the reionisation of cosmic hydrogen using semi-analytic models (such as MERAXES) requires N-body simulations within large volumes and high mass resolutions. For this, we use a simulation of side-length $210~h^{-1}$ Mpc with $4320^3$ particles resolving dark matter haloes to masses of $5\times10^8~h^{-1}~M_\odot$. To reach the mass resolution of atomically cooled galaxies, thought to be the dominant population contributing to reionisation, at $z=20$ of $\sim 2\times10^7~h^{-1}~M_\odot$, we augment this simulation using the DARKFOREST Monte-Carlo merger tree algorithm (achieving an effective particle count of $\sim10^{12}$). Using this augmented simulation we explore the impact of mass resolution on the predicted reionisation history as well as the impact of X-ray heating on the 21-cm global signal and the 21-cm power spectra. We also explore the cosmic variance of 21-cm statistics within $70^{3}$ $h^{-3}$ Mpc$^3$ sub-volumes. We find that the midpoint of reionisation varies by $Δz\sim0.8$ and that the cosmic variance on the power spectrum is underestimated by a factor of $2-4$ at $k\sim 0.1-0.4$ Mpc$^{-1}$ due to the non-Gaussian nature of the 21-cm signal. To our knowledge, this work represents the first model of both reionisation and galaxy formation which resolves low-mass atomically cooled galaxies while simultaneously sampling sufficiently large scales necessary for exploring the effects of X-rays in the early Universe.

astro-ph.CO↗

arXiv2023

Search for the Epoch of Reionisation with HERA: Upper Limits on the Closure Phase Delay Power Spectrum

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.

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