arXiv subjects

Eloy de Lera Acedo

Publications and source records attributed to Eloy de Lera Acedo.

At least 37 records · Page 2Linked to original sources

arXiv2025

Narrowing the discovery space of the cosmological 21-cm signal using multi-wavelength constraints

The cosmic 21-cm signal is a promising probe of the early Universe, owing to its sensitivity to the thermal state of the neutral intergalactic medium (IGM) and properties of the first luminous sources. Here, we constrain the 21-cm signal and infer IGM properties using the Population II galaxy parameters derived in a previous study through multi-wavelength synergies. This includes high-redshift UV luminosity functions (UVLFs) from Hubble Space Telescope (HST) and James Webb Space Telescope (JWST), cosmic X-ray and radio backgrounds (CXB and CRB), the SARAS 3 global 21-cm signal non-detection, and HERA 21-cm power spectrum upper limits. From CXB and HERA data, we infer the IGM kinetic temperature to be $T_\text{K}(z=15)\lesssim 7.7~\text{K}$, $2.5~\text{K} \lesssim T_\text{K}(z=10) \lesssim 66~\text{K}$, and $20~\text{K}\lesssim T_\text{K}(z=6) \lesssim 2078~\text{K}$ at 95% credible interval (C.I.). Similarly, CRB and HERA data limit the radio emission efficiency of galaxies, giving $T_\text{rad}(z=15) \lesssim 47~\text{K}$, $T_\text{rad}(z=10)\lesssim 51~\text{K}$, and $T_\text{rad}(z=6)\lesssim 101~\text{K}$. These constraints, strengthened by UVLFs from HST and JWST, enable the first $\textit{lower bound}$ on the cosmic 21-cm signal. We infer an absorption trough of depth ${-201~\text{mK}\lesssim T_\text{21,min} \lesssim -68~\text{mK}}$ at $z_\text{min}\approx10-16$, and a power spectrum of $8.7~\text{mK}^2 < Δ_{21}^2(z=15) < 197~\text{mK}^2$ at $k=0.35~h\text{Mpc}^{-1}$. Our results highlight the power of multi-wavelength synergies in constraining the early Universe. While promising for upcoming 21-cm experiments, the results depend on our assumption of a redshift-independent X-ray and radio efficiency of galaxies, and the exclusion of a flexible model for Population III stars.

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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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arXiv2025

RFSoC receiver calibration system for 21-cm global spectrum experiments from space: The CosmoCube case

The CosmoCube project plans to deploy a global 21-cm spectrometer with 10-100 MHz observation band in a lunar orbit. The farside part of such an orbit, i.e. the part of orbit behind the Moon, offers an ideal site for accurately measuring the 21-cm signal from the Dark Ages, Cosmic Dawn and Epoch of Reionization, as the effects of the Earth's ionosphere, artificial radio frequency interference (RFI), and complex terrain and soil are all avoided. Given the limitations of a satellite platform, we propose a receiver calibration system design based on a Radio Frequency system-on-chip, consisting of a Vector Network Analyzer (VNA) sub-system, and a source switching sub-system. We introduce the measurement principle of the VNA, and discuss the effect of quantization error. The accuracy, stability and trajectory noise of the VNA are tested in laboratory experiments. We also present the design of the source-switching sub-system, generating mock datasets, showing that the imperfect return loss, insertion loss, and isolation of surface-mounted microwave switches have a minimal effect on the sky foreground fitting residuals, which are within $\pm10$ mK under optimal fitting condition. When all possible measurement errors in reflection coefficients and physical temperatures are taken into account, the foreground fitting residuals for the 50-90 MHz part of the spectrum remain around $\pm20$ mK.

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arXiv2025

Capturing System Drift with Time Series Calibration for Global 21-cm Cosmology Experiments

To achieve the sensitivity required to detect signals from neutral hydrogen from the Cosmic Dawn and Epoch of Reionisation it is critical to have a well-calibrated instrument which has a stable calibration over the course of the observation. Previous calibration methods do not explicitly use the time information available and make assumptions on the impedance matching of the reference sources. Here we present a new calibration method based on noise wave parameters which fits a calibration solution over time and frequency to the data, interpolating the solutions to the times at which the antenna is being measured. To test this method we simulate a dataset using measurements of the REACH receiver, modelling a low noise amplifier which is drifting over time. Fitting a polynomial surface in frequency and time to the simulated data demonstrates that we can remove the drift in the calibrated solution over time but leaves a chromatic residual. We further show that we can remove assumptions on the reflection coefficients of the reference noise source and the cold load, reducing degeneracies in the parameter fits. Applying this new calibration equation and surface fitting method to the simulated data removes the chromatic residual in the calibrated spectrum and recovers the parameters to within 0.06% of the truth and a 97% reduction in the RMSE of the spectrum of the validation source compared with previous calibration methods. For two parameters we report up to six times smaller fit error after the degeneracies are removed from the time-based calibration.

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arXiv2025

Quantifying the Impact of Lunar and Planetary Occultation on Experimental Global 21 cm Cosmology

The global 21 cm signal from the hyperfine transition of cosmic atomic hydrogen is theorised to track the state of the early Universe via the analysis of its absorption and emission with respect to the radio background. Detecting this signal has been a challenge for astronomers since it was first postulated due to the presence of strong galactic foregrounds obfuscating the transition. Forward modelling techniques that aim to simulate and then remove these foregrounds have been suggested as a workaround to this problem. This technique, however, requires a precise and accurate understanding of the foregrounds in question. As we move into the next major lunar standstill, the moon will be able to occult high power areas of the sky in ways that are unaccounted for by maps used to simulate these foregrounds, and thereby disrupt signal recovery. We show that in toy cases an occultation from the moon, or other proximate object, leading to a mismatch in our expected and actual foregrounds of 15 parts per million increases the error in signal recovery of up to 20\%. We show that this level of disruption can happen when the moon is found towards the centre of the galaxy and is amplified when this alignment happens at high directivity regions of the antenna beam, causing a disruption of up to 180 parts per million, leading to a signal recovery error of 115\%. This allows us to identify lunar alignment scenarios that should be actively avoided to preserve signal fidelity. We also demonstrate that a body with a smaller apparent size than the moon, such as Venus, is unlikely to cause any signal disruption due to occultation, giving a base map error of <2 parts per million.

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arXiv2025

Exploiting synergies between JWST and cosmic 21-cm observations to uncover star formation in the early Universe

In the current era of JWST, we continue to uncover a wealth of information about the Universe deep into the Epoch of Reionization. In this work, we use a suite of simulations with 21cmSPACE, to explore the astrophysical properties of early galaxies and their imprint on high-redshift observables. Our analysis incorporates a range of multi-wavelength datasets including UV luminosity functions (UVLFs) from HST and JWST spanning $z=6-14.5$, the 21-cm global signal and power spectrum limits from SARAS 3 and HERA respectively, as well as present-day diffuse X-ray and radio backgrounds. We constrain a flexible halo-mass and redshift dependent model of star-formation efficiency (SFE), defined as the fraction of gas converted into stars, and find that it is best described by minimal redshift evolution at $z\approx 6-10$, followed by rapid evolution at $z\approx10-15$. Using Bayesian inference, we derive functional posteriors of the SFE, inferring that halos of mass $M_h=10^{10}\,\mathrm{M}_\odot$ have efficiencies of $\approx 1 - 2\%$ at $z\lesssim10$, $\approx8\%$ at $z=12$ and $\approx21\%$ at $z=15$. We also highlight the synergy between UVLFs and global 21-cm signal from SARAS 3 in constraining the minimum virial conditions required for star-formation in halos. In parallel, we find the X-ray and radio efficiencies of early galaxies to be $f_X = 0.8^{+9.7}_{-0.4}$ and $f_r \lesssim 16.9$ respectively, improving upon previous works that exclude UVLF data. Our results underscore the critical role of UVLFs in constraining early galaxy properties, and their synergy with 21-cm and other multi-wavelength observations.

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arXiv2025

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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arXiv2025

Simulation-Based Inference of the sky-averaged 21-cm signal from CD-EoR with REACH

The redshifted 21-cm signal from the Cosmic Dawn and Epoch of Reionization carries invaluable information about the cosmology and astrophysics of the early Universe. Analyzing data from a sky-averaged 21-cm signal experiment requires navigating through an intricate parameter space addressing various factors such as foregrounds, beam uncertainties, ionospheric distortions, and receiver noise for the search of the 21-cm signal. The traditional likelihood-based sampling methods for modeling these effects could become computationally demanding for such complex models, which makes it infeasible to include physically motivated 21-cm signal models in the analysis. Moreover, the inference is driven by the assumed functional form of the likelihood. We demonstrate how Simulation-Based Inference through Truncated Marginal Neural Ratio Estimation (TMNRE) can naturally handle these issues at a reduced computational cost. We estimate the posterior distribution on our model parameters with TMNRE for simulated mock observations, incorporating beam-weighted foregrounds, physically motivated 21-cm signal, and radiometric noise. We find that maximizing information content by analyzing data from multiple time slices and antennas significantly improves the parameter constraints and enhances the exploration of the cosmological signal. We discuss the application of TMNRE for the current configuration of the REACH experiment and demonstrate its potential for exploring new avenues.

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arXiv2025

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

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

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arXiv2025

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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arXiv2025

Cosmological super-resolution of the 21-cm signal

In this study, we train score-based diffusion models to super-resolve gigaparsec-scale cosmological simulations of the 21-cm signal. We examine the impact of network and training dataset size on model performance, demonstrating that a single simulation is sufficient for a model to learn the super-resolution task regardless of the initial conditions. Our best-performing model achieves pixelwise $\mathrm{RMSE}\sim0.57\ \mathrm{mK}$ and dimensionless power spectrum residuals ranging from $10^{-2}-10^{-1}\ \mathrm{mK^2}$ for $128^3$, $256^3$ and $512^3$ voxel simulation volumes at redshift $10$. The super-resolution network ultimately allows us to utilize all spatial scales covered by the SKA1-Low instrument, and could in future be employed to help constrain the astrophysics of the early Universe.

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arXiv2025

Accounting for Noise and Singularities in Bayesian Calibration Methods for Global 21-cm Cosmology Experiments

Due to the large dynamic ranges involved with separating the cosmological 21-cm signal from the Cosmic Dawn from galactic foregrounds, a well-calibrated instrument is essential to avoid biases from instrumental systematics. In this paper we present three methods for calibrating a global 21-cm cosmology experiment using the noise wave parameter formalisation to characterise a low noise amplifier including a careful consideration of how calibrator temperature noise and singularities will bias the result. The first method presented in this paper builds upon the existing conjugate priors method by weighting the calibrators by a physically motivated factor, thereby avoiding singularities and normalising the noise. The second method fits polynomials to the noise wave parameters by marginalising over the polynomial coefficients and sampling the polynomial orders as parameters. The third method introduces a physically motivated noise model to the marginalised polynomial method. Running these methods on a suite of simulated datasets based on the REACH receiver design and a lab dataset, we found that our methods produced a calibration solution which is equally as or more accurate than the existing conjugate priors method when compared with an analytic estimate of the calibrator's noise. We find in the case of the measured lab dataset the conjugate priors method is biased heavily by the large noise on the shorted load calibrator, resulting in incorrect noise wave parameter fits. This is mitigated by the methods introduced in this paper which calibrate the validation source spectra to within 5% of the noise floor.

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arXiv2025

Uncovering the Effects of Array Mutual Coupling in 21-cm Experiments with the SKA-Low Radio Telescope

We investigate the impact of Mutual Coupling (MC) between antennas on the time-delay power spectrum response of the core of the SKA-Low radio telescope. Using two in-house tools - Fast Array Simulation Tool (FAST) (a fast full-wave electromagnetic solver) and OSKAR (a GPU-accelerated radio telescope simulator) - we simulate station beams and compute visibilities for various array layouts (regular, sunflower, and random). Simulations are conducted in an Epoch of Reionisation subband between 120-150~MHz, with a fine frequency resolution of 100~kHz, enabling the investigation of longer delays. Our results show that MC effects significantly increase foreground leakage into longer delays, especially for regular station layouts. For 21-cm science, foreground spill-over into the 21-cm window extends beyond $k_{\parallel} \sim 2$~h$^{-1}$Mpc for all station layouts and across all $k_{\perp}$ modes, completely obscuring the detection window. We find that attempting to remove the foreground contribution from the visibilities using an approximated beam model, based on the average embedded element pattern or interpolating the embedded element patterns from a coarse channel rate of 781~kHz, results in residuals around 1% ($\sim 10^{11}~\mathrm{mK}^2$h$^{-3}\mathrm{Mpc}^3$) which is still around 7 orders of magnitude brighter than the expected level of the EoR signal ($\sim 10^{4}~\mathrm{mK}^2$h$^{-3}\mathrm{Mpc}^3$). We also find that station beam models with at least 4-5 significant digits in the far-field pattern and high spectral resolution are needed for effective foreground removal. Our research provides critical insights into the role of MC in SKA-Low experiments and highlights the computational challenges of fully integrating array patterns that account for MC effects into processing pipelines.

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arXiv2025

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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arXiv2024

The Spectrometer Development of CosmoCube, Lunar Orbiting Satellite to Detect 21-cm Hydrogen Signal from Cosmic Dark Ages

The cosmic Dark Ages represent a pivotal epoch in the evolution of the Universe, marked by the emergence of the first cosmic structures under the influence of dark matter. The 21-cm hydrogen line, emanating from the hyperfine transition of neutral hydrogen, serves as a critical probe into this era. We describe the development and implementation of the spectrometer for CosmoCube, a novel lunar orbiting CubeSat designed to detect the redshifted 21-cm signal within the redshift range of 13 to 150. Our instrumentation utilizes a Xilinx RFSoC, which integrates both Analog-to-Digital Converters (ADCs) and Digital-to-Analog Converters (DACs), tailored for the spectrometer component of the radiometer. This system is characterized by a 4096 FFT length at 62.5 kHz steps using a Polyphase Filter Bank (PFB), achieving an average Effective Number of Bits (ENOB) of 11.5 bits throughout the frequency of interest, from 10 MHz to 100 MHz. The spectrometer design is further refined through loopback tests involving both DAC and ADC of the RFSoC, with DAC outputs varying between high (+1 dBm) and low (-3 dBm) power modes to characterize system performance. The power consumption was optimized to 5.45 W using three ADCs and one DAC for the radiometer. Additionally, the stability of the ADC noise floor was investigated in a thermal chamber with environmental temperatures ranging from 5°C to 40°C. A consistent noise floor of approximately -152.5 dBFS/Hz was measured, with a variation of $\pm$0.2 dB, ensuring robust performance under varying thermal conditions.

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arXiv2024

Bayesian data analysis for sky-averaged 21-cm experiments with contamination from linearly polarised foreground

The precise measurement of the sky-averaged HI absorption signal between 50 and 200 MHz is the primary goal of global 21-cm cosmology. This measurement has the potential to unravel the underlying physics of cosmic structure formation and evolution during the Cosmic Dawn. It is, however, hindered by various non-smooth, frequency-dependent effects, whose structures resemble those of the signal. One such effect is the leakage of polarised foregrounds into the measured intensity signal: polarised foreground emission undergoes Faraday rotation as it passes through the magnetic fields of the interstellar medium, imprinting a chromatic structure in the relevant frequency range which complicates the extraction of the cosmological HI absorption feature. We investigate the effect of polarised Galactic foregrounds on extracting the global 21-cm signal from simulated data using REACH's data analysis pipeline; the Radio Experiment for the Analysis of Cosmic Hydrogen (REACH) is an experiment designed to detect the sky-averaged 21-cm HI signal from the early Universe using physically informed models. Using the REACH pipeline, we successfully recover an injected global 21-cm signal with an amplitude of approximately 0.16 K, centred between 80 and 120 MHz, achieving a low root-mean-square error (less than 30\% of the injected signal strength) in all the tested cases. This includes scenarios with simulated polarised Galactic diffuse emissions and polarised point source emissions, provided the overall polarisation fraction is below $\sim 3\%$. The linear mixing of contamination, caused by the superposition of multiple patches with varying strengths of Faraday rotation, produces patterns that are more distinct from the global signal. This distinction makes global signal recovery easier compared to contamination resulting from a single, slow oscillation pattern.

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arXiv2024

A Generalized Method for Characterizing 21-cm Power Spectrum Signal Loss from Temporal Filtering of Drift-scanning Visibilities

A successful detection of the cosmological 21-cm signal from intensity mapping experiments (for example, during the Epoch of Reioinization or Cosmic Dawn) is contingent on the suppression of subtle systematic effects in the data. Some of these systematic effects, with mutual coupling a major concern in interferometric data, manifest with temporal variability distinct from that of the cosmological signal. Fringe-rate filtering -- a time-based Fourier filtering technique -- is a powerful tool for mitigating these effects; however, fringe-rate filters also attenuate the cosmological signal. Analyses that employ fringe-rate filters must therefore be supplemented by careful accounting of the signal loss incurred by the filters. In this paper, we present a generalized formalism for characterizing how the cosmological 21-cm signal is attenuated by linear time-based filters applied to interferometric visibilities from drift-scanning telescopes. Our formalism primarily relies on analytic calculations and therefore has a greatly reduced computational cost relative to traditional Monte Carlo signal loss analyses. We apply our signal loss formalism to a filtering strategy used by the Hydrogen Epoch of Reionization Array (HERA) and compare our analytic predictions against signal loss estimates obtained through a Monte Carlo analysis. We find excellent agreement between the analytic predictions and Monte Carlo estimates and therefore conclude that HERA, as well as any other drift-scanning interferometric experiment, should use our signal loss formalism when applying linear, time-based filters to the visibilities.

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arXiv2024

Impact of extragalactic point sources on the low-frequency sky spectrum and cosmic dawn global 21-cm measurements

Contribution of resolved and unresolved extragalactic point sources to the low-frequency sky spectrum is a potentially non-negligible part of the astrophysical foregrounds for cosmic dawn 21-cm experiments. The clustering of such point sources on the sky, combined with the frequency-dependence of the antenna beam, can also make this contribution chromatic. By combining low-frequency measurements of the luminosity function and the angular correlation function of extragalactic point sources, we develop a model for the contribution of these sources to the low-frequency sky spectrum. Using this model, we find that the contribution of sources with flux density $>10^{-6}\,$Jy to the sky-averaged spectrum is smooth and of the order of a few kelvins at 50--$200\,$MHz. We combine this model with measurements of the galactic foreground spectrum and weigh the resultant sky by the beam directivity of the conical log-spiral antenna planned as part of the Radio Experiment for the Analysis of Cosmic Hydrogen (REACH) project. We find that the contribution of point sources to the resultant spectrum is $\sim0.4\%$ of the total foregrounds, but still larger by at least an order of magnitude than the standard predictions for the cosmological 21-cm signal. As a result, not accounting for the point-source contribution leads to a systematic bias in 21-cm signal recovery. We show, however, that in the REACH case, this reconstruction bias can be removed by modelling the point-source contribution as a power law with a running spectral index. We make our code publicly available as a Python package labelled epspy.

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