arXiv subjects

Zhaoting Chen

Publications and source records attributed to Zhaoting Chen.

At least 19 recordsLinked to original sources

arXiv2026

Cosmology with HI Intensity Mapping

The redshifted spectral emission from neutral hydrogen (HI) at rest wavelength 21 cm can be used as a tracer of large-scale structure and its evolution. Within the HI intensity mapping method, sufficient signal-to-noise is achieved by integrating the line emission within large voxels over a wide sky area and line of sight depth which allows access to the largest scales of the matter distribution. The resulting tomographic maps usually feature low angular and high redshift resolution. The SKAO will be able to conduct HI intensity mapping experiments observing up to 20,000 square degrees over a wide range of redshifts. For SKA-Mid, we will employ the array in a fast-scanning single-dish mode using Band 1 and 2 to access 0<z<3, mapping an enormous volume with fast survey speed, allowing for the possibility of a commensal survey producing high angular resolution maps via the on-the-fly imaging of the visibilities. For SKA-Low, we will focus on deep observations to detect the HI signal in a frequency band matching 3<z<6. In this chapter, we will give an overview of HI intensity mapping with the SKAO, including an outline of planned surveys, a discussion of observational challenges, and methodology for power spectrum methodology and forecasts. We present predictions on the constraining power on LambdaCDM cosmology from HI intensity mapping data via power spectrum, and other observables such as bi-spectrum and HI stacking. We also demonstrate the synergy power of HI intensity mapping with other cosmological surveys.

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arXiv2026

meer21cm: an Analysis Pipeline and Comprehensive Toolkit for HI Intensity Mapping

We present meer21cm, a comprehensive python package for cosmological data analysis of single-dish HI intensity mapping surveys. This package is simple to use, with a modularised code structure designed for interactive usage. meer21cm is designed for data analysis, with particular focus on the UHF-band observation of MeerKAT Large Area Synoptic Survey (MeerKLASS). We explicitly impose meer21cm to be survey-oriented, ensuring consistent modelling of observational effects in the clustering power spectrum with the survey specifications and data analysis choices. meer21cm covers a large range of data analysis procedures post calibration, including data read-in, foreground cleaning, power spectrum estimation, mock simulation, transfer function corrections and parameter inference. It handles both meer21cm intensity maps and overlapping galaxy catalogues, allowing for multi-tracer and cross-correlation analysis between MeerKLASS and optical galaxy surveys. Tested with a simulated survey of ten $750\,$deg$^2$ sky patches in the redshift sub-band $0.6\,{<}\,z\,{<}\,0.8$, the meer21cm pipeline achieves per-cent accuracy in the power spectrum estimation for $k \in [0.02, 0.2]\,{h{\rm Mpc}^{-1}}$, with deviations $\lesssim 0.5\sigma$ between the mock and the model power spectra, where $\sigma$ is the signal variance. The meer21cm package is publicly available and easy to install, with a comprehensive documentation website at https://meer21cm.readthedocs.io

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arXiv2026

Cosmology with Intensity Mapping via Statistics Beyond the Power Spectrum in the SKAO Era

The cosmological distribution of neutral hydrogen (HI) during the post-reionization era is highly non-Gaussian due to the underlying non-linear structure formation, complex galaxy biasing, and potential primordial non-Gaussianity. One needs higher-order (beyond two-point) statistics to maximally extract the non-Gaussian information out of the 21-cm intensity maps. This chapter summarizes the potential of several higher-order statistics, including voxel intensity distribution, emission line stacking, probability density functions, $\ell_1$-norm, bispectrum, and various marked statistics. Additionally, image-based morphological descriptors, such as the Largest Cluster Statistic, local dimensions, and Minkowski functionals, etc., can potentially characterize the morphology and geometry of the cosmic web encoded in the 21-cm intensity maps. This chapter presents forecasts of the detectability of these higher-order statistics in the context of the future SKAO observations. These forecasts incorporate instrumental noise, observational effects, and, in some cases, foreground removal in their analyses. With its unprecedented sensitivity, the future SKAO 21-cm observations will enable us to measure these higher-order statistics more precisely, possibly helping to break degeneracies between astrophysical and cosmological parameters, and maximizing the science outcome from these surveys.

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arXiv2026

Methodological Frontiers in 21-cm Intensity Mapping: the Treatment of Systematics and Foreground Contamination

The distribution of neutral hydrogen (HI) in the post-reionization universe traces the cosmic large-scale structure and therefore serves as a powerful cosmological probe. An efficient way to measure its distribution over wide sky areas and redshift ranges is through single-dish intensity mapping, which exploits the autocorrelation signal of each dish in a telescope array while scanning the same sky patch. Thanks to its broad frequency coverage and technical capabilities, SKA-Mid will enable measurements of the integrated 21 cm emission from HI up to redshift $z\sim3$, making single-dish intensity mapping a key observable for probing dark matter and dark energy. Isolating the faint 21 cm cosmological signal without introducing biases is, however, challenging. The 21 cm signal is several orders of magnitude weaker than the astrophysical foregrounds, and its analysis is further affected by instrumental systematics. Overcoming these difficulties requires detailed modelling together with continuous improvements and innovations in data-analysis techniques. Over the past decade, the international community has developed and tested new methods to address current observational challenges and prepare for forthcoming SKA-Mid observations. This chapter reviews recent advances in map-making and component-separation techniques, with particular emphasis on telescope-specific systematics such as beam response and correlated noise. We focus on results obtained in controlled simulation environments, providing a valuable framework for assessing the strengths and limitations of different approaches. Developing robust algorithms capable of accurately handling instrumental effects and sky-model uncertainties is a crucial step toward fully exploiting the cosmological potential of HI intensity-mapping surveys in the SKA Observatory era.

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arXiv2026

Single-dish HI Intensity Mapping with the SKAO: Precursor Progress with MeerKAT's Large Area Synoptic Survey (MeerKLASS)

Using the SKAO to map the intensity of neutral hydrogen's 21cm emission line will be a golden opportunity to constrain models of cosmology. To access the largest cosmological scales, wide-sky surveys should ideally reach thousands of square degrees, requiring SKA-Mid's dishes to scan the sky in auto-correlation mode, so-called single-dish observations. In this chapter, we overview the latest results from MeerKAT's Large Area Synoptic Survey (MeerKLASS), which has been pioneering this single-dish observing strategy, and motivating its continuation with the SKA-Mid AA4 deployment. MeerKLASS, operating on the same Karoo site where the SKA-Mid is being built, has now achieved multiple cosmological detections from single-dish observations, including high-significance cross-correlations with optical galaxy surveys and continually improving measurements of the HI auto-power spectrum. These results demonstrate that stable calibration, effective foreground mitigation, and statistical recovery of cosmological signal are all achievable with a large multi-dish telescope in total-power mode. The success of MeerKLASS therefore validates the observational strategies required for SKA-Mid and marks a key milestone in demonstrating the viability of single-dish HI intensity mapping for cosmology. Looking ahead, SKA-Mid's increased sensitivity and Band 1 coverage (350-1050 MHz) will allow the same methodology to probe redshifts up to $z\,{\sim}\,3$, mapping volumes several orders of magnitude larger than currently accessible. The techniques refined with MeerKLASS thus form the operational and scientific foundation for a large portion of the SKAO's cosmology programme.

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arXiv2026

Interferometric HI Intensity Mapping of the Late Time Universe with SKA-Mid

We discuss the progress towards using the SKA-Mid for interferometric neutral hydrogen (HI) intensity mapping surveys. By mapping the distribution of cosmic HI distribution through the 21cm line, SKA-Mid will be able to measure the HI power spectrum at small angular separations in interferometric mode. We review the measurements made from the precursor MeerKAT telescope, using the MeerKAT DEEP2 as well as the MIGHTEE survey data, yielding tentative detection as well as upper limits on HI clustering. The methodology for MeerKAT can be naturally extended to SKA-Mid. Forecasts suggest that SKA-Mid AA4 will be able to measure the HI power spectrum with high statistical significance across a wide range of redshifts from $z\sim1.0$ to $z\sim 3.0$, around nonlinear scales $k\sim 1.0\,{\rm Mpc}^{-1}$. The precise measurements can be used to constrain the properties of HI galaxies, providing a novel window into probing galaxy evolution at $1.0\lesssim z \lesssim 3.0$.

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arXiv2026

Transformer-Based Source Detection and Morphological Classification in LOFAR Deep-Field Continuum Images

Radio source detection and morphological classification are fundamental for exploiting the scientific potential of modern radio continuum surveys. However, the rapidly increasing data volumes and the wide diversity of radio morphologies make traditional visual inspection infeasible and pose significant challenges for automated source finding. We apply a transformer-based set-prediction detector (RF-DETR) to 150\,MHz continuum images from the LOFAR Deep Fields for instance-level source detection and morphological classification. The method is adapted to multi-frequency-synthesis images of interferometric data and trained with a morphology-driven scheme using five mutually exclusive classes. The model is trained on the ELAIS-N1 Deep Field, where it achieves high detection and classification performance ($\mathrm{F1}\simeq 91$ per cent), and is then applied without retraining to the other three LOFAR Deep Fields. Across all four fields, the model yields consistent catalogues with modest field-to-field differences arising from survey depth and calibration. Compared with widely used PyBDSF catalogues, RF-DETR recovers the majority of PyBDSF sources while representing classical multi-component radio galaxies as single source-level detections rather than fragmented Gaussian components. Artefact-affected and spurious detections are identified as explicit classes, allowing these detections to be distinguished from general astrophysical sources in the resulting catalogues. As external validation, RF-DETR recovers the majority of visually identified extended and giant radio galaxies in the LOFAR Deep Fields and assigns them predominantly to extended morphological classes. These results indicate that transformer-based detectors provide a practical, scalable, morphology-aware approach to source finding in deep radio surveys, with clear relevance for forthcoming facilities such as SKA-Low.

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arXiv2026

Measurements of the HI intensity mapping power spectrum at low redshifts with MIGHTEE data: comparison with detected HI galaxies

Line intensity mapping provides a statistical approach to tracing the large-scale distribution of matter in the Universe. We apply the HI intensity mapping technique to interferometric data from the MeerKAT International GHz-Tiered Extragalactic Explorations (MIGHTEE) Survey, analysing 17.5 hours of a single pointing in the COSMOS field, using a 60 MHz sub-band in the frequency range 1332 - 1392 MHz ($0.02 \lesssim z \lesssim 0.07$). Using a delay-spectrum-based estimator, we measure the HI power spectrum on sub-megaparsec scales and compare it directly to the power spectrum inferred from a catalogue of individually detected HI galaxies in the same field. After mitigating low-level broadband contamination through conservative outlier flagging in the three-dimensional power spectrum, cross-correlation of time-split visibilities yields a statistically significant detection on scales $3 \lesssim k \lesssim 20 \, \mathrm{Mpc}^{-1}$ with a total signal-to-noise ratio of $\sim 13$. Over this range, the power spectra obtained from visibilities and detected galaxies are consistent within uncertainties and have comparable amplitudes of order $10^{-2}$ - $10^{-1}$ $\mathrm{mK}^2 \mathrm{Mpc}^3$. End-to-end validation is performed by propagating detected galaxies through the power spectrum estimator via both direct intensity-field construction and simulated visibilities, demonstrating agreement up to $k \sim 20 \ \mathrm{Mpc}^{-1}$, beyond which measurements become noise-dominated. A statistically significant correlation is also observed between the data and the simulated visibilities from the detected HI galaxies, which should be free of systematics. These results provide a self-consistent validation of interferometric HI intensity mapping at low redshift and demonstrate agreement with galaxy-based measurements within the same cosmological volume.

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arXiv2025

Revealing cosmological fluctuations in 21cm intensity maps with MeerKLASS: from maps to power spectra

Mapping the integrated 21cm emission line from dark matter-tracing neutral hydrogen gas is the primary science goal for MeerKLASS (MeerKAT's Large Area Synoptic Survey). Prior to the arrival of MeerKAT, this intensity mapping technique had only been tested on a couple of pre-existing single-dish radio telescopes with a handful of observational hours with which to make early pioneering detections. The 64-dish MeerKAT array, precursor to the Square Kilometre Array Observatory (SKAO), can scan the sky in auto-correlation mode and perform intensity mapping across large sky areas, presenting the exciting potential for a wide-sky (${\gtrsim}\,10{,}000\,{\rm deg}^2$) spectroscopic survey across redshift $0.4\,{<}\,z\,{<}\,1.45$. Validating the auto-correlation (or single-dish) mode of observation for a multi-dish array and developing the analysis pipeline with which to make unbiased measurements has presented major challenges to this endeavour. In this work, we overview the advances in the field that have facilitated a robust analysis framework for single-dish intensity mapping, and review some results that showcase its success using early MeerKLASS surveys. We demonstrate our control of foreground cleaning, signal loss and map regridding to deliver detections of cosmological clustering within the intensity maps through cross-correlation power spectrum measurements with overlapping galaxy surveys. Finally, we discuss the prospects for future MeerKLASS observations and forecast its potential, making our code publicly available: https://github.com/meerklass/MeerFish.

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arXiv2025

A quadratic estimator view of the transfer function correction in intensity mapping surveys

In single dish neutral hydrogen (HI) intensity mapping, signal separation methods such as principal component analysis (PCA) are used to clean the astrophysical foregrounds. PCA induces a signal loss in the estimated power spectrum, which can be corrected by a transfer function (TF). By injecting mock signals of HI into the data and performing the PCA cleaning, we can use the cleaned mock HI signal to cross-correlate with the original mock, and estimate the signal loss as a TF, ${T}(\vec{k})$. As expected, a correction of ${T} (\vec{k})^{-1}$ restores the cross-power between the HI and optical galaxies. However, contrary to intuition, the HI autopower also requires a ${T}(\vec{k})^{-1}$ correction, not ${T}(\vec{k})^{-2}$. The ${T}(\vec{k})^{-1}$ correction is only known empirically through simulations. In this Letter, we show that the ${T}(\vec{k})^{-1}$ correction in autopower is universal, and can be analytically proven using the quadratic estimator formalism through window function normalization. The normalization can also be used to determine the TF correction for any type of linear process. Using the window function, we demonstrate that PCA induces mode-mixing in the power spectrum estimation, which may lead to biases in the model inference.

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arXiv2025

Emission-line Stacking of 21cm Intensity Maps with MeerKLASS: Inference Pipeline and Application to the L-band Deep-field Data

We present a novel analysis of observational systematics through the emission-line stacking of the MeerKLASS L-band deep-field intensity maps, following the detection in arXiv:2407.21626. A stacking signal is obtained by stacking the 21cm intensity map cubelets around the galaxy positions from the GAMA survey at $0.39\lesssim z \lesssim0.46$. An extensive simulation framework is built to study the viability of the stacking detection, the covariance estimation, and the model inference, which are then applied to the data. The statistical significance of the detection is $8.66\sigma$ when averaged into an angular map, and $7.45\sigma$ when averaged into a spectrum. The stacked spectrum exhibits an oscillating component of systematics, and we provide evidence that these systematics are a convolutional effect on the map data. The oscillation frequency matches the diffraction from the secondary reflector into the primary beam of the MeerKAT telescope. Bayesian inference can be used to constrain the systematics and the average HI emission of the galaxies. The fitting of the parameters gives a constraint on the systematics frequency $\nu_{\rm sys}\,[{\rm MHz}] = 17.90^{+6.53}_{-4.27}$. The posterior of the systematics amplitude reaches the wide prior and gives $A_{\rm sys}=0.50^{+0.33}_{-0.33}$. A tentative measurement of the average HI mass of the sources is achieved at $\log_{10}[\langle M_{HI}\rangle/M_\odot ]=9.84^{+0.48}_{-0.59}$, which is an underestimation limited by the narrow redshift bin, the strong degeneracy with the systematics, and the low-density galaxy sample. These shortfalls will be resolved for future MeerKLASS data to enable accurate measurements of the HI density through stacking of intensity maps.

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arXiv2025

Cosmology with ESO-SKAO Synergies

We discuss the possible synergies for cosmology between SKAO and ESO facilities, focusing on the combinations SKA-Mid with the Multi-Object Spectrograph Telescope (4MOST) instrument built for ESO's Visible and Infrared Survey Telescope for Astronomy (VISTA), and SKA-Low with ESO's Extremely Large Telescope (ELT) multi-object spectrograph MOSAIC. Combining multiple tracers allows for tackling systematics and lifting parameter degeneracies. It will play a crucial role in the pursuit of precision cosmology.

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arXiv2025

HI Intensity Mapping with the MIGHTEE Survey: First Results of the HI Power Spectrum

We present the first results of the HI intensity mapping power spectrum analysis with the MeerKAT International GigaHertz Tiered Extragalactic Exploration (MIGHTEE) survey. We use data covering $\sim$4 square degrees in the COSMOS field using a frequency range 962.5 MHz to 1008.42 MHz, equivalent to HI emission in $0.4<z<0.48$. The data consists of 15 pointings with a total of 94.2 hours on-source. We verify the suitability of the MIGHTEE data for HI intensity mapping by testing for residual systematics across frequency, baselines and pointings. We also vary the window used for HI signal measurements and find no significant improvement using stringent Fourier mode cuts. Averaging in the power spectrum domain, i.e. using incoherent averaging, we calculate the first upper limits from MIGHTEE on the HI power spectrum at scales 0.5 Mpc$^{-1} \lesssim k \lesssim$ 10 Mpc$^{-1}$. We obtain the best 1$\sigma$ upper limit of 28.6 mK$^{2}$Mpc${^3}$ on $k\sim$2 Mpc$^{-1}$. Our results are consistent with the power spectrum detected with observations in the DEEP2 field with MeerKAT. The data we use here constitutes a small fraction of the MIGHTEE survey and demonstrates that combined analysis of the full MIGHTEE survey can potentially detect the HI power spectrum at $z\lesssim0.5$ in the range 0.1 Mpc$^{-1} \lesssim k \lesssim$ 10 Mpc$^{-1}$ or quasi-linear scales.

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arXiv2024

MeerKLASS L-band deep-field intensity maps: entering the HI dominated regime

We present results from MeerKAT single-dish HI intensity maps, the final observations to be performed in L-band in the MeerKAT Large Area Synoptic Survey (MeerKLASS) campaign. The observations represent the deepest single-dish HI intensity maps to date, produced from 41 repeated scans over $236\,{\rm deg}^2$, providing 62 hours of observational data for each of the 64 dishes before flagging. By introducing an iterative self-calibration process, the estimated thermal noise of the reconstructed maps is limited to ${\sim}\,1.21\,$mK ($1.2\,\times$ the theoretical noise level). This thermal noise will be sub-dominant relative to the HI fluctuations on large scales ($k\,{\lesssim}\,0.15\,h\,\text{Mpc}^{-1}$), which demands upgrades to power spectrum analysis techniques, particularly for covariance estimation. In this work, we present the improved MeerKLASS analysis pipeline, validating it on both a suite of mock simulations and a small sample of overlapping spectroscopic galaxies from the Galaxy And Mass Assembly (GAMA) survey. Despite only overlapping with ${\sim}\,25\%$ of the MeerKLASS deep field, and a conservative approach to covariance estimation, we still obtain a ${>}\,4\,\sigma$ detection of the cross-power spectrum between the intensity maps and the 2269 galaxies at the narrow redshift range $0.39\,{<}\,z\,{<}\,0.46$. We briefly discuss the HI auto-power spectrum from this data, the detection of which will be the focus of follow-up work. For the first time with MeerKAT single-dish intensity maps, we also present evidence of HI emission from stacking the maps onto the positions of the GAMA galaxies.

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arXiv2024

Reionization Parameter Inference from 3D Minkowski Functionals of the 21 cm Signals

The Minkowski Functionals (MFs), a set of topological summary statistics, have emerged as a powerful tool for extracting non-Gaussian information. We investigate the prospect of constraining the reionization parameters using the MFs of the 21 cm brightness temperature field from the epoch of reionization (EoR). Realistic effects, including thermal noise, synthesized beam, and foreground avoidance, are applied to the mock observations from the radio interferometric array experiments such as the Hydrogen Epoch of Reionization Array (HERA) and the Square Kilometre Array (SKA). We demonstrate that the MFs of the 21 cm signal measured with SKA-Low can be used to distinguish different reionization models, whereas the MF measurement with a HERA-like array cannot be made accurately enough. We further forecast the accuracies with which the MF measurements can place constraints on reionization parameters, using the standard MCMC analysis for parameter inference based on forward modeling. We find that for SKA-Low observation, MFs provide unbiased estimations of the reionization parameters with accuracies comparable to the power spectrum (PS) analysis. Furthermore, joint constraints using both MFs and PS can improve the constraint accuracies by up to $30\%$ compared to those with the PS alone. Nevertheless, the constraint accuracies can be degraded if the EoR window is shrunk with strong foreground avoidance. Our analysis demonstrates the promise of MFs as a set of summary statistics that extract complementary information from the 21 cm EoR field to the two-point statistics, which suggests a strong motivation for incorporating the MFs into the data analysis of future 21 cm observations.

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arXiv2024

Power spectrum multipoles and clustering wedges during the Epoch of Reionization

We study the viability of using power spectrum clustering wedges as summary statistics of 21cm surveys during the Epoch of Reionization (EoR). For observations in a wide redshift range $z\sim 7-9$ corresponding to a line-of-sight scale of $\sim 500$Mpc, the power spectrum is subject to anisotropic effects due to the evolution along the light-of-sight. Information on the physics of reionization can be extracted from the anisotropy using the power spectrum multipoles. Signals of the power spectrum monopole are highly correlated at scales smaller than the typical ionization bubble, which can be disentangled by including higher-order multipoles. By simulating observations of the low frequency part of the Square Kilometre Array (SKA) Observatory, we find that the sampling of the cylindrical wavenumber $k$-space is highly non-uniform due to the baseline distribution, i.e. the distribution of antenna pairs sampling different transverse ${k}_\perp$ scales. Measurements in clustering wedges partition the cylindrical $k$-space into different radial $k_\parallel$ scales, and can be used for isolating parts of $k$-space with relatively uniform sampling, allowing for more precise parameter inference. Using Fisher Matrix forecasts, we find that the reionization model can be inferred with per-cent level precision with $\sim 120$hrs of integration time using SKA-Low. Compared to model inference using only the power spectrum monopole above the foreground wedge, model inference using multipole power spectra in clustering wedges yields a factor of $\sim 3$ improvement on the marginalised 1D parameter constraints.

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arXiv2023

Detecting the HI Power Spectrum in the Post-Reionization Universe with SKA-Low

We present a survey strategy to detect the neutral hydrogen (HI) power spectrum at $5<z<6$ using the SKA-Low radio telescope in presence of foregrounds and instrumental effects. We simulate observations of the inherently weak HI signal post-reionization with varying levels of noise and contamination with foreground amplitudes equivalent to residuals after sky model subtraction. We find that blind signal separation methods on imaged data are required in order to recover the HI signal at large cosmological scales. Comparing different methods of foreground cleaning, we find that Gaussian Process Regression (GPR) performs better than Principle Component Analysis (PCA), with the key difference being that GPR uses smooth kernels for the total data covariance. The integration time of one field needs to be larger than $\sim 250$ h to provide large enough signal-to-noise ratio (SNR) to accurately model the data covariance for foreground cleaning. Images within the primary beam field-of-view give measurements of the HI power spectrum at scales $k\sim 0.02\,{\rm Mpc^{-1}}-0.3\,{\rm Mpc^{-1} }$ with SNR $\sim 2-5$ in $\Delta[{\rm log}( k/{\rm Mpc^{-1}})] = 0.25$ bins assuming an integration time of $600$ h. Systematic effects, which introduce small-scale fluctuations across frequency channels, need to be $\lesssim 5\times 10^{-5}$ to enable unbiased measurements outside the foreground wedge. Our results provide an important validation towards using the SKA-Low array for measuring the HI power spectrum in the post-reionization Universe.

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arXiv2023

A direct detection of neutral hydrogen intensity mapping on Mpc scales at $z\approx 0.32$ and $z\approx 0.44$

We report the detection of the cosmological power spectrum using the intensity mapping signal from 21-cm emission of neutral hydrogen (HI), derived from interferometric observations with the L-band receivers of the MeerKAT radio telescope. Intensity mapping is a promising technique to map the three-dimensional matter distribution of the Universe at radio frequencies and probe the underlying Cosmology. So far, detections have only been achieved through cross-correlations with galaxy surveys. Here we present independent measurements of the HI power spectrum at redshifts $0.32$ and $0.44$ with the foreground avoidance method. We utilize two distinct frameworks for mitigating systematics, where a conservative baseline flagging based approach achieves detections at $3.2\sigma$ and $3.5\sigma$, and a power spectrum based flagging method enhances the significance to $5.9\sigma$ and $9.18\sigma$, respectively. The information contained in the power spectrum measurements allows us to probe the parameters of the HI mass function and HI halo model. These results are a significant step towards precision cosmology with HI intensity mapping using the new generation of radio telescopes.

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