21-cm Power Spectrum Research Articles

A galaxy-free phenomenological model for the 21-cm power spectrum during reionization

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

The large-scale 21-cm power spectrum from reionization

ABSTRACT Radio interferometers, such as the Low-Frequency Array and the future Square Kilometre Array, are attempting to measure the spherically averaged 21-cm power spectrum from the epoch of reionization. Understanding of the dominant physical processes which influence the power spectrum at each length-scale is therefore crucial for interpreting any future detection. We study a decomposition of the 21-cm power spectrum and quantify the evolution of its constituent terms for a set of numerical and semi-numerical simulations of a volume of (714 Mpc)3, focusing on large scales with k ≲ 0.3 Mpc−1. We find that after ∼10 per cent of the universe has been ionized, the 21-cm power spectrum follows the power spectrum of neutral hydrogen fluctuations, which itself beyond a certain scale follows the matter power spectrum. Hence the signal has a two-regime form where the large-scale signal is a biased version of the cosmological density field, and the small-scale power spectrum is determined by the astrophysics of reionization. We construct a bias parameter to investigate the relation between the large-scale 21-cm signal and the cosmological density field. We find that the transition scale between the scale-independent and scale-dependent bias regimes is directly related to the value of the mean free path of ionizing photons (λMFP), and is characterised by the empirical formula ktrans ≈ 2/λMFP. Furthermore, we show that the numerical implementation of the mean free path effect has a significant impact on the shape of this transition. Most notably, the transition is more gradual if the mean free path effect is implemented as an absorption process rather than as a barrier.

Improved treatments of the ionizing photon mean free path in seminumerical simulations of reionization

ABSTRACT Efficient and accurate simulations of the reionization epoch are crucial to exploring the vast uncharted parameter space that will soon be constrained by measurements of the 21-cm power spectrum. One of these parameters, Rmax, is meant to characterize the absorption of photons by residual neutral gas inside of ionized regions, but has historically been implemented in a very simplistic fashion acting only as a maximum distance that ionizing photons can travel. We leverage the correspondence between excursion set methods and the integrated flux from ionizing sources to define two physically motivated prescriptions of the mean free path (MFP) of ionizing photons that smoothly attenuate the contribution from distant sources. Implementation of these methods in seminumerical reionization codes requires only modest additional computational effort due to the fact that spatial filtering is still performed on scales larger than the characteristic absorption distance. We find that our smoothly defined MFP prescriptions more effectively suppress large-scale structures in the ionization field in seminumerical reionization simulations compared to the standard Rmax approach, and the magnitude of the MFP modulates the power spectrum in a much smoother manner. We show that this suppression of large-scale power is significant enough to be relevant for upcoming 21-cm power spectrum observations. Finally, we show that in our model, the MFP plays a larger role in regulating the reionization history than in models using Rmax.

Improving constraints on the reionization parameters using 21-cm bispectrum

Radio interferometric experiments aim to constrain the reionization model parameters by measuring the 21-cm signal statistics, primarily the power spectrum. However the Epoch of Reionization (EoR) 21-cm signal is highly non-Gaussian, and this non-Gaussianity encodes important information about this era. The bispectrum is the lowest order statistic able to capture this inherent non-Gaussianity. Here we are the first to demonstrate that bispectra for large and intermediate length scales and for all unique k-triangle shapes provide tighter constraints on the EoR parameters compared to the power spectrum or the bispectra for a limited number of shapes of k-triangles. We use the Bayesian inference technique to constrain EoR parameters. We have also developed an Artificial Neural Network (ANN) based emulator for the EoR 21-cm power spectrum and bispectrum which we use to remarkably speed up our parameter inference pipeline. Here we have considered the sample variance and the system noise uncertainties corresponding to 1000 hrs of SKA-Low observations for estimating errors in the signal statistics. We find that using all unique k-triangle bispectra improves the constraints on parameters by a factor of 2 – 4 (depending on the stage of reionization) over the constraints that are obtained using power spectrum alone.

Extracting the 21-cm power spectrum and the reionization parameters from mock data sets using artificial neural networks

ABSTRACT Detection of the H i 21-cm power spectrum is one of the key science drivers of several ongoing and upcoming low-frequency radio interferometers. However, the major challenge in such observations come from bright foregrounds, whose accurate removal or avoidance is key to the success of these experiments. In this work, we demonstrate the use of artificial neural networks (ANNs) to extract the H i 21-cm power spectrum from synthetic data sets and extract the reionization parameters from the H i 21-cm power spectrum. For the first time, using a suite of simulations, we present an ANN-based framework capable of extracting the H i signal power spectrum directly from the total observed sky power spectrum (which contains the 21-cm signal, along with the foregrounds and effects of the instrument). We have used a combination of two ANNs sequentially. In the first step, ANN1 predicts the 21-cm power spectrum directly from foreground corrupted synthetic data sets. In the second step, ANN2 predicts the reionization parameters from the predicted H i power spectra from ANN1. The two-step ANN framework can be used as an alternative method to extract the 21-cm power spectrum and the reionization parameters directly from foreground dominated data sets. Our ANN-based framework is trained at a redshift of 9.01, and for $\boldsymbol {k}$ modes in the range, $\rm {0.17\lt {\boldsymbol {k}}\lt 0.37~Mpc^{-1}}$. We have tested the network’s performance with mock data sets corrupted with thermal noise corresponding to 1080 h of observations of the SKA-1 LOW and HERA. We have recovered the H i power spectra from foreground dominated synthetic data sets, with an accuracy of $\approx 95{\!-\!}99{{\ \rm per\ cent}}$. We have achieved an accuracy of $\approx ~81{\!-\!}90{{\ \rm per\ cent}}$ and $\approx ~50{\!-\!}60{{\ \rm per\ cent}}$ for the predicted reionization parameters, for test sets corrupted with thermal noise corresponding to the SKA-1 LOW and HERA, respectively.

Shot noise and scatter in the star formation efficiency as a source of 21-cm fluctuations

ABSTRACT The 21-cm signal from cosmic dawn and the epoch of reionization probes the characteristics of the high redshift galaxy population. Many of the astrophysical properties of galaxies at high redshifts are currently unconstrained due to the lack of observations. This creates a vast space of possible astrophysical scenarios where the 21-cm signal needs to be modeled in order to plan for, and eventually fit, future observations. This is done with fast numerical methods which make simplifying approximations for the underlying physical processes. In this work, we quantify the effect of Poisson fluctuations and scatter in the star formation efficiency; while Poisson fluctuations are included in some works and not in others, scatter in the star formation efficiency is usually neglected, and all galaxies of a given mass are assumed to have the same properties. We show that both features can have a significant effect on the 21-cm power spectrum, most importantly in scenarios where the signal is dominated by massive galaxies. Scatter in the star formation efficiency does not simply enhance the effect of Poisson fluctuations; for example, we show that the power spectrum shape at cosmic dawn has a feature corresponding to the width of the galaxy brightness distribution. We also discuss some of the consequences for 21-cm imaging, and the signature of reduced correlation between the density and radiation fields.

The impact of the first galaxies on cosmic dawn and reionization

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

Detecting the non-Gaussianity of the 21-cm signal during reionization with the wavelet scattering transform

ABSTRACT Detecting the 21-cm hyperfine transition from neutral hydrogen in the intergalactic medium is our best probe for understanding the astrophysical processes driving the Epoch of Reionization (EoR). The primary means for a detection of this 21-cm signal is through a statistical measurement of the spatial fluctuations using the 21-cm power spectrum (PS). However, the 21-cm signal is non-Gaussian meaning the PS, which only measures the Gaussian fluctuations, is suboptimal for characterizing all of the available information. The upcoming Square Kilometre Array (SKA) will perform a deep, 1000 h observation over 100 deg2 specifically designed to recover direct images of the 21-cm signal. In this work, we use the Wavelet Scattering Transform (WST) to extract the non-Gaussian information directly from these 2D images of the 21-cm signal. The key advantage of the WST is its stability with respect to statistical noise for measuring non-Gaussian information, unlike the bispectrum whose statistical noise diverges. In this work, we specifically focus on introducing a novel method to isolate non-Gaussian information from an image and apply this methodology to individual mock 21-cm images to quantify the strength of the non-Gaussian information contained within a single image. For example, at 150 (177) MHz (z ∼ 8.5 and ∼7) for a fiducial reionization model we recover a signal to noise of ∼5 (8) for the non-Gaussian information assuming perfect foreground removal and ∼2 (3) assuming foreground wedge avoidance.

Optimising MWA EoR data processing for improved 21-cm power spectrum measurements—fine-tuning ionospheric corrections

AbstractThe redshifted cosmological 21-cm signal emitted by neutral hydrogen during the first billion years of the universe is much fainter relative to other galactic and extragalactic radio emissions, posing a great challenge towards detection of the signal. Therefore, precise instrumental calibration is a vital prerequisite for the success of radio interferometers such as the Murchison Widefield Array (MWA), which aim for a 21-cm detection. Over the previous years, novel calibration techniques targeting the power spectrum paradigm of EoR science have been actively researched and where possible implemented. Some of these improvements, for the MWA, include the accuracy of sky models used in calibration and the treatment of ionospheric effects, both of which introduce unwanted contamination to the EoR window. Despite sophisticated non-traditional calibration algorithms being continuously developed over the years to incorporate these methods, the large datasets needed for EoR measurements require high computational costs, leading to trade-offs that impede making use of these new tools to maximum benefit. Using recently acquired computation resources for the MWA, we test the full capabilities of the state-of-the-art calibration techniques available for the MWA EoR project, with a focus on both direction-dependent and direction-independent calibration. Specifically, we investigate improvements that can be made in the vital calibration stages of sky modelling, ionospheric correction, and compact source foreground subtraction as applied in the hybrid foreground mitigation approach (one that combines both foreground subtraction and avoidance). Additionally, we investigate a method of ionospheric correction using interpolated ionospheric phase screens and assess its performance in the power spectrum space. Overall, we identify a refined RTS calibration configuration that leads to an at least 2 factor reduction of the EoR window power contamination at the$0.1 \; \textrm{hMpc}^{-1}$scale. The improvement marks a step further towards detecting the 21-cm signal using the MWA and the forthcoming SKA low telescope.

Forecasts on interacting dark energy from the 21-cm angular power spectrum with BINGO and SKA observations

ABSTRACT Neutral hydrogen (H i) intensity mapping is a promising technique to probe the large-scale structure of the Universe, improving our understanding of the late-time accelerated expansion. In this work, we first scrutinize how an alternative cosmology, interacting dark energy (IDE), can affect the 21-cm angular power spectrum relative to the concordance ΛCDM model. We re-derive the 21-cm brightness temperature fluctuation in the context of such an interaction and uncover an extra new contribution. Then we estimate the noise level of three upcoming H i intensity mapping surveys, namely Baryon Acoustic Oscillations from Integrated Neutral Gas Observations (BINGO), Square Kilometre Array (SKA1)-MID Band 1 and Band 2, and employ a Fisher matrix approach to forecast their constraints on the IDE model. We find that while Planck 2018 maintains its dominion over early-Universe parameter constraints, BINGO and SKA1-MID Band 2 provide complementary bounding to the latest cosmic microwave background measurements on the dark energy equation of state w, the interacting strength λi and the reduced Hubble constant h, and that SKA1-MID Band 1 even outperforms Planck 2018 in these late-Universe parameter constraints. The expected minimum uncertainties are given by SKA1-MID Band 1 + Planck: $\sim 0.34{{\ \rm per\ cent}}$ on w, $\sim 0.22{{\ \rm per\ cent}}$ on h, $\sim 0.64{{\ \rm per\ cent}}$ on H i bias bHi, and an absolute uncertainty of about 3 × 10−4 (7 × 10−4) on λ1 (λ2). Moreover, we quantify the effects from systematics of the redshift bin number, redshift-space distortions, foreground residuals and uncertainties on the measured H i fraction, ΩHi(z). Our results indicate a bright prospect for H i intensity mapping surveys in constraining IDE, whether on their own or by synergies with other measurements.

Exploring the consequences of chromatic data excision in 21-cm epoch of reionization power spectrum observations

ABSTRACT We explore how chromatic radio frequency interference (RFI) flags affect 21-cm power spectrum measurements. We particularly study flags that are coarser than the analysis resolution. We find that such RFI flags produce excess power in the EoR window in much the same way as residual RFI. We use Fast Holographic Deconvolution (fhd) simulations to explain this as a result of chromatic disruptions in the interferometric sampling function of the array. We also use these simulations in conjunction with Error Propagated Power Spectrum with InterLeaved Observed Noise to show that without modifying current flagging strategies or implementing extremely accurate and complete foreground subtraction, 21-cm EoR experiments will fail to make a significant detection. As a mitigation strategy, we find that circumventing the chromatic structure altogether by flagging the entire analysis band when RFI is detected is simple to implement and highly successful. This demands a detection strategy with a low false-positive rate in order to prevent excessive data loss.

Extracting the astrophysics of reionization from the Lyα forest power spectrum: a first forecast

ABSTRACT The impact of cosmic reionization on the Lyα forest power spectrum has recently been shown to be significant even at low redshifts (z ∼ 2). This memory of reionization survives cosmological time-scales because high-entropy mean-density gas is heated to ∼3 × 104 K by reionization, which is inhomogeneous, and subsequent shocks from denser regions. In the near future, the first measurements of the Lyα forest 3D power spectrum will be very likely achieved by upcoming observational efforts such as the Dark Energy Spectroscopic Instrument (DESI). In addition to abundant cosmological information, these observations have the potential to extract the astrophysics of reionization from the Lyα forest. We forecast, for the first time, the accuracy with which the measurements of Lyα forest 3D power spectrum can place constraints on the reionization parameters with DESI. Specifically, we demonstrate that the constraints on the ionization efficiency, ζ, and the threshold mass for haloes that host ionizing sources, mturn, will have the 1σ error at the level of ζ = 25.0 ± 11.6 and $\log _{10} (m_{\rm turn}/{\rm M}_\odot) = 8.7^{+0.36}_{-0.70}$, respectively. The Lyα forest 3D power spectrum will thus provide an independent probe of reionization, probably even earlier in detection with DESI, with a sensitivity only slightly worse than the upcoming 21-cm power spectrum measurement with the Hydrogen Epoch of Reionization Array (HERA), i.e. σDESI/σHERA ≈ 1.5 for ζ and σDESI/σHERA ≈ 2.0 for log10(mturn/M⊙). Nevertheless, the Lyα forest constraint will be improved about three times tighter than the current constraint from reionization observations with high-z galaxy priors, i.e. σDESI/σcurrent ≈ 1/3 for ζ.

Implications of the z > 5 Lyman-α forest for the 21-cm power spectrum from the epoch of reionization

ABSTRACT Our understanding of the intergalactic medium at redshifts z = 5–6 has improved considerably in the last few years due to the discovery of quasars with z > 6 that enable Lyman-α forest studies at these redshifts. A realization from this has been that hydrogen reionization could end much later than previously thought, so that large ‘islands’ of cold, neutral hydrogen could exist in the IGM at redshifts z = 5–6. By using radiative transfer simulations of the IGM, we consider the implications of the presence of these neutral hydrogen islands for the 21-cm power spectrum signal and its potential detection by experiments such as hera, ska, lofar, and mwa. In contrast with previous models of the 21-cm signal, we find that thanks to the late end of reionization the 21-cm power in our simulation continues to be as high as $\Delta ^2_{21}=10~\mathrm{mK}^2$ at k ∼ 0.1 h cMpc−1 at z = 5–6. This value of the power spectrum is several orders of magnitude higher than that in conventional models considered in the literature for these redshifts. Such high values of the 21-cm power spectrum should be detectable by hera and ska1-low in ∼1000 h, assuming optimistic foreground subtraction. This redshift range is also attractive due to relatively low sky temperature and potentially greater abundance of multiwavelength data.

A 21-cm power spectrum at 48 MHz, using the Owens Valley Long Wavelength Array

ABSTRACT The Large-aperture Experiment to detect the Dark Age (LEDA) was designed to measure the 21-cm signal from neutral hydrogen at Cosmic Dawn, z ≈ 15–30. Using observations made with the ≈ 200 m diameter core of the Owens Valley Radio Observatory Long Wavelength Array (OVRO–LWA), we present a 2D cylindrical spatial power spectrum for data at 43.1–53.5 MHz (zmedian ≈ 28) incoherently integrated for 4 h, and an analysis of the array sensitivity. Power from foregrounds is localized to a ‘wedge’ within k⊥, $k_\parallel$ space. After calibration of visibilities using five bright compact sources including Vir A, we measure Δ2(k) ≈ 2 × 1012 mK2 outside the foreground wedge, where an uncontaminated cosmological signal would lie, in principle. The measured Δ2(k) is an upper limit that reflects a combination of thermal instrumental and sky noise, and unmodelled systematics that scatter power from the wedge, as will be discussed. By differencing calibrated visibilities for close pairs of frequency channels, we suppress foreground sky structure and systematics, extract thermal noise, and use a mix of coherent and incoherent integration to simulate a noise-dominated power spectrum for a 3000 h observation and z = 16−37. For suitable calibration quality, the resulting noise level, Δ2(k) ≈ 100 mK2 (k = 0.3 Mpc−1), would be sufficient to detect peaks in the 21-cm spatial power spectrum due to early Ly-α and X-ray sources, as predicted for a range of theoretical model parameters.

Halo model approach for the 21-cm power spectrum at cosmic dawn

Prior to the epoch of reionisation, the 21-cm signal of the cosmic dawn is dominated by the Lyman-$\alpha$ coupling and gas temperature fluctuations caused by the first sources of radiation. While early efforts to model this epoch relied on analytical techniques, the community quickly transitioned to more expensive semi-numerical models. Here, we re-assess the viability of simpler approaches that allow for rapid explorations of the vast astrophysical parameter space. We propose a new analytical method to calculate the 21-cm power spectrum based on the framework of the halo model. Both the Lyman-$\alpha$ coupling and temperature fluctuations are described by overlapping radiation flux profiles that include spectral red-shifting and source attenuation due to look-back (light-cone) effects. The 21-cm halo model is compared to the semi-numerical code 21cmFAST exhibiting generally good agreement, i.e., the power spectra differ by less than a factor of three over a large range of $k$-modes and redshifts. We show that the remaining differences between the two methods are comparable to the expected variations from modelling uncertainties associated with the abundance, bias, and accretion rates of haloes. While these current uncertainties must be reduced in the future, our work suggests that inference at acceptable accuracy will become feasible with very efficient halo models of the cosmic dawn.

ETHOS ‐ an effective theory of structure formation: Impact of dark acoustic oscillations on cosmic dawn

Upcoming data of the 21-cm hydrogen line during cosmic dawn ($z\sim 10-30$) will revolutionize our understanding of the astrophysics of the first galaxies. Here we present a case study on how to exploit those same measurements to learn about the nature of dark matter (DM) at small scales. Focusing on the Effective Theory of Structure Formation (ETHOS) paradigm, we run a suite of simulations covering a broad range of DM microphysics, connecting the output of $N$-body simulations to dedicated 21-cm simulations to predict the evolution of the 21-cm signal across the entire cosmic dawn. We find that observatories targeting both the global signal and the 21-cm power spectrum are sensitive to all ETHOS models we study, and can distinguish them from CDM if the suppression wavenumber is smaller than $k\approx 300\, h/$Mpc, even when accounting for feedback with a phenomenological model. This is an order of magnitude smaller comoving scales than currently constrained by other data sets, including the Lyman-$\alpha$ forest. Moreover, if a prospective 21-cm detection confirmed a deficiency of power at small scales, we show that ETHOS models with strong dark acoustic oscillations can be discriminated from the pure suppression of warm dark matter, showing the power of 21-cm data to understand the behavior of DM at the smallest physical scales.

Quantiles as robust probes of non-Gaussianity in 21-cm images

ABSTRACT The epoch in which the first stars and galaxies formed is among the most exciting unexplored eras of the Universe. A major research effort is focused on probing this era with the 21-cm spectral line of hydrogen. While most research works focus on statistics like the 21-cm power spectrum or the sky-averaged global signal, there are other ways to analyse tomographic 21-cm maps, which may lead to novel insights. We suggest statistics based on quantiles as a method to probe non-Gaussianities of the 21-cm signal. We show that they can be used in particular to probe the variance, skewness, and kurtosis of the temperature distribution, but are more flexible and robust than these standard statistics. We test these statistics on a range of possible astrophysical models, including different galactic halo masses, star formation efficiencies, and spectra of the X-ray heating sources, plus an exotic model with an excess early radio background. Simulating data with angular resolution and thermal noise as expected for the Square Kilometre Array (SKA), we conclude that these statistics can be measured out to redshifts above 20 and offer a promising statistical method for probing early cosmic history.

Modelling population III stars for seminumerical simulations

ABSTRACT Theoretically modelling the 21-cm signals caused by Population III stars (Pop III stars) is the key to extracting fruitful information on Pop III stars from current and forthcoming 21-cm observations. In this work, we develop a new module of Pop III stars in which the escape fractions of ionizing photons and Lyman–Werner (LW) photons, photoheating by UV radiation, and LW feedback are consistently incorporated. By implementing the module into a public 21-cm seminumerical simulation code, 21cmfast, we demonstrate 21-cm signal calculations, neglecting X-ray heating and focusing on the high redshifts when we assume that the formation of Pop III stars dominates that of other populations. What we find is that the contribution from Pop III stars to cosmic reionization significantly depends on the treatment of the escape fraction. With our escape fraction model, Pop III stars hardly contribute to reionization because less massive haloes, whose escape fraction are high, cannot host Pop III stars due to LW feedback. On the other hand, massive minihaloes contribute to reionization with the conventional constant escape fraction. We also find that UV photoheating has non-negligible impact on the 21-cm global signal and the 21-cm power spectrum if the ionization fraction of the Universe is higher than roughly 1 per cent. In this case, the strength of the 21-cm global signal depends on the photoheating efficiency and thus on the Pop III star mass. We conclude that detailed modelling of Pop III stars is imperative to predict 21-cm observables accurately for future observations.

Demonstrating the Tapered Gridded Estimator (TGE) for the Cosmological HI 21-cm Power Spectrum using 150 MHz GMRT observations

Abstract We apply the Tapered Gridded Estimator (TGE) for estimating the cosmological 21-cm power spectrum from 150 MHz GMRT observations which corresponds to the neutral hydrogen (HI) at redshift z = 8.28. Here TGE is used to measure the Multi-frequency Angular Power Spectrum (MAPS) Cℓ(Δν) first, from which we estimate the 21-cm power spectrum P(k⊥, k∥). The data here are much too small for a detection, and the aim is to demonstrate the capabilities of the estimator. We find that the estimated power spectrum is consistent with the expected foreground and noise behaviour. This demonstrates that this estimator correctly estimates the noise bias and subtracts this out to yield an unbiased estimate of the power spectrum. More than $47\%$ of the frequency channels had to be discarded from the data owing to radio-frequency interference, however the estimated power spectrum does not show any artifacts due to missing channels. Finally, we show that it is possible to suppress the foreground contribution by tapering the sky response at large angular separations from the phase center. We combine the k modes within a rectangular region in the ‘EoR window’ to obtain the spherically binned averaged dimensionless power spectra Δ2(k) along with the statistical error σ associated with the measured Δ2(k). The lowest k-bin yields Δ2(k) = (61.47)2 K2 at k = 1.59 Mpc−1, with σ = (27.40)2 K2. We obtain a 2 σ upper limit of (72.66)2 K2 on the mean squared HI 21-cm brightness temperature fluctuations at k = 1.59 Mpc−1.

Interpreting LOFAR 21-cm signal upper limits at z ≈ 9.1 in the context of high-z galaxy and reionization observations

ABSTRACT Using the latest upper limits on the 21-cm power spectrum at z ≈ 9.1 from the Low Frequency Array (LOFAR), we explore the regions of parameter space which are inconsistent with the data. We use 21cmmc, a Monte Carlo Markov chain sampler of 21cmfast which directly forward models the three dimensional (3D) cosmic 21-cm signal in a fully Bayesian framework. We use the astrophysical parametrization from 21cmfast, which includes mass-dependent star formation rates and ionizing escape fractions as well as soft-band X-ray luminosities to place limits on the properties of the high-z galaxies. Further, we connect the disfavoured regions of parameter space with existing observational constraints on the Epoch of Reionization such as ultra-violet (UV) luminosity functions, background UV photoionization rate, intergalactic medium (IGM) neutral fraction, and the electron scattering optical depth. We find that all models exceeding the 21-cm signal limits set by LOFAR at z ≈ 9.1 are excluded at ≳2σ by other probes. Finally, we place limits on the IGM spin temperature from LOFAR, disfavouring at 95 per cent confidence spin temperatures below ∼2.6 K across an IGM neutral fraction range of $0.15 \lesssim \bar{x}_{\rm H\, \rm {\small I}} \lesssim 0.6$. Note, these limits are only obtained from 141 h of data in a single redshift bin. With tighter upper limits, across multiple redshift bins expected in the near future from LOFAR, more viable models will be ruled out. Our approach demonstrates the potential of forward modelling tools such as 21cmmc in combining 21-cm observations with other high-z probes to constrain the astrophysics of galaxies.