Multi-frequency Angular Power Spectrum Research Articles

Calibration requirement for Epoch of Reionization 21-cm signal observation. Part III. Bias and variance in uGMRT ELAIS-N1 field power spectrum

Power spectrum of H i 21-cm radiation is one of the promising probes to study large scale structure of the universe and understand galaxy formation and evolution. The presence of foregrounds, that are orders of magnitude larger in the same frequency range of the redshifted 21-cm signal has been one of the largest observational challenges. The foreground contamination also hinders the calibration procedures and introduces residual calibration errors in the interferometric data. It has been shown that the calibration errors can introduce bias in the 21-cm power spectrum estimates and introduce additional systematics. In this work, we assess the efficacy of 21-cm power spectrum estimation for the uGMRT Band-3 observations of the ELAIS-N1 field. We first evaluate the statistics of the residual gain errors and perform additional flagging based on these statistics. We then use an analytical method to estimate the bias and variance in the power spectrum. We found that (a) the additional flagging based on calibration accuracy help reduce the bias and systematics in the power spectrum, (b) the majority of the systematics at the lower angular scales, ℓ< 6000, are due to the residual gain errors, (c) for the uGMRT baseline configuration and system parameters, the standard deviation is always higher than the bias in the power spectrum estimates. Based on our analysis we observe that for an angular multipole of ℓ∼3000, 2000 hours of `on source time' is required with the uGMRT to detect redshifted 21-cm signal at 3-σ significance from a redshift of 2.55. In this work we only consider the power spectrum measurement in the plane of the sky, an assessment of residual gain statistics and its effect on multifrequency angular power spectrum estimation for the uGMRT and the SKA like telescopes will be presented in a companion paper.

Towards 21-cm intensity mapping at z = 2.28 with uGMRT using the tapered gridded estimator – IV. Wide-band analysis

ABSTRACT We present a Wide-band tapered gridded estimator (TGE), which incorporates baseline migration and variation of the primary beam pattern for neutral hydrogen ($H\, {\small I}$) 21-cm intensity mapping (IM) with large frequency bandwidth radio-interferometric observations. Here we have analysed $394-494 \, {\rm MHz}$ (z = 1.9–2.6) uGMRT data to estimate the Multifrequency Angular Power Spectrum (MAPS) Cℓ(Δν) from which we have removed the foregrounds using the polynomial fitting (PF) and Gaussian Process Regression (GPR) methods developed in our earlier work. Using the residual Cℓ(Δν) to estimate the mean-squared 21-cm brightness temperature fluctuation Δ2(k), we find that this is consistent with 0 ± 2σ in several k bins. The resulting 2σ upper limit $\Delta ^2(k) \lt (4.68)^2 \, \rm {mK^2}$ at $k=0.219\, \rm {Mpc^{-1}}$ is nearly 15 times tighter than earlier limits obtained from a smaller bandwidth ($24.4 \, {\rm MHz}$) of the same data. The 2σ upper limit $[\Omega _{H\, {\small I}} b_{H\, {\small I}}] \lt 1.01 \times 10^{-2}$ is within an order of magnitude of the value expected from independent estimates of the $H\, {\small I}$ mass density $\Omega _{H\, {\small I}}$ and the $H\, {\small I}$ bias $b_{H\, {\small I}}$. The techniques used here can be applied to other telescopes and frequencies, including $\sim 150 \, {\rm MHz}$ Epoch of Reionization observations.

Towards 21-cm intensity mapping at z = 2.28 with uGMRT using the tapered gridded estimator – III. Foreground removal

ABSTRACT Neutral hydrogen (${\rm H\, \small {I}}$) 21-cm intensity mapping (IM) is a promising probe of the large-scale structures in the Universe. However, a few orders of magnitude brighter foregrounds obscure the IM signal. Here, we use the tapered gridded estimator to estimate the multifrequency angular power spectrum Cℓ(Δν) from a $24.4\hbox{-} \rm {MHz}$ bandwidth upgraded Giant Metrewave Radio Telescope Band 3 data at $432.8\ \rm {MHz}$. In Cℓ(Δν) foregrounds remain correlated across the entire Δν range, whereas the 21-cm signal is localized within Δν ≤ [Δν] (typically, 0.5–1 MHz). Assuming the range Δν &amp;gt; [Δν] to have minimal 21-cm signal, we use Cℓ(Δν) in this range to model the foregrounds. This foreground model is extrapolated to Δν ≤ [Δν], and subtracted from the measured Cℓ(Δν). The residual [Cℓ(Δν)]res in the range Δν ≤ [Δν] is used to constrain the 21-cm signal, compensating for the signal loss from foreground subtraction. [Cℓ(Δν)]res is found to be noise-dominated without any trace of foregrounds. Using [Cℓ(Δν)]res, we constrain the 21-cm brightness temperature fluctuations Δ2(k), and obtain the 2σ upper limit $\Delta _{\rm UL}^2(k)\le (18.07)^2\ \rm {mK^2}$ at $k=0.247\ \rm {Mpc}^{-1}$. We further obtain the 2σ upper limit $[\Omega _{{\rm H\, \small {I}}}b_{{\rm H\, \small {I}}}]_{\rm UL}\le 0.022$, where $\Omega _{{\rm H\, \small {I}}}$ and $b_{{\rm H\, \small {I}}}$ are the comoving ${\rm H\, \small {I}}$ density and bias parameters, respectively. Although the upper limit is nearly 10 times larger than the expected 21-cm signal, it is 3 times tighter over previous works using foreground avoidance on the same data.

Studying the multifrequency angular power spectrum of the cosmic dawn 21-cm signal

ABSTRACT The light-cone (LC) anisotropy arises due to cosmic evolution of the cosmic dawn (CD) 21-cm signal along the line-of-sight (LoS) axis of the observation volume. The LC effect makes the signal statistically non-ergodic along the LoS axis. The multifrequency angular power spectrum (MAPS) provides an unbiased alternative to the popular three-dimensional (3D) power spectrum as it does not assume statistical ergodicity along every direction in the signal volume. Unlike the 3D power spectrum which mixes the cosmic evolution of the 21-cm signal along the LoS k modes, MAPS keeps the evolution information disentangled. Here, we first study the impact of different underlying physical processes during CD on the behaviour of the 21-cm MAPS using simulations of various different scenarios and models. We also make error predictions in 21-cm MAPS measurements considering only the system noise and cosmic variance for mock observations of Hydrogen Epoch of Reionization Array (HERA), NenuFAR, and SKA-Low. We find that 100 h of HERA observations will be able to measure 21-cm MAPS at ≥3σ for ℓ ≲ 1000 with $0.1\, {\rm MHz}$ channel-width. The better sensitivity of SKA-Low allows reaching this sensitivity up to ℓ ≲ 3000. Note that due to the difference in the frequency coverage of the various experiments, the CD–epoch of reionization model considered for NenuFAR is different than those used for the HERA and SKA-Low predictions. Considering NenuFAR with the new model, measurements ≥2σ are possible only for ℓ ≲ 600 with $0.2\, {\rm MHz}$ channel-width and for a 10 times longer observation time of tobs = 1000 h. However, for the range 300 ≲ ℓ ≲ 600 and tobs = 1000 h more than 3σ measurements are still possible for NenuFAR when combining consecutive frequency channels within a 5 MHz band.

Towards 21-cm intensity mapping at z = 2.28 with uGMRT using the tapered gridded estimator – II. Cross-polarization power spectrum

ABSTRACT Neutral hydrogen (H i) 21-cm intensity mapping (IM) offers an efficient technique for mapping the large-scale structures in the Universe. We introduce the ‘Cross’ Tapered Gridded Estimator (Cross TGE), which cross-correlates two cross-polarizations (RR and LL) to estimate the multifrequency angular power spectrum Cℓ(Δν). We expect this to mitigate several effects like noise bias, calibration errors, etc., which affect the ‘Total’ TGE that combines the two polarizations. Here, we apply the Cross TGE on $24.4 \text{-} \rm {MHz}$-bandwidth uGMRT (upgraded Giant Metrewave Radio Telescope) Band 3 data centred at $432.8 \, \rm {MHz}$ aiming H i IM at z = 2.28. The measured Cℓ(Δν) is modelled to yield maximum likelihood estimates of the foregrounds and the spherical power spectrum P(k) in several k bins. Considering the mean squared brightness temperature fluctuations, we report a 2σ upper limit $\Delta _{\mathrm{ UL}}^{2}(k) \le (58.67)^{2} \, {\rm mK}^{2}$ at $k=0.804 \, {\rm Mpc}^{-1}$, which is a factor of 5.2 improvement on our previous estimate based on the Total TGE. Assuming that the H i traces the underlying matter distribution, we have modelled Cℓ(Δν) to simultaneously estimate the foregrounds and $[\Omega _{\rm{ H}\, {\small {I}}} b_{\rm{ H}\, {\small {I}}}]$, where $\Omega _{\rm{ H}\, {\small {I}}}$ and $b_{\rm{ H}\, {\small {I}}}$ are the H i density and linear bias parameters, respectively. We obtain a best-fitting value of $[\Omega _{\rm{ H}\, {\small {I}}}b_{\rm{ H}\, {\small {I}}}]^2 = 7.51\times 10^{-4} \pm 1.47\times 10^{-3}$ that is consistent with noise. Although the 2σ upper limit $[\Omega _{\rm{ H}\, {\small {I}}}b_{\rm{ H}\, {\small {I}}}]_{\mathrm{ UL}} \le 0.061$ is ∼50 times larger than the expected value, this is a considerable improvement over earlier works at this redshift.

Multi-frequency angular power spectrum of the 21 cm signal from the Epoch of Reionisation using the Murchison Widefield Array

Context. The Multi-frequency Angular Power Spectrum (MAPS) is an alternative to spherically averaged power spectra, and computes local fluctuations in the angular power spectrum without need for line-of-sight spectral transform. Aims. We aimed to test different approaches to MAPS and treatment of the foreground contamination, and compare with the spherically averaged power spectrum, and the single-frequency angular power spectrum. Methods. We applied the MAPS to 110 h of data in z = 6.2 − 7.5 obtained for the Murchison Widefield Array Epoch of Reionisation experiment to compute the statistical power of 21 cm brightness temperature fluctuations. In the presence of bright foregrounds, a filter was applied to remove large-scale modes prior to MAPS application, significantly reducing MAPS power due to systematics. Results. The MAPS showed a contrast of 102–103 to a simulated 21 cm cosmological signal for spectral separations of 0−4 MHz after application of the filter, reflecting results for the spherically averaged power spectrum. The single-frequency angular power spectrum was also computed. At z = 7.5 and l = 200, we found an angular power of 53 mK2, exceeding a simulated cosmological signal power by a factor of one thousand. Residual spectral structure, inherent to the calibrated data, and not spectral leakage from large-scale modes, was the dominant source of systematic power bias. The single-frequency angular power spectrum yielded slightly poorer results compared with the spherically averaged power spectrum, having applied a spectral filter to reduce foregrounds. Exploration of other filters may improve this result, along with consideration of wider bandwidths.

Towards 21-cm intensity mapping at z = 2.28 with uGMRT using the tapered gridded estimator I: Foreground avoidance

ABSTRACT The post-reionization (z ≤ 6) neutral hydrogen (H i) 21-cm intensity mapping signal holds the potential to probe the large-scale structures, study the expansion history, and constrain various cosmological parameters. Here, we apply the Tapered Gridded Estimator (TGE) to estimate P(k⊥, k∥) the power spectrum of the $z = 2.28\, (432.8\, {\rm MHz})$ redshifted 21-cm signal using a $24.4\, {\rm MHz}$ sub-band drawn from uGMRT Band 3 observations of European Large-Area ISO Survey-North 1 (ELAIS-N1). The TGE allows us to taper the sky response, which suppresses the foreground contribution from sources in the periphery of the telescope’s field of view. We apply the TGE on the measured visibility data to estimate the multifrequency angular power spectrum (MAPS) Cℓ(Δν) from which we determine P(k⊥, k∥) using maximum likelihood that naturally overcomes the issue of missing frequency channels (55 per cent here). The entire methodology is validated using simulations. For the data, using the foreground avoidance technique, we obtain a $2\, \sigma$ upper limit of $\Delta ^2(k) \le (133.97)^2 \, {\rm mK}^{2}$ for the 21-cm brightness temperature fluctuation at $k = 0.347 \, \textrm {Mpc}^{-1}$. This corresponds to $[\Omega _{\rm H\, {\small I}~}b_{\rm H\, {\small I}~}] \le 0.23$, where $\Omega _{\rm H\, {\small I}~}$ and $b_{\rm H\, {\small I}~}$, respectively, denote the cosmic H i mass density and the H i bias parameter. A previous work has analysed $8 \, {\rm MHz}$ of the same data at z = 2.19, and reported $\Delta ^{2}(k) \le (61.49)^{2} \, {\rm mK}^{2}$ and $[\Omega _{\rm H\, {\small I}~} b_{\rm H\, {\small I}~}] \le 0.11$ at $k=1 \, {\rm Mpc}^{-1}$. The upper limits presented here are still orders of magnitude larger than the expected signal corresponding to $\Omega _{\rm H\, {\small I}~} \sim 10^{-3}$ and $b_{\rm H\, {\small I}~} \sim 2$.

The multifrequency angular power spectrum in parameter studies of the cosmic 21-cm signal

ABSTRACT The light-cone effect breaks the periodicity and statistical homogeneity (ergodicity) along the line-of-sight direction of cosmological emission/absorption line surveys. The spherically averaged power spectrum (SAPS), which by definition assumes ergodicity and periodicity in all directions, can only quantify some of the second-order statistical information in the 3D light-cone signals, and therefore, gives a biased estimate of the true statistics. The multifrequency angular power spectrum (MAPS), by extracting more information from the data, does not rely on these assumptions. It is therefore better aligned with the properties of the signal. We have compared the performance of the MAPS and SAPS metrics for parameter estimation of a mock 3D light-cone observation of the 21-cm signal from the Epoch of Reionization. Our investigation is based on a simplified 3-parameter 21cmFAST model. We find that the MAPS produces parameter constraints, which are a factor of ∼2 more stringent than when the SAPS is used. The significance of this result does not change much even in the presence of instrumental noise expected for 128 h of SKA-Low observations. Our results therefore suggest that a parameter estimation framework based on the MAPS metric would yield superior results over one using the SAPS metric.

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.

Predictions for measuring the 21-cm multifrequency angular power spectrum using SKA-Low

ABSTRACT The light-cone effect causes the mean as well as the statistical properties of the redshifted 21-cm signal ${T_{\rm b}}(\hat{\boldsymbol {n}}, \nu)$ to change with frequency ν (or cosmic time). Consequently, the statistical homogeneity (ergodicity) of the signal along the line-of-sight (LoS) direction is broken. This is a severe problem particularly during the Epoch of Reionization (EoR) when the mean neutral hydrogen fraction ($\bar{x}_{\rm {H\,{\small I}}}$) changes rapidly as the Universe evolves. This will also pose complications for large bandwidth observations. These effects imply that the 3D power spectrum P(k) fails to quantify the entire second-order statistics of the signal as it assumes the signal to be ergodic and periodic along the LoS. As a proper alternative to P(k), we use the multifrequency angular power spectrum (MAPS) ${\mathcal {C}}_{\ell }(\nu _1,\nu _2)$, which does not assume the signal to be ergodic and periodic along the LoS. Here, we study the prospects for measuring the EoR 21-cm MAPS using future observations with the upcoming SKA-Low. Ignoring any contribution from the foregrounds, we find that the EoR 21-cm MAPS can be measured at a confidence level ≥5σ at angular scales ℓ ∼ 1300 for total observation time tobs ≥ 128 h across ∼44 MHz observational bandwidth. We also quantitatively address the effects of foregrounds on MAPS detectability forecast by avoiding signal contained within the foreground wedge in $({\boldsymbol {k}}_\perp , k_\parallel)$ plane. These results are very relevant for the upcoming large bandwidth EoR experiments as previous predictions were all restricted to individually analysing the signal over small frequency (or equivalent redshift) intervals.

Detailed study of ELAIS N1 field with the uGMRT – II. Source properties and spectral variation of foreground power spectrum from 300–500 MHz observations

ABSTRACT Understanding the low-frequency radio sky in depth is necessary to subtract foregrounds in order to detect the redshifted 21 cm signal of neutral hydrogen from the cosmic dawn, the epoch of reionization and the post-reionization era. In this second paper of the series, we present the upgraded Giant Metrewave Radio Telescope (uGMRT) observation of the ELAIS N1 field made at 300–500 MHz. The image covers an area of ∼1.8 deg2 and has a central background rms noise of ∼ 15 μJy beam−1. We present a radio source catalogue containing 2528 sources (with flux densities &gt; 100 μJy) and normalized source counts derived from that. A detailed comparison of detected sources with previous radio observations is shown. We discuss flux-scale accuracy, positional offsets, spectral index distribution and correction factors in source counts. The normalized source counts are in agreement with previous observations of the same field, as well as model source counts from the Square Kilometre Array Design Study simulation. It shows a flattening below ∼1 mJy that corresponds to a rise in populations of star-forming galaxies and radio-quiet active galactic nuclei. For the first time, we estimate the spectral characteristics of the angular power spectrum or multi-frequency angular power spectrum of diffuse Galactic synchrotron emission over a wide frequency bandwidth of 300–500 MHz from radio interferometric observations. This work demonstrates the improved capabilities of the uGMRT.

A Tapered Gridded Estimator (TGE) for the multifrequency angular power spectrum (MAPS) and the cosmological H i21-cm power spectrum

In this work we present a new approach to estimate the power spectrum $P({\bf k})$ of redshifted HI 21-cm brightness temperature fluctuations. The MAPS $C_{\ell}(\nu_a,\nu_b)$ completely quantifies the second order statistics of the sky signal under the assumption that the signal is statistically homogeneous and isotropic on the sky. Here we generalize an already existing visibility based estimator for $C_{\ell}$, namely TGE, to develop an estimator for $C_{\ell}(\nu_a,\nu_b)$. The 21-cm power spectrum is the Fourier transform of $C_{\ell}(\Delta \nu)$ with respect to $\Delta \nu=\mid \nu_a-\nu_b \mid$, and we use this to estimate $P({\bf k})$. Using simulations of $150 \, {\rm MHz}$ GMRT observations, we find that this estimator is able to recover $P(k)$ with an accuracy of $5-20 \%$ over a reasonably large $k$ range even when the data in $80 \%$ randomly chosen frequency channels is flagged.

A method to determine the evolution history of the mean neutral Hydrogen fraction

ABSTRACT The light-cone (LC) effect imprints the cosmological evolution of the redshifted 21-cm signal $T_{\rm b} (\hat{\boldsymbol {n}}, \nu)$ along the frequency axis that is the line-of-sight (LoS) direction of an observer. The effect is particularly pronounced during the epoch of reionization (EoR) when the mean hydrogen neutral fraction $\bar{x}_{\rm \rm{H\,{\small I}}}(\nu)$ falls rapidly as the universe evolves. The multifrequency angular power spectrum ${\mathcal {C}}_{\ell }(\nu _1,\nu _2)$ quantifies the entire second-order statistics of $T_{\rm b}(\hat{\boldsymbol {n}},\nu)$ considering both the systematic variation along ν due to the cosmological evolution and also the statistically homogeneous and isotropic fluctuations along all the three spatial directions encoded in $\hat{\boldsymbol {n}}$ and ν. Here, we propose a simple model where the systematic frequency (ν1, ν2) dependence of ${\mathcal {C}}_{\ell }(\nu _1,\nu _2)$ arises entirely due to the evolution of $\bar{x}_{\rm \rm{H\,{\small I}}}(\nu)$. This provides a new method to observationally determine the reionization history. Considering an LC simulation of the EoR 21-cm signal, we use the diagonal elements ν1 = ν2 of ${\mathcal {C}}_{\ell }(\nu _1,\nu _2)$ to validate our model. We demonstrate that it is possible to recover the reionization history across the entire observational bandwidth provided we have the value $\bar{x}_{\rm \rm{H\,{\small I}}}$ at a single frequency as an external input.

The Zeldovich approximation and wide-angle redshift-space distortions

The contribution of line-of-sight peculiar velocities to the observed redshift of objects breaks the translational symmetry of the underlying theory, modifying the predicted 2-point functions. These `wide angle effects' have mostly been studied using linear perturbation theory in the context of the multipoles of the correlation function and power spectrum. In this work we present the first calculation of wide angle terms in the Zeldovich approximation, which is known to be more accurate than linear theory on scales probed by the next generation of galaxy surveys. We present the exact result for dark matter and perturbatively biased tracers as well as the small angle expansion of the configuration- and Fourier-space two-point functions and the connection to the multi-frequency angular power spectrum. We compare different definitions of the line-of-sight direction and discuss how to translate between them. We show that wide angle terms can reach tens of percent of the total signal in a measurement at low redshift in some approximations, and that a generic feature of wide angle effects is to slightly shift the Baryon Acoustic Oscillation scale.

A spherical harmonic analysis of the Ooty Wide Field Array (OWFA) visibility signal

Considering redshifted $21$-cm intensity mapping with the upcoming OWFA whose field of view subtends $\sim 57^{\circ}$ in the N-S direction, we present a formalism which relates the measured visibilities to the spherical harmonic coefficients of the sky signal. We use this to calculate window functions which relate the two-visibility correlations {\it i.e.} the correlation between the visibilities measured at two baselines and two frequencies, to different multipoles of the multi-frequency angular power spectrum $C_{\ell}(\nu_1,\nu_2)$. The formalism here is validated using simulations. We also present approximate closed form analytical expressions which can be used to calculate the window functions. Comparing the widely adopted flat sky approximation, we find that its predictions match those of our spherical harmonic formalism to within $16 \%$ across the entire OWFA baseline range. The match improves at large baselines where we have $< 5 \%$ deviations.

Towards simulating and quantifying the light-cone EoR 21-cm signal

The light-cone (LC) effect causes the Epoch of Reionization (EoR) 21-cm signal $T_{\rm b} (\hat{\bf{n}}, \nu)$ to evolve significantly along the line of sight (LoS) direction $\nu$. In the first part of this paper, we present a method to properly incorporate the LC effect in simulations of the EoR 21-cm signal that include peculiar velocities. Subsequently, we discuss how to quantify the second order statistics of the EoR 21-cm signal in the presence of the LC effect. We demonstrate that the 3D power spectrum $P({\bf{k}})$ fails to quantify the entire information because it assumes the signal to be ergodic and periodic, whereas the LC effect breaks these conditions along the LoS. Considering a LC simulation centered at redshift $8$ where the mean neutral fraction drops from $0.65$ to $0.35$ across the box, we find that $P({\bf{k}})$ misses out $\sim 40 \%$ of the information at the two ends of the $17.41 \, {\rm MHz}$ simulation bandwidth. The multi-frequency angular power spectrum (MAPS) ${\mathcal C}_{\ell}(\nu_1,\nu_2)$ quantifies the statistical properties of $T_{\rm b} (\hat{\bf{n}}, \nu)$ without assuming the signal to be ergodic and periodic along the LoS. We expect this to quantify the entire statistical information of the EoR 21-cm signal. We apply MAPS to our LC simulation and present preliminary results for the EoR 21-cm signal.

Understanding the impact of Light cone effect on the EoR/CD 21-cm power spectrum

AbstractRedshifted HI 21-cm signal from the cosmic dawn and epoch of reionization evolve considerably along the LoS. We study the impact of this evolution (so called the light cone effect) on the HI 21-cm power spectrum. It is found that the LC effect has a significant impact on the 3D power spectrum and the change could be up to a factor of few. The LC effect is particularly strong during the cosmic dawn near the ‘peaks’ and ‘dips’ in the power spectrum when plotted with redshift. We also show that the 3D power spectrum, which could fully describe ergodic and periodic signal, losses out some information regarding the second order statistics of the signal as the EoR/CD 21-cm signal is non-ergodic and non-periodic along the line of sight. We show that the multi-frequency angular power spectrum (MAPS)${\mathcal {C}}_{\ell }(\nu _1, \nu _2)$captures all the information regarding the second order statistics of the signal even in the presence of the LC effect.

Simulated predictions for H i at z = 3.35 with the Ooty Wide Field Array – I. Instrument and the foregrounds

Foreground removal is the most important step in detecting the large-scale redshifted HI 21-cm signal. Modelling foreground spectra is challenging and is further complicated by the chromatic response of the telescope. We present a multi-frequency angular power spectrum (MAPS) estimator for use in a survey for redshifted HI 21-cm emission from z~3.35, and demonstrate its ability to accurately characterize the foregrounds. This survey will be carried out with the two wide-field interferometer modes of the upgraded Ooty Radio Telescope, called the Ooty Wide Field Array (OWFA), at 326.5 MHz. We have tailored the two-visibility correlation for OWFA to estimate the MAPS and test it with simulated foregrounds. In the process, we describe a software model that encodes the geometry and the details of the telescope, and simulates a realistic model for the bright radio sky. This article presents simulations which include the full chromatic response of the telescope, in addition to the frequency dependence intrinsic to the foregrounds. We find that the visibility correlation MAPS estimator recovers the input angular power spectrum accurately, and that the instrument response to the foregrounds dominates the systematic errors in the recovered foreground power spectra.

Characterizing the diffuse foreground for redshifted 21-cm HI signal: GMRT 153 MHz observation

Detailed knowledge of the foreground structure on the angular scales of ~ 1° to sub-arcminute will be essential for extracting the redshifted 21-cm HI signal from the observed data. We have presented results from the GMRT observations at 153 MHz, which was used to characterize the statistical properties of the diffuse radiation, using the multi-frequency angular power spectrum, across sub-degree angular scales. We have detected fluctuations in the diffuse emission on angular scales greater than 10' in a low galactic latitude area. The total intensity angular spectrum shows a power-law behaviour, while the detection of diffuse emission at smaller angular scales is limited by residual point sources. Also, we have estimated the level of foreground contamination.

Characterizing foreground for redshifted 21 cm radiation: 150 MHz Giant Metrewave Radio Telescope observations

Foreground removal is a major challenge for detecting the redshifted 21-cm neutral hydrogen (HI) signal from the Epoch of Reionization (EoR). We have used 150 MHz GMRT observations to characterize the statistical properties of the foregrounds in four different fields of view. The measured multi-frequency angular power spectrum C_l(Delta nu) is found to have values in the range 10^4 mK^2 to 2 x 10^4 mK^2 across 700 <= l <= 2 x 10^4 and Delta nu <= 2.5 MHz, which is consistent with model predictions where point sources are the most dominant foreground component. The measured C_l(Delta nu) does not show a smooth Delta nu dependence, which poses a severe difficulty for foreground removal using polynomial fitting. The observational data was used to assess point source subtraction. Considering the brightest source (~ 1 Jy) in each field, we find that the residual artifacts are less than 1.5% in the most sensitive field (FIELD I). We have used FIELD I, which has a rms noise of 1.3 mJy/Beam, to study the properties of the radio source population to a limiting flux of 9 mJy. The differential source count is well fitted with a single power law of slope -1.6. We find there is no evidence for flattening of the source counts towards lower flux densities which suggests that source population is dominated by the classical radio-loud Active Galactic Nucleus (AGN). The diffuse Galactic emission is revealed after the point sources are subtracted out from FIELD I . We find C_l \propto l^{-2.34} for 253 <= l <= 800 which is characteristic of the Galactic synchrotron radiation measured at higher frequencies and larger angular scales. We estimate the fluctuations in the Galactic synchrotron emission to be sqrt{l(l+1)C_l/2 pi} ~ 10 K at l=800 (theta > 10'). The measured C_l is dominated by the residual point sources and artifacts at smaller angular scales where C_l ~ 10^3 mK^2 for l > 800.