Sk. Saiyad Ali

On using visibility correlations to probe the Hi distribution from the dark ages to the present epoch – I. Formalism and the expected signal

Redshifted 21-cm radiation originating from the cosmological distribution of neutral hydrogen (H i) appears as background radiation in low-frequency radio observations. The angular and frequency domain fluctuations in this radiation carry information concerning cosmological structure formation. We propose that correlations between visibilities measured at different baselines and frequencies in radio-interferometric observations be used to quantify the statistical properties of these fluctuations. This has an inherent advantage over other statistical estimators in that it deals directly with the visibilities which are the primary quantities measured in radio-interferometric observations. Also, the visibility correlation has a very simple relation with the power spectrum. We present estimates of the expected signal for nearly the entire post-recombination era, from the dark ages to the present epoch. The epoch of reionization, where H I has a patchy distribution, has a distinct signature where the signal is determined by the size of the discrete ionized regions. The signal at other epochs, where H I follows the dark matter, is determined largely by the power spectrum of dark matter fluctuations. The signal is strongest for baselines where the antenna separations are within a few hundred times the wavelength of observation, and an optimal strategy would preferentially sample these baselines. In the frequency domain, for most baselines the visibilities at two different frequencies are uncorrelated beyond Δν ∼ 1 MHz, a signature which, in principle, would allow the HI signal to be easily distinguished from the continuum sources of contamination.

Foregrounds for redshifted 21-cm studies of reionization: Giant Meter Wave Radio Telescope 153-MHz observations

Foreground subtraction is the biggest challenge for future redshifted 21-cm observations to probe reionization. We use a short Giant Meter Wave Radio Telescope (GMRT) observation at 153 MHz to characterize the statistical properties of the background radiation across ~ 1° to subarcmin angular scales, and across a frequency band of 5 MHz with 62.5 kHz resolution. The statistic we use is the visibility correlation function, or equivalently the angular power spectrum Cl. We present the results obtained from using relatively unsophisticated, conventional data calibration procedures. We find that even fairly simple-minded calibration allows one to estimate the visibility correlation function at a given frequency V 2 (U, 0). From our observations, we find that V 2 (U, 0) is consistent with foreground model predictions at all angular scales except the largest ones probed by our observations where the model predictions are somewhat in excess. On the other hand, the visibility correlation between different frequencies κ(U, Δν) seems to be much more sensitive to calibration errors. We find a rapid decline in κ(U, Δν), in contrast with the prediction of less than 1 per cent variation across 2.5 MHz. In this case, however, it seems likely that a substantial part of the discrepancy may be due to limitations of data reduction procedures.

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 (H i) signal from the Epoch of Reionization. We have used 150 MHz Giant Metrewave Radio Telescope observations to characterize the statistical properties of the foregrounds in four different fields of view. The measured multifrequency angular power spectrum Cl(Δν) is found to have values in the range 104–2 × 104 mK2 across 700 ≤ l ≤ 2 × 104 and Δν ≤ 2.5 MHz, which is consistent with model predictions where point sources are the most dominant foreground component. The measured Cl(Δν) does not show a smooth Δν dependence, which poses a severe difficulty for foreground removal using polynomial fitting. The observational data were used to assess point source subtraction. Considering the brightest source (∼1 Jy) in each field, we find that the residual artefacts are less than 1.5 per cent in the most sensitive field (FIELD I). Considering all the sources in the fields, we find that the bulk of the image is free of artefacts, the artefacts being localized to the vicinity of the brightest sources. We have used FIELD I, which has an rms noise of 1.3 mJy beam−1, 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. The diffuse Galactic emission is revealed after the point sources are subtracted out from FIELD I. We find Cl ∝ 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 at l = 800 (θ > 10 arcmin). The measured Cl is dominated by the residual point sources and artefacts at smaller angular scales where Cl ∼ 103 mK2 for l > 800.

GMRT observation towards detecting the post-reionization 21-cm signal

The redshifted 21-cm signal from neutral hydrogen (H I) is an important future probe of the high-redshift Universe. We have analysed 610 MHz Giant Metrewave Radio Telescope (GMRT) observations towards detecting this signal from z = 1.32. The multi-frequency angular power spectrum Cl(Δν) is used to characterize the statistical properties of the background radiation across angular scales ∼20 arcsec to 10 arcmin, and a frequency bandwidth of 7.5 MHz with resolution 125 kHz. The measured C l (Δν) which ranges from 7 to 18 mK 2 is dominated by foregrounds, the expected H I signal C HI l (Δν) ∼ 10- 6 to 10 ―7 mK 2 is several orders of magnitude smaller and detecting this is a big challenge. The foregrounds, believed to originate from continuum sources, is expected to vary smoothly with Δν whereas the H I signal decorrelates within ∼0.5 MHz, and this holds the promise of separating the two. For each l, we use the interval 0.5 ≤ Δν ≤ 7.5 MHz to fit a fourth-order polynomial which is subtracted from the measured C l (Δν) to remove any smoothly varying component across the entire bandwidth Δν ≤ 7.5 MHz. The residual Cl(Δν), we find, has an oscillatory pattern with amplitude and period, respectively, ∼0.1 mK 2 and Δν = 3 MHz at the smallest value of 1476, and the amplitude and period decreasing with increasing l. Applying a suitably chosen high pass filter, we are able to remove the residual oscillatory pattern for = 1476 where the residual C l (Δν) is now consistent with zero at the 3σ noise level. Based on this we conclude that we have successfully removed the foregrounds at l = 1476 and the residuals are consistent with noise. We use this to place an upper limit on the H I signal whose amplitude is determined by x H I b (C HI l (Δν) ∝ [x H I b] 2 ), where x H I and b are the H I neutral fraction and the H I bias, respectively. A value of x H I b greater than 7.95 would have been detected in our observation, and is therefore ruled out at the 3σ level. For comparison, studies of quasar absorption spectra indicate x H I ∼ 2.5 × 10 ―2 which is ∼330 times smaller than our upper limit. We have not succeeded in completely removing the residual oscillatory pattern, whose cause is presently unknown to us, for the larger l values.

Prospects for Detecting the 326.5 MHz Redshifted 21-cm HI Signal with the Ooty Radio Telescope (ORT)

Observations of the redshifted 21-cm HI fluctuations promise to be an important probe of the post-reionization era (z≤ 6). In this paper we calculate the expected signal and foregrounds for the upgraded Ooty Radio Telescope (ORT) which operates at frequency νo = 326.5 MHz which corresponds to redshift z = 3.35. Assuming that the visibilities contain only the HI signal and system noise, we show that a 3 σ detection of the HI signal (∼1 mK) is possible at angular scales 11′ to 3∘ with ≈1000 h of observation. Foreground removal is one of the major challenges for a statistical detection of the redshifted 21 cm HI signal. We assess the contribution of different foregrounds and find that the 326.5 MHz sky is dominated by the extragalactic point sources at the angular scales of our interest. The expected total foregrounds are 104−105 times higher than the HI signal.

What will anisotropies in the clustering pattern in redshifted 21 cm maps tell us

The clustering pattern in high-redshift H I maps is expected to be anisotropic for two distinct reasons: the Alcock-Paczynski effect and the peculiar velocities, both of which are sensitive to the cosmological parameters. The signal is also expected to be sensitive to the details of the H I distribution at the epoch when the radiation originated. We use simple models for the H i distribution at the epoch of reionization and the post-reionization era to investigate exactly what we hope to learn from future observations of the anisotropy pattern in H I maps. We find that such observations will probably tell us more about the H I distribution than about the background cosmological model. Assuming that reionization can be described by spherical, ionized bubbles all of the same size with their centres possibly being biased with respect to the dark matter, we find that the anisotropy pattern at small angles is expected to have a bump at the characteristic angular size of the individual bubbles whereas the large-scale anisotropy pattern will reflect the size and the bias of the bubbles. The anisotropy also depends on the background cosmological parameters, but the dependence is much weaker. Under the assumption that the H i in the post-reionization era traces the dark matter with a possible bias, we find that changing the bias and changing the background cosmology have similar effects on the anisotropy pattern. Combining observations of the anisotropy with independent estimates of the bias, possibly from the bi-spectrum, may allow these observations to constrain cosmological parameters.

Visibility-based angular power spectrum estimation in low-frequency radio interferometric observations

We present two estimators to quantify the angular power spectrum of the sky signal directly from the visibilities measured in radio interferometric observations. This is relevant for both the foregrounds and the cosmological 21-cm signal buried therein. The discussion here is restricted to the Galactic synchrotron radiation, the most dominant foreground component after point source removal. Our theoretical analysis is validated using simulations at 150 MHz, mainly for GMRT and also briefly for Low-Frequency Array. The Bare Estimator uses pairwise correlations of the measured visibilities, while the Tapered Gridded Estimator uses the visibilities after gridding in the uv plane. The former is very precise, but computationally expensive for large data. The latter has a lower precision, but takes less computation time which is proportional to the data volume. The latter also allows tapering of the sky response leading to sidelobe suppression, an useful ingredient for foreground removal. Both estimators avoid the positive bias that arises due to the system noise. We consider amplitude and phase errors of the gain, and the w-term as possible sources of errors. We find that the estimated angular power spectrum is exponentially sensitive to the variance of the phase errors but insensitive to amplitude errors. The statistical uncertainties of the estimators are affected by both amplitude and phase errors. The w-term does not have a significant effect at the angular scales of our interest. We propose the Tapered Gridded Estimator as an effective tool to observationally quantify both foregrounds and the cosmological 21-cm signal.

Tapering the sky response for angular power spectrum estimation from low-frequency radio-interferometric data

It is important to correctly subtract point sources from radio-interferometric data in order to measure the power spectrum of diffuse radiation like the Galactic synchrotron or the Epoch of Reionization 21-cm signal. It is computationally very expensive and challenging to image a very large area and accurately subtract all the point sources from the image. The problem is particularly severe at the sidelobes and the outer parts of the main lobe where the antenna response is highly frequency dependent and the calibration also differs from that of the phase centre. Here, we show that it is possible to overcome this problem by tapering the sky response. Using simulated 150 MHz observations, we demonstrate that it is possible to suppress the contribution due to point sources from the outer parts by using the Tapered Gridded Estimator to measure the angular power spectrum Cℓ of the sky signal. We also show from the simulation that this method can self-consistently compute the noise bias and accurately subtract it to provide an unbiased estimation of Cℓ.

Fisher Matrix Predictions for Detecting the Cosmological 21-cm Signal with the Ooty Wide Field Array (OWFA)

We have used the Fisher matrix formalism to quantify the prospects of detecting the z=3.35 redshifted 21-cm HI power spectrum with the upcoming radio-imterferometric array OWFA. OWFA’s frequency and baseline coverage spans comoving Fourier modes in the range 1.8×10−2≤k≤2.7 Mpc−1. The OWFA HI signal, however, is predominantly from the range k≤0.2 Mpc−1. The larger modes, though abundant, do not contribute much to the HI signal. In this work, we have focused on combining the entire signal to achieve a detection. We find that a 5−σ detection of AHI is possible with ∼150 h of observations, here AHI2

The visibility-based tapered gridded estimator (TGE) for the redshifted 21-cm power spectrum

A_{\text {HI}}^{2}