Suman Majumdar

Upper Limits on the 21 cm Epoch of Reionization Power Spectrum from One Night with LOFAR

We present the first limits on the Epoch of Reionization 21 cm H I power spectra, in the redshift range z = 7.9–10.6, using the Low-Frequency Array (LOFAR) High-Band Antenna (HBA). In total, 13.0 hr of data were used from observations centered on the North Celestial Pole. After subtraction of the sky model and the noise bias, we detect a non-zero Δ^2_I = (56 ± 13 mK)^2 (1-σ) excess variance and a best 2-σ upper limit of Δ^2_(21) < (79.6 mK)^2 at k = 0.053 h cMpc^(−1) in the range z = 9.6–10.6. The excess variance decreases when optimizing the smoothness of the direction- and frequency-dependent gain calibration, and with increasing the completeness of the sky model. It is likely caused by (i) residual side-lobe noise on calibration baselines, (ii) leverage due to nonlinear effects, (iii) noise and ionosphere-induced gain errors, or a combination thereof. Further analyses of the excess variance will be discussed in forthcoming publications.

On the use of seminumerical simulations in predicting the 21-cm signal from the epoch of reionization

We present a detailed comparison of three different simulations of the epoch of reionization (EoR). The radiative transfer simulation (C-2-RAY) among them is our benchmark. Radiative transfer codes can produce realistic results, but are computationally expensive. We compare it with two seminumerical techniques: one using the same haloes as C-2-RAY as its sources (Sem-Num), and one using a conditional Press-Schechter scheme (CPS+GS). These are vastly more computationally efficient than C-2-RAY, but use more simplistic physical assumptions. We evaluate these simulations in terms of their ability to reproduce the history and morphology of reionization. We find that both Sem-Num and CPS+GS can produce an ionization history and morphology that is very close to C-2-RAY, with Sem-Num performing slightly better compared to CPS+GS. We also study different redshift-space observables of the 21-cm signal from EoR: the variance, power spectrum and its various angular multipole moments. We find that both seminumerical models perform reasonably well in predicting these observables at length scales relevant for present and future experiments. However, Sem-Num performs slightly better than CPS+GS in producing the reionization history, which is necessary for interpreting the future observations. The CPS+GS scheme, however, has the advantage that it is not restricted by the mass resolution of the dark matter density field.

Light cone effect on the reionization 21-cm signal - II. Evolution, anisotropies and observational implications

Measurements of the H I 21-cm power spectra from the reionization epoch will be influenced by the evolution of the signal along the line-of-sight direction of any observed volume. We use numerical as well as seminumerical simulations of reionization in a cubic volume of 607 Mpc across to study this so-called light-cone effect on the H I 21-cm power spectrum. We find that the light-cone effect has the largest impact at two different stages of reionization: one when reionization is ∼20 per cent and other when it is ∼80 per cent completed. We find a factor of ∼4 amplification of the power spectrum at the largest scale available in our simulations. We do not find any significant anisotropy in the 21-cm power spectrum due to the light-cone effect. We argue that for the power spectrum to become anisotropic, the light-cone effect would have to make the ionized bubbles significantly elongated or compressed along the line of sight, which would require extreme reionization scenarios. We also calculate the two-point correlation functions parallel and perpendicular to the line of sight and find them to differ. Finally, we calculate an optimum frequency bandwidth below which the light-cone effect can be neglected when extracting power spectra from observations. We find that if one is willing to accept a 10 per cent error due to the light-cone effect, the optimum frequency bandwidth for k = 0.056 Mpc−1 is ∼7.5 MHz. For k = 0.15 and 0.41 Mpc−1, the optimum bandwidth is ∼11 and ∼16 MHz, respectively.

The effect of peculiar velocities on the epoch of reionization 21-cm signal

We have used seminumerical simulations of reionization to study the behaviour of the power spectrum of the epoch of reionization 21-cm signal in redshift space. We have considered two models of reionization, one which has homogeneous recombination (HR) and the other incorporating inhomogeneous recombination (IR). We have estimated the observable quantities – quadrupole and monopole moments of H i power spectrum at redshift space from our simulated data. We find that the magnitude and nature of the ratio between the quadrupole and monopole moments of the power spectrum (Ps2/Ps0) can be a possible probe for the epoch of reionization. We observe that this ratio becomes negative at large scales for x¯HI≤0.7 irrespective of the reionization model, which is a direct signature of an inside-out reionization at large scales. It is possible to qualitatively interpret the results of the simulations in terms of the fluctuations in the matter distribution and the fluctuations in the neutral fraction which have power spectra and cross-correlation PΔΔ(k), Pxx(k) and PΔx(k), respectively. We find that at large scales the fluctuations in matter density and neutral fraction are exactly anticorrelated through all stages of reionization. This provides a simple picture where we are able to qualitatively interpret the behaviour of the redshift-space power spectra at large scales with varying x¯HI entirely in terms of a just two quantities, namely x¯HI and the ratio Pxx/PΔΔ. The nature of PΔx becomes different for HR and IR scenarios at intermediate and small scales. We further find that it is possible to distinguish between an inside-out and an outside-in reionization scenario from the nature of the ratio Ps2/Ps0 at intermediate length scales.

Simulating the impact of H I fluctuations on matched filter search for ionized bubbles in redshifted 21-cm maps

Extending the formalism of Datta, Bharadwaj & Choudhury for detecting ionized bubbles in redshifted 21-cm maps using a matched filtering technique, we use different simulations to analyse the impact of H i fluctuations outside the bubble on the detectability of the bubble. In the first three kinds of simulations there is a spherical bubble of comoving radius R b , the one that we are trying to detect, located at the centre, and the neutral hydrogen (H i) outside the bubble traces the underlying dark matter distribution. We consider three different possible scenarios of re-ionization, i.e. (i) there is a single bubble (SB) in the field of view (FoV) and the hydrogen neutral fraction is constant outside this bubble, (ii) patchy re-ionization (PR) with many small ionized bubbles in the FoV (PR1) and (iii) many spherical ionized bubbles of the same radius R b (PR2). The centres of the extra bubbles trace the dark matter distribution. The fourth kind of simulation uses more realistic maps based on seminumeric modelling (SM) of ionized regions. We make predictions for the currently functioning Giant Metrewave Radio Telescope (GMRT) and a forthcoming instrument, the Murchison Widefield Array (MWA) at a redshift of 6 (corresponding to an observed frequency 203 MHz) for 1000 h observations. We find that for both the SB and PR1 scenarios the fluctuating intergalactic medium restricts bubble detection to size Rb ≤ 6Mpc and R b ≤ 12 Mpc for the GMRT and the MWA, respectively, however large be the integration time. These results are well explained by analytical predictions. In the PR2 scenario, we find that bubble detection is almost impossible for neutral fraction x HI < 0.6 because of large uncertainty due to the Hi fluctuations. Applying the matched filter technique to the SM scenario, we find that it works well even when the targeted ionized bubble is non-spherical due to surrounding bubbles and inhomogeneous recombination. We find that determining the size and positions of the bubbles is not limited by the Hi fluctuations in the SB and PR1 scenario but limited by the instruments angular resolution instead, and this can be done more precisely for larger bubble. We also find that for bubble detection the GMRT configuration is somewhat superior to the proposed MWA.

Constraining quasar and intergalactic medium properties through bubble detection in redshifted 21-cm maps

The infrared detection of a z>7 quasar has opened up a new window to directly probe the IGM during the epoch of reionization. In this paper we theoretically consider the possibility of detecting the ionized bubble around a z=8 quasar using targeted redshifted 21-cm observations with the GMRT. The apparent shape and size of the ionized bubble, as seen by a distant observer, depends on the parameters \dot{N}_{phs}/C, x_HI/C and \tau_Q where \dot{N}_{phs}, \tau_Q, x_HI and C are respectively the photon emission rate, age of the quasar, the neutral fraction and clumping factor of the IGM.Here we have analytically estimated the shape and size of a quasars ionized bubble assuming an uniform IGM and ignoring other ionizing sources besides the quasar, and used this as a template for matched filter bubble search with the GMRT visibility data. We have assumed that \dot{N}_{phs} is known from the infrared spectrum and C from theoretical considerations, which gives us two free parameters x_HI and \tau_Q for bubble. Considering 1,000 hr of observation, we find that there is a reasonably large region of parameter space where a 3\sigma detection is possible. We also find that it will be possible to place lower limits on x_HI and \tau_Q with this observation. Deeper follow up observations can place upper limits on \tau_Q and x_HI. Value of C affect the estimation of x_HI but the estimation of \tau_Q remains unaffected.We have used a semi-numerical technique to simulate the apparent shape and size of quasar ionized bubbles considering the presence of other ionizing sources and inhomogeneities in the IGM. The presence of other sources increase the size of the quasar bubble, leading to underestimation of x_HI. Clustering of other ionizing sources around the quasar can produce severe distortions in bubbles shape. However, this does not severely affect parameter estimation in the bubbles that are large.

Constraining Quasar and IGM Properties Through Bubble Detection in Redshifted 21-cm Maps

The infrared detection of a z>7 quasar has opened up a new window to directly probe the IGM during the epoch of reionization. In this paper we theoretically consider the possibility of detecting the ionized bubble around a z=8 quasar using targeted redshifted 21-cm observations with the GMRT. The apparent shape and size of the ionized bubble, as seen by a distant observer, depends on the parameters \dot{N}_{phs}/C, x_HI/C and \tau_Q where \dot{N}_{phs}, \tau_Q, x_HI and C are respectively the photon emission rate, age of the quasar, the neutral fraction and clumping factor of the IGM.Here we have analytically estimated the shape and size of a quasars ionized bubble assuming an uniform IGM and ignoring other ionizing sources besides the quasar, and used this as a template for matched filter bubble search with the GMRT visibility data. We have assumed that \dot{N}_{phs} is known from the infrared spectrum and C from theoretical considerations, which gives us two free parameters x_HI and \tau_Q for bubble. Considering 1,000 hr of observation, we find that there is a reasonably large region of parameter space where a 3\sigma detection is possible. We also find that it will be possible to place lower limits on x_HI and \tau_Q with this observation. Deeper follow up observations can place upper limits on \tau_Q and x_HI. Value of C affect the estimation of x_HI but the estimation of \tau_Q remains unaffected.We have used a semi-numerical technique to simulate the apparent shape and size of quasar ionized bubbles considering the presence of other ionizing sources and inhomogeneities in the IGM. The presence of other sources increase the size of the quasar bubble, leading to underestimation of x_HI. Clustering of other ionizing sources around the quasar can produce severe distortions in bubbles shape. However, this does not severely affect parameter estimation in the bubbles that are large.

The effect of non-Gaussianity on error predictions for the Epoch of Reionization (EoR) 21-cm power spectrum

The Epoch of Reionization (EoR) 21-cm signal is expected to become increasingly non-Gaussian as reionization proceeds. We have used seminumerical simulations to study how this affects the error predictions for the EoR 21-cm power spectrum. We expect SNR = root N-k for a Gaussian random field where N-k is the number of Fourier modes in each k bin. We find that non-Gaussianity is important at high SNR where it imposes an upper limit [SNR](l). For a fixed volume V, it is not possible to achieve SNR > [SNR](l) even if N-k is increased. The value of [SNR](l) falls as reionization proceeds, dropping from similar to 500 at (x) over bar}(H1) = 0.15 for a [150.08 Mpc](3) simulation. We show that it is possible to interpret [SNR](l) in terms of the trispectrum, and we expect [SNR](l) proportional to root V if the volume is increased. For SNR << [SNR](l) we find SNR = root N-k/A with A similar to 0.95-1.75, roughly consistent with the Gaussian prediction. We present a fitting formula for the SNR as a function of N-k, with two parameters A and [SNR](l) that have to be determined using simulations. Our results are relevant for predicting the sensitivity of different instruments to measure the EoR 21-cm power spectrum, which till date have been largely based on the Gaussian assumption.

Statistics of the epoch of reionization 21-cm signal – I. Power spectrum error-covariance

The non-Gaussian nature of the epoch of reionization (EoR) 21-cm signal has a significant impact on the error variance of its power spectrum P(k). We have used a large ensemble of seminumerical simulations and an analytical model to estimate the effect of this non-Gaussianity on the entire error-covariance matrix C-ij. Our analytical model shows that C-ij has contributions from two sources. One is the usual variance for a Gaussian random field which scales inversely of the number of modes that goes into the estimation of P(k). The other is the trispectrum of the signal. Using the simulated 21-cm Signal Ensemble, an ensemble of the Randomized Signal and Ensembles of Gaussian Random Ensembles we have quantified the effect of the trispectrum on the error variance C-ii. We find that its relative contribution is comparable to or larger than that of the Gaussian term for the k range 0.3 = k = 0.5Mpc(-1)), and a weak correlation between the smallest and largest k values. There is also a small anticorrelation between the errors in the smallest and intermediate k values. These results are relevant for the k range that will be probed by the current and upcoming EoR 21-cm experiments.

The wedge bias in reionization 21-cm power spectrum measurements

A proposed method for dealing with foreground emission in upcoming 21-cm observations from the epoch of reionization is to limit observations to an uncontaminated window in Fourier space. Foreground emission can be avoided in this way, since it is limited to a wedge-shaped region in k∥, k⊥ space. However, the power spectrum is anisotropic owing to redshift-space distortions from peculiar velocities. Consequently, the 21-cm power spectrum measured in the foreground avoidance window – which samples only a limited range of angles close to the line-of-sight direction – differs from the full redshift-space spherically averaged power spectrum which requires an average over all angles. In this paper, we calculate the magnitude of this ‘wedge bias’ for the first time. We find that the bias amplifies the difference between the real-space and redshift-space power spectra. The bias is strongest at high redshifts, where measurements using foreground avoidance will overestimate the redshift-space power spectrum by around 100 per cent, possibly obscuring the distinctive rise and fall signature that is anticipated for the spherically averaged 21-cm power spectrum. In the later stages of reionization, the bias becomes negative, and smaller in magnitude (≲20 per cent).