arXiv subjects

Somnath Bharadwaj

Publications and source records attributed to Somnath Bharadwaj.

At least 73 records · Page 4Linked to original sources

arXiv2018

An Image-based Tapered Gridded Estimator (ITGE) for the angular power spectrum

We present the Image-based Tapered Gridded Estimator (ITGE) to measure the angular power spectrum $(C_{\ell})$ of the sky signal directly from the visibilities measured in radio-interferometric observations. The ITGE allows us to modulate the sky response through a window function which is implemented in the image plane, and it is possible to choose a wide variety of window functions. In the context of the cosmological HI 21-cm signal, this is useful for masking out the sky signal from specific directions which have strong residual foregrounds. In the context of the ISM in external galaxies, this is useful to separately estimate the $C_{\ell}$ of different parts of the galaxy. The ITGE deals with gridded data, hence it is computationally efficient. It also calculates the noise bias internally and exactly subtracts this out to give an unbiased estimate of $C_{\ell}$. We validate the ITGE using realistic VLA simulations at $1.4 {\rm GHz}$. We have applied the ITGE to estimate the $C_{\ell}$ of HI 21-cm emission from different regions of the galaxy NGC 628. We find that the slope of the measured $C_{\ell}$ in the outer region is significantly different as compared with the inner region. This indicates that the statistical properties of ISM turbulence possibly differ in different regions of the galaxy.

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arXiv2018

On the Prospects of Measuring the Cosmic Dawn 21-cm Power Spectrum using the Upgraded Giant Meterwave Radio Telescope (uGMRT)

A recent observation by the EDGES collaboration shows a strong absorption signal in the global 21-cm spectrum from around a redshift of $z = 17$. This absorption is stronger than the maximum prediction by existing models and indicates that the spatial fluctuations of the \HI 21-cm brightness temperature at Cosmic Dawn could be an order of magnitude larger than previously expected. In this paper, we investigate the prospects of detecting the \HI 21-cm power spectrum from Cosmic Dawn using uGMRT. We find that a $10σ$ detection of the enhanced \HI 21-cm signal power spectrum is possible within $70, 140$ and $400$ Hours of observation for an optimistic, moderate and pessimistic scenario respectively, using the Band-1 of uGMRT. This could be an useful probe of the interaction between the baryon and dark matter particles in the early Universe. We also present a comparison of the uGMRT predictions with those for the future SKA-Low.

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arXiv2018

The Shape and Size distribution of HII Regions near the percolation transition

Using Shapefinders, which are ratios of Minkowski functionals, we study the morphology of neutral hydrogen (HI) density fields, simulated using semi-numerical technique (inside-out), at various stages of reionization. Accompanying the Shapefinders, we also employ the 'largest cluster statistic' (LCS), originally proposed in Klypin and Shandarin (1993), to study the percolation in both neutral and ionized hydrogen. We find that the largest ionized region is percolating below the neutral fraction $x_{HI} \lesssim 0.728$ (or equivalently $z \lesssim 9$). The study of Shapefinders reveals that the largest ionized region starts to become highly filamentary with non-trivial topology near the percolation transition. During the percolation transition, the first two Shapefinders - 'thickness' ($T$) and 'breadth' ($B$) - of the largest ionized region do not vary much, while the third Shapefinder - 'length' ($L$) - abruptly increases. Consequently, the largest ionized region tends to be highly filamentary and topologically quite complex. The product of the first two Shapefinders, $T\times B$, provides a measure of the 'cross-section' of a filament-like ionized region. We find that, near percolation, the value of $T\times B$ for the largest ionized region remains stable at $\sim 7$ Mpc$^2$ (in comoving scale) while its length increases with time. Interestingly all large ionized regions have similar cross-sections. However their length shows a power-law dependence on their volume, $L\propto V^{0.72}$, at the onset of percolation.

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arXiv2018

Predictions for measuring the cross power spectrum of the HI 21-cm signal and the Lyman-$α$ forest using OWFA

We have studied the possibility of measuring the cross-correlation of the redshifted HI 21-cm signal and the Lyman-$α$ forest using an upcoming radio-interferometric array OWFA and an spectroscopic observation like SDSS-IV. Our results shows that it is possible to have a $6 σ$ detection of the cross-correlation signal with OWFA PII using an observing time of $200$ hrs each in $N_p = 25$ independent fields-of-view. However, not much can be done beyond this using the cross-correlation signal for $z_c = 3.35$ and $B = 30 \, {\rm MHz}$. Apart from this, we have also envisaged a situation where observations are carried out at $z_c = 3.05$ and $2.55$ which lie closer to the peak of the quasar distribution at $z = 2.25$ and with a larger bandwidth of $B = 60 \, {\rm MHz}$. We see that the SNR of the cross-correlation detection can be significantly enhanced to $\sim 17$ for $z_c = 2.55$ and $B = 60 \, {\rm MHz}$. It is then possible to measure $β_T$ and $β_F$ individually with an ${\rm SNR} \ge 5$ by combining the cross-correlation with the HI 21-cm auto-correlation measurements. We further find that a measurement of the binned cross-correlation power spectrum with ${\rm SNR} \ge 5$ is also possible in several bins at $k \le 0.3 \, {\rm Mpc}^{-1}$.

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arXiv2018

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 $C_{\ell}(ν_1,ν_2)$. 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.

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arXiv2018

Quantifying the non-Gaussianity in the EoR 21-cm signal through bispectrum

The epoch of reionization (EoR) 21-cm signal is expected to be highly non-Gaussian in nature and this non-Gaussianity is also expected to evolve with the progressing state of reionization. Therefore the signal will be correlated between different Fourier modes ($k$). The power spectrum will not be able capture this correlation in the signal. We use a higher-order estimator -- the bispectrum -- to quantify this evolving non-Gaussianity. We study the bispectrum using an ensemble of simulated 21-cm signal and with a large variety of $k$ triangles. We observe two competing sources driving the non-Gaussianity in the signal: fluctuations in the neutral fraction ($x_{\rm HI}$) field and fluctuations in the matter density field. We find that the non-Gaussian contribution from these two sources vary, depending on the stage of reionization and on which $k$ modes are being studied. We show that the sign of the bispectrum works as a unique marker to identify which among these two components is driving the non-Gaussianity. We propose that the sign change in the bispectrum, when plotted as a function of triangle configuration $\cosθ$ and at a certain stage of the EoR can be used as a confirmative test for the detection of the 21-cm signal. We also propose a new consolidated way to visualize the signal evolution (with evolving $\overline{x}_{\rm HI}$ or redshift), through the trajectories of the signal in a power spectrum and equilateral bispectrum i.e. $P(k)-B(k, k, k)$ space.

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arXiv2018

Modelling redshift-space distortion in the post-reionization ${\rm HI}$ 21-cm power spectrum

The post-reionization ${\rm HI}$ 21-cm signal is an excellent candidate for precision cosmology, this however requires accurate modelling of the expected signal. Sarkar et al. (2016) have simulated the real space ${\rm HI}$ 21-cm signal, and have modelled the ${\rm HI}$ power spectrum as $P_{\rm HI}(k)=b^2 P(k)$ where $P(k)$ is the dark matter power spectrum and $b(k)$ is a (possibly complex) scale dependent bias for which fitting formulas have been provided. This paper extends these simulations to incorporate redshift space distortion and predict the expected redshift space ${\rm HI}$ 21-cm power spectrum $P^s_{\rm HI}(k_{\perp},k_{\parallel})$ using two different prescriptions for the ${\rm HI}$ distributions and peculiar velocities. We model $P^s_{\rm HI}(k_{\perp},k_{\parallel})$ assuming that it is the product of $P_{\rm HI}(k)=b^2 P(k)$ with a Kaiser enhancement term and a Finger of God (FoG) damping which has $σ_p$ the pair velocity dispersion as a free parameter. Considering several possibilities for the bias and the damping profile, we find that the models with a scale dependent bias and a Lorentzian damping profile best fit the simulated $P^s_{\rm HI}(k_{\perp},k_{\parallel})$ over the entire range $1 \le z \le 6$. The best fit value of $σ_p$ falls approximately as $(1+z)^{-m}$ with $m=2$ and $1.2$ respectively for the two different prescriptions. The model predictions are consistent with the simulations for $k < 0.3 \, {\rm Mpc}^{-1}$ over the entire $z$ range for the monopole $P^s_0(k)$, and at $z \le 3$ for the quadrupole $P^s_2(k)$. At $z \ge 4$ the models underpredict $P^s_2(k)$ at large $k$, and the fit is restricted to $k < 0.15 \, {\rm Mpc}^{-1}$.

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arXiv2017

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 $T_{\rm b} (\hat{\bf{n}}, ν)$ to evolve significantly along the line of sight (LoS) direction $ν$. 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) ${\mathcal C}_{\ell}(ν_1,ν_2)$ quantifies the statistical properties of $T_{\rm b} (\hat{\bf{n}}, ν)$ 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.

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arXiv2017

An analytical method to simulate the HI 21-cm visibility signal for intensity mapping experiments

Simulations play a vital role in testing and validating HI 21-cm power spectrum estimation techniques. Conventional methods use techniques like N-body simulations to simulate the sky signal which is then passed through a model of the instrument. This makes it necessary to simulate the HI distribution in a large cosmological volume, and incorporate both the light-cone effect and the telescope's chromatic response. The computational requirements may be particularly large if one wishes to simulate many realizations of the signal. In this paper we present an analytical method to simulate the HI visibility signal. This is particularly efficient if one wishes to simulate a large number of realizations of the signal. Our method is based on theoretical predictions of the visibility correlation which incorporate both the light-cone effect and the telescope's chromatic response. We have demonstrated this method by applying it to simulate the HI visibility signal for the upcoming Ooty Wide Field Array Phase I.

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arXiv2017

Simulated foreground predictions for HI 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.

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arXiv2017

Validating a novel angular power spectrum estimator using simulated low frequency radio-interferometric data

The "Tapered Gridded Estimator" (TGE) is a novel way to directly estimate the angular power spectrum from radio-interferometric visibility data that reduces the computation by efficiently gridding the data, consistently removes the noise bias, and suppresses the foreground contamination to a large extent by tapering the primary beam response through an appropriate convolution in the visibility domain. Here we demonstrate the effectiveness of TGE in recovering the diffuse emission power spectrum through numerical simulations. We present details of the simulation used to generate low frequency visibility data for sky model with extragalactic compact radio sources and diffuse Galactic synchrotron emission. We then use different imaging strategies to identify the most effective option of point source subtraction and to study the underlying diffuse emission. Finally, we apply TGE to the residual data to measure the angular power spectrum, and assess the impact of incomplete point source subtraction in recovering the input power spectrum $C_{\ell}$ of the synchrotron emission. This estimator is found to successfully recovers the $C_{\ell}$ of input model from the residual visibility data. These results are relevant for measuring the diffuse emission like the Galactic synchrotron emission. It is also an important step towards characterizing and removing both diffuse and compact foreground emission in order to detect the redshifted $21\, {\rm cm}$ signal from the Epoch of Reionization.

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arXiv2017

The angular power spectrum measurement of the Galactic synchrotron emission in two fields of the TGSS survey

Characterizing the diffuse Galactic synchrotron emission at arcminute angular scales is needed to reliably remove foregrounds in cosmological 21-cm measurements. The study of this emission is also interesting in its own right. Here, we quantify the fluctuations of the diffuse Galactic synchrotron emission using visibility data for two of the fields observed by the TIFR GMRT Sky Survey (TGSS). We have used the 2D Tapered Gridded Estimator (TGE) to estimate the angular power spectrum $(C_{\ell})$ from the visibilities. We find that the sky signal, after subtracting the point sources, is likely dominated by the diffuse Galactic synchrotron radiation across the angular multipole range $240 \le \ell \lesssim 500$. We present a power law fit, $C_{\ell}=A\times\big(\frac{1000}{l}\big)^β$, to the measured $C_{\ell}$ over this $\ell$ range. We find that $(A,β)$ have values $(356\pm109~{\rm mK^2},2.8\pm0.3)$ and $(54\pm26~{\rm mK^2},2.2\pm0.4)$ in the two fields. For the second field, however, there is indication of a significant residual point source contribution, and for this field we interpret the measured $C_{\ell}$ as an upper limit for the diffuse Galactic synchrotron emission. While in both fields the slopes are consistent with earlier measurements, the second field appears to have an amplitude which is considerably smaller compared to similar measurements in other parts of the sky.

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arXiv2017

Fisher Matrix Based Predictions for Measuring the z = 3.35 Binned 21-cm Power Spectrum using the Ooty Wide Field Array (OWFA)

We use the Fisher matrix formalism to predict the prospects of measuring the redshifted 21-cm power spectrum in different $k$-bins using observations with the upcoming Ooty Wide Field Array (OWFA) which will operate at $326.5 {\rm MHZ}$. This corresponds to neutral hydrogen (HI) at $z=3.35$, and a measurement of the 21-cm power spectrum provides an unique method to probe the large-scale structures at this redshift. Our analysis indicates that a $5 σ$ detection of the binned power spectrum is possible in the $k$ range $0.05 \leq k \leq 0.3 \, {\rm Mpc}^{-1}$ with $1,000$ hours of observation. We find that the Signal-to-Noise ratio (${\rm SNR}$) peaks in the $k$ range $0.1- 0.2\, {\rm Mpc}^{-1}$ where a $10 σ$ detection is possible with $2,000$ hours of observations. Our analysis also indicates that it is not very advantageous to observe much beyond $1,000$ hours in a single field of view as the ${\rm SNR}$ increases rather slowly beyond this in many of the small $k$-bins. The entire analysis reported here assumes that the foregrounds have been completely removed.

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arXiv2017

FRB event rate predictions for the Ooty Wide Field Array

We developed a generic formalism to estimate the event rate and the redshift distribution of Fast Radio Bursts (FRBs) in our previous publication (Bera et al. 2016), considering FRBs are of an extragalactic origin. In this paper we present (a) the predicted pulse widths of FRBs by considering two different scattering models, (b) the minimum total energy required to detect events, (c) the redshift distribution and (d) the detection rates of FRBs for the Ooty Wide Field Array (OWFA). The energy spectrum of FRBs is modelled as a power law with an exponent $-α$ and our analysis spans a range $-3\leq α\leq 5$. We find that OWFA will be capable of detecting FRBs with $α\geq 0$. The redshift distribution and the event rates of FRBs are estimated by assuming two different energy distribution functions; a Delta function and a Schechter luminosity function with an exponent $-2\le γ\le 2$. We consider an empirical scattering model based on pulsar observations (model I) as well as a theoretical model (model II) expected for the intergalactic medium. The redshift distributions peak at a particular redshift $z_p$ for a fixed value of $α$, which lie in the range $0.3\leq z_p \leq 1$ for the scattering model I and remain flat and extend up to high redshifts ($z\lesssim 5$) for the scattering model II.

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arXiv2016

Statistics of the epoch of reionization (EoR) 21-cm signal -- II. The evolution of the power spectrum error-covariance

The EoR 21-cm signal is expected to become highly non-Gaussian as reionization progresses. This severely affects the error-covariance of the EoR 21-cm power spectrum which is important for predicting the prospects of a detection with ongoing and future experiments. Most earlier works have assumed that the EoR 21-cm signal is a Gaussian random field where (1) the error variance depends only on the power spectrum and the number of Fourier modes in the particular $k$ bin, and (2) the errors in the different $k$ bins are uncorrelated. Here we use an ensemble of simulated 21-cm maps to analyze the error-covariance at various stages of reionization. We find that even at the very early stages of reionization ($\bar{x}_{\rm HI} \sim 0.9 $) the error variance significantly exceeds the Gaussian predictions at small length-scales ($k > 0.5 \,{\rm Mpc}^{-1}$) while they are consistent at larger scales. The errors in most $k$ bins (both large and small scales), are however found to be correlated. Considering the later stages ($\bar{x}_{\rm HI} = 0.15$), the error variance shows an excess in all $k$ bins within $k \ge 0.1 \, {\rm Mpc}^{-1}$, and it is around $200$ times larger than the Gaussian prediction at $k \sim 1 \, {\rm Mpc}^{-1}$. The errors in the different $k$ bins are all also highly correlated, barring the two smallest $k$ bins which are anti-correlated with the other bins. Our results imply that the predictions for different 21-cm experiments based on the Gaussian assumption underestimate the errors, and it is necessary to incorporate the non-Gaussianity for more realistic predictions.

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arXiv2016

The prospects of measuring the angular power spectrum of the diffuse Galactic synchrotron emission with SKA1 Low

The diffuse Galactic synchrotron emission (DGSE) is the most important diffuse foreground component for future cosmological 21-cm observations. The DGSE is also an important probe of the cosmic ray electron and magnetic field distributions in the turbulent interstellar medium (ISM) of our Galaxy. In this paper we briefly review the Tapered Gridded Estimator (TGE) which can be used to quantify the angular power spectrum of the sky signal directly from the visibilities measured in radio-interferometric observations. The salient features of the TGE are (1.) it deals with the gridded data which makes it computationally very fast (2.) it avoids a positive noise bias which normally arises from the system noise inherent to the visibility data, and (3.) it allows us to taper the sky response and thereby suppresses the contribution from unsubtracted point sources in the outer parts and the sidelobes of the antenna beam pattern. We also summarize earlier work where the TGE was used to measure the C_l of the DGSE using 150 MHz GMRT data. Earlier measurements of the angular power spectrum are restricted to smaller angular multipole l ~ 10^3 for the DGSE, the signal at the larger l values is dominated by the residual point sources after source subtraction. The higher sensitivity of the upcoming SKA1 Low will allow the point sources to be subtracted to a fainter level than possible with existing telescopes. We predict that it will be possible to measure the angular power spectrum of the DGSE to larger values of l with SKA1 Low. Our results show that it should be possible to achieve l_{max} ~ 10^4 and ~ 10^5 with 2 minutes and 10 hours of observations respectively.

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arXiv2016

Line of sight anisotropies in the Cosmic Dawn and EoR 21-cm power spectrum

The line of sight direction in the redshifted 21-cm signal coming from the cosmic dawn and the epoch of reionization is quite unique in many ways compared to any other cosmological signal. Different unique effects, such as the evolution history of the signal, non-linear peculiar velocities of the matter etc will imprint their signature along the line of sight axis of the observed signal. One of the major goals of the future SKA-LOW radio interferometer is to observe the cosmic dawn and the epoch of reionization through this 21-cm signal. It is thus important to understand how these various effects affect the signal for it's actual detection and proper interpretation. For more than one and half decades, various groups in India have been actively trying to understand and quantify the different line of sight effects that are present in this signal through analytical models and simulations. In many ways the importance of this sub-field under 21-cm cosmology have been identified, highlighted and pushed forward by the Indian community. In this article we briefly describe their contribution and implication of these effects in the context of the future surveys of the cosmic dawn and the epoch of reionization that will be conducted by the SKA-LOW.

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arXiv2016

Modelling the 21 cm Signal From the Epoch of Reionization and Cosmic Dawn

Studying the cosmic dawn and the epoch of reionization through the redshifted 21 cm line are among the major science goals of the SKA1. Their significance lies in the fact that they are closely related to the very first stars in the universe. Interpreting the upcoming data would require detailed modelling of the relevant physical processes. In this article, we focus on the theoretical models of reionization that have been worked out by various groups working in India with the upcoming SKA in mind. These models include purely analytical and semi-numerical calculations as well as fully numerical radiative transfer simulations. The predictions of the 21 cm signal from these models would be useful in constraining the properties of the early galaxies using the SKA data.

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