Somnath Bharadwaj

The cosmic microwave background radiation fluctuations from H i perturbations prior to reionization

Loeb and Zaldarriaga (2003) have recently proposed that observations of the CMBR brightness temperature fluctuations produced by the HI inhomogeneities prior to reionization hold the promise of probing the primordial power spectrum to a hitherto unprecedented level of accuracy. This requires a precise quantification of the relation between density perturbations and brightness temperature fluctuations. Brightness temperature fluctuations arise from two sources (1.) fluctuations in the spin temperature, and (2.) fluctuations in the HI optical depth, both of which are caused by density perturbations. For the spin temperature, we investigate in detail its evolution in the presence of HI fluctuations. For the optical depth, we find that it is affected by density perturbations both directly and through peculiar velocities which move the absorption features around in frequency. The latter effect, which has not been included in earlier studies, is similar to the redshift space distortion seen in galaxy surveys and this can cause changes of 50% or more in the birghtness temperature fluctuations.

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.

Testing homogeneity on large scales in the Sloan Digital Sky Survey Data Release One

The assumption that the Universe is homogeneous and isotropic on large scales is one of the fundamental postulates of cosmology. We have tested the large-scale homogeneity of the galaxy distribution in the Sloan Digital Sky Survey Data Release One (SDSS-DR1) using volumelimited subsamples extracted from the two equatorial strips that are nearly two-dimensional. The galaxy distribution was projected on the equatorial plane and we carried out a 2D multifractal analysis by counting the number of galaxies inside circles of different radii, r ,i nthe range 5‐150 h −1 Mpc centred on galaxies. Different moments of the count-in-cells were analysed to identify a range of length-scales (60‐70 h −1 Mpc to 150 h −1 Mpc ), where the moments show ap ower-law scaling behaviour, and to determine the scaling exponent that gives the spectrum of generalized dimension Dq .I fthe galaxy distribution is homogeneous, Dq does not vary with q and is equal to the Euclidean dimension, which in our case is 2. We find that Dq varies in the range 1.7‐2.2. We also constructed mock data from random, homogeneous point distributions and from lambda cold dark matter (�CDM) N-body simulations with bias b = 1, 1.6 and 2, and analysed these in exactly the same way. The values of Dq in the random distribution and the unbiased simulations show much smaller variations and these are not consistent with the actual data. The biased simulations, however, show larger variations in Dq and these are consistent with both the random and the actual data. Interpreting the actual data as a realization of

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.

The scale of homogeneity of the galaxy distribution in SDSS DR6

The assumption that the Universe, on sufficiently large scales, is homogeneous and isotropic is crucial to our current understanding of cosmology. In this Letter, we test if the observed galaxy distribution is actually homogeneous on large scales. We have carried out a multifractal analysis of the galaxy distribution in a volume-limited subsample from the Sloan Digital Sky Survey (SDSS) Data Release 6. This considers the scaling properties of different moments of galaxy number counts in spheres of varying radius, r, centred on galaxies. This analysis gives the spectrum of generalized dimension Dq(r), where q> 0 quantifies the scaling properties in overdense regions and q< 0 in underdense regions. We expect Dq(r) = 3 for a homogeneous, random point distribution. In our analysis, we have determined Dq(r) in the range −4 ≤ q ≤ 4 and 7 ≤ r ≤ 98 h −1 Mpc. In addition to the SDSS data, we have analysed several random samples which are homogeneous by construction. Simulated galaxy samples generated from dark matter N-body simulations and the Millennium Run were also analysed. The SDSS data is considered to be homogeneous if the measured Dq is consistent with that of the random samples. We find that the galaxy distribution becomes homogeneous at a length-scale between 60 and 70 h −1 Mpc. The galaxy distribution, we find, is homogeneous at length-scales greater than 70 h −1 Mpc. This is consistent with earlier works which find the transition to homogeneity at around 70 h −1 Mpc.

The multifrequency angular power spectrum of the epoch of reionization 21-cm signal

Observations of redshifted 21cm radiation from neutral hydrogen (HI) at high redshifts is an important future probe of reionization. We consider the Multi-frequency Angular Power Spectrum (MAPS) to quantify the statistics of the HI signal as a joint function of the angular multipole l and frequency separation �ν. The signal at two different frequencies is expected to decorrelate as �ν is increased, and quantifying this is particularly importa nt in deciding the frequency resolution for future HI observations. This is al so expected to play a very crucial role in extracting the signal from foregrounds as the signal is expected to decorrelate much faster than the foregrounds (which are largely continuum sources) with increasing �ν. In this paper we develop formulae relating MAPS to different components of the three dimensional HI power spectrum taking into account HI peculiar velocities. We show that the flat-sky approximation provides a very good representation over the angular scales of interest, and a final expression which is very simple to calculate and in terpret. We present results for z = 10 assuming a neutral hydrogen fraction of 0.6 considering two models for the HI distribution, namely, (i) DM: where the HI traces the dark matter and (ii) PR: where the effects of patchy reionization are incorporated through two parameters which are the bubble size and the clustering of the bubble centers relative to the dark mat ter (bias) respectively. We find that while the DM signal is largely featureless, the PR signal peaks at the angular scales of the individual bubbles where it is Poisson fluctuation dominate d, and the signal is considerably enhanced for large bubble size. For most cases of interest at l � 100 the signal is uncorrelated beyond �ν � 1MHz or even less, whereas this occurs around � 0.1MHz at l � 10 3 . The �ν dependence also carries an imprint of the bubble size and the bias, and is expected to be an important probe of the reionization scenario. Finally we find that the l range 10 3 10 4 is optimum for separating out the cosmological HI signal from the foregrounds, while this will be extremely demanding at l < 100 where it is necessary to characterize the �ν dependence of the foreground MAPS to an accuracy better than 1%.

Characterizing Foreground for redshifted 21-cm radiation: 150 MHz GMRT 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.

The Size of the Longest Filaments in the Universe

We analyze the filamentarity in the Las Campanas redshift survey (LCRS) and determine the length scale at which filaments are statistically significant. The largest length scale at which filaments are statistically significant, real objects is between 70 and 80 h-1 Mpc for the LCRS -3° slice. Filamentary features longer than 80 h-1 Mpc, although identified, are not statistically significant; they arise from chance alignments. For the five other LCRS slices, filaments of lengths 50-70 h-1 Mpc are statistically significant, but not beyond. These results indicate that while individual filaments up to 80 h-1 Mpc are statistically significant, the impression of structure on larger scales is a visual effect. On scales larger than 80 h-1 Mpc, the filaments interconnect by statistical chance to form the filament-void network. The reality of the 80 h-1 Mpc features in the -3° slice makes them the longest coherent features in the LCRS. While filaments are a natural outcome of gravitational instability, any numerical model that attempts to describe the formation of large-scale structure in the universe must produce coherent structures on scales that match these observations.

Modeling galaxy halos using dark matter with pressure

We investigate whether a dark matter with substantial amounts of pressure, comparable in magnitude to the energy density, could be a viable candidate for the constituent of dark matter halos. We find that galaxy halos models, consistent with observations of flat rotation curves, are possible for a variety of equations of state with anisotropic pressures. It turns out that the gravitational bending of light rays passing through such halos is very sensitive to the pressure. We propose that combined observations of rotation curves and gravitational lensing can be used to determine the equation of state of the dark matter. Alternatively, if the equation of state is known from other observations, rotation curves and gravitational lensing can together be used to test General Relativity on galaxy scales.