Rajib Saha

A reanalysis of the 3 year Wilkinson microwave anisotropy probe temperature power spectrum and likelihood

We analyze the 3 yr Wilkinson Microwave Anisotropy Probe (WMAP) temperature anisotropy data seeking to confirm the power spectrum and likelihoods published by the WMAP team. We apply five independent implementations of four algorithms to the power spectrum estimation and two implementations to the parameter estimation. Our single most important result is that we broadly confirm the WMAP power spectrum and analysis. Still, we do find two small but potentially important discrepancies. On large angular scales there is a small power excess in the WMAP spectrum (5%-10% at ell lesssim 30) primarily due to likelihood approximation issues between 13 ≤ ell lesssim 30. On small angular scales there is a systematic difference between the V- and W-band spectra (few percent at ell gtrsim 300). Recently, the latter discrepancy was explained by Huffenberger et al. (2006) in terms of oversubtraction of unresolved point sources. As far as the low-ell bias is concerned, most parameters are affected by a few tenths of a σ. The most important effect is seen in ns. For the combination of WMAP, ACBAR, and BOOMERANG, the significance of ns ≠ 1 drops from ~2.7 σ to ~2.3 σ when correcting for this bias. We propose a few simple improvements to the low-ell WMAP likelihood code, and introduce two important extensions to the Gibbs sampling method that allows for proper sampling of the low signal-to-noise ratio regime. Finally, we make the products from the Gibbs sampling analysis publicly available, thereby providing a fast and simple route to the exact likelihood without the need of expensive matrix inversions.We analyze the three-year WMAP temperature anisotropy data seeking to confirm the power spectrum and likelihoods published by the WMAP team. We apply five independent implementations of four algorithms to the power spectrum estimation and two implementations to the parameter estimation. Our single most important result is that we broadly confirm the WMAP power spectrum and analysis. Still, we do find two small but potentially important discrepancies: On large angular scales there is a small power excess in the WMAP spectrum (5-10% at l ~300). Recently, the latter discrepancy was explained by Huffenberger et al. (2006) in terms of over-subtraction of unresolved point sources. As far as the low-l bias is concerned, most parameters are affected by a few tenths of a sigma. The most important effect is seen in n_s. For the combination of WMAP, Acbar and BOOMERanG, the significance of n_s =/ 1 drops from ~2.7 sigma to ~2.3 sigma when correcting for this bias. We propose a few simple improvements to the low-l WMAP likelihood code, and introduce two important extensions to the Gibbs sampling method that allows for proper sampling of the low signal-to-noise regime. Finally, we make the products from the Gibbs sampling analysis publically available, thereby providing a fast and simple route to the exact likelihood without the need of expensive matrix inversions.

Testing Isotropy of Cosmic Microwave Background Radiation

We introduce new symmetry-based methods to test for isotropy in cosmic microwave background radiation. Each angular multipole is factored into unique products of power eigenvectors, related multipoles and singular values that provide 2 new rotationally invariant measures mode by mode. The power entropy and directional entropy are new tests of randomness that are independent of the usual CMB power. Simulated galactic plane contamination is readily identified, and the new procedures mesh perfectly with linear transformations employed for windowed-sky analysis. The ILC -WMAP data maps show 7 axes well aligned with one another and the direction Virgo. Parameter free statistics find 12 independent cases of extraordinary axial alignment, low power entropy, or both having 5% probability or lower in an isotropic distribution. Isotropy of the ILC maps is ruled out to confidence levels of better than 99.9%, whether or not coincidences with other puzzles coming from the Virgo axis are included. Our work shows that anisotropy is not confined to the low l region, but extends over a much larger l range.

Signals of statistical anisotropy in WMAP foreground-cleaned maps

Recently, a symmetry-based method to test for statistical isotropy of the cosmic microwave background was developed. We apply the method to template-cleaned 3- and 5-years Wilkinson Microwave Anisotropy Probe-Differencing Assembly maps. We examine a wide range of angular multipoles from 2 < l < 300. The analysis detects statistically significant signals of anisotropy inconsistent with an isotropic cosmic microwave background in some of the foreground-cleaned maps. We are unable to resolve whether the anomalies have a cosmological, local astrophysical or instrumental origin. Assuming the anisotropy arises due to residual foreground contamination, we estimate the residual foreground power in the maps. For the W-band maps, we also find a highly improbable degree of isotropy we cannot explain. We speculate that excess isotropy may be caused by faulty modelling of detector noise.

CMB anisotropy power spectrum using linear combinations of WMAP maps

In recent years the goal of estimating different cosmological parameters precisely has set new challenges in the effort to accurately measure the angular power spectrum of the CMB. This has required removal of foreground contamination as well as detector noise bias with reliability and precision. Recently, a novel, model-independent method for the estimation of the CMB angular power spectrum solely from multifrequency observations has been proposed and implemented on the first year WMAP data by Saha et al. 2006. All previous estimates of the power spectrum of the CMB are based upon foreground templates using data sets from different experiments. However, our methodology demonstrates that the CMB angular spectrum can be reliably estimated with precision from a self-contained analysis of the WMAP data. In this work we provide a detailed description of this method. We also study and identify the biases present in our power spectrum estimate. We apply our methodology to extract the power spectrum from the WMAP data.

A Blind Estimation of the Angular Power Spectrum of CMB Anisotropy from WMAP

Accurate measurements of the angular power spectrum of cosmic microwave background (CMB) radiation have lead to a marked improvement in the estimates of different cosmological parameters. This has required removal of foreground contamination as well as detector noise bias with reliability and precision. We present the estimation of the CMB angular power spectrum from the multifrequency observations of the Wilkinson Microwave Anisotropy Probe (WMAP) using a novel model-independent method. The primary results of WMAP are the observations of the CMB in 10 independent difference assemblies (DAs) that have uncorrelated noise. Our method utilizes the maximum information available within the WMAP data by linearly combining all the DA maps in order to remove foreground contamination and by estimating the power spectrum from cross-power spectra of clean maps with independent noise. We compute 24 cross-power spectra that are the basis of the final power spectrum. The binned average power matches the WMAP teams published power spectrum closely. A small systematic difference at large multipoles is accounted for by the correction for the expected residual power from unresolved point sources. The correction is small and significantly tempered. Previous estimates have depended on foreground templates built using extraneous observational input. This is the first demonstration that the CMB angular spectrum can be reliably estimated with precision from a self-contained analysis of the WMAP data.

COSMIC MICROWAVE BACKGROUND POLARIZATION AND TEMPERATURE POWER SPECTRA ESTIMATION USING LINEAR COMBINATION OF WMAP 5 YEAR MAPS

We estimate cosmic microwave background (CMB) polarization and temperature power spectra using Wilkinson Microwave Anisotropy Probe (WMAP) 5 year foreground contaminated maps. The power spectrum is estimated by using a model-independent method, which does not utilize directly the diffuse foreground templates nor the detector noise model. The method essentially consists of two steps: (1) removal of diffuse foregrounds contamination by making linear combination of individual maps in harmonic space and (2) cross-correlation of foreground cleaned maps to minimize detector noise bias. For the temperature power spectrum we also estimate and subtract residual unresolved point source contamination in the cross-power spectrum using the point source model provided by the WMAP science team. Our TT, TE, and EE power spectra are in good agreement with the published results of the WMAP science team. We perform detailed numerical simulations to test for bias in our procedure. We find that the bias is small in almost all cases. A negative bias at low l in TT power spectrum has been pointed out in an earlier publication. We find that the bias-corrected quadrupole power (l(l + 1)Cl /2π) is 532 μK2, approximately 2.5 times the estimate (213.4 μK2) made by the WMAP team.

Non-circular beam correction to the CMB power spectrum

Abstract In the era of high precision CMB measurements, systematic effects are beginning to limit the ability to extract subtler cosmological information. The non-circularity of the experimental beam has become progressively important as CMB experiments strive to attain higher angular resolution and sensitivity. The effect of non-circular beam on the power spectrum is important at multipoles larger than the beam-width. For recent experiments with high angular resolution, optimal methods of power spectrum estimation are computationally prohibitive and sub-optimal approaches, such as the Pseudo- C l method are used. We provide an analytic framework for correcting the power spectrum for the effect of beam non-circularity and non-uniform sky coverage (including incomplete/masked sky maps). The approach is perturbative in the distortion of the beam from non-circularity allowing for rapid computations when the beam is mildly non-circular. We advocate that when the non-circular beams are important, it is computationally advantageous to employ ‘soft’ azimuthally apodized masks whose spherical harmonic transforms die down fast with m .

The dynamical mixing of light and pseudoscalar fields

We solve the general problem of mixing of electromagnetic and scalar or pseudoscalar fields coupled by axion-type interactions Lint = gϕϕεμναβFμνFαβ. The problem depends on several dimensionful scales, including the magnitude and direction of background magnetic field, the pseudoscalar mass, plasma frequency, propagation frequency, wave number, and finally the pseudoscalar coupling. We apply the results to the first consistent calculations of the mixing of light propagating in a background magnetic field of varying directions, which show a great variety of fascinating resonant and polarization effects.

Angular power spectrum of CMB anisotropy from WMAP

Abstract The remarkable improvement in the estimates of different cosmological parameters in recent years has been largely spearheaded by accurate measurements of the angular power spectrum of cosmic microwave background (CMB) radiation. This has required removal of foreground contamination as well as detector noise bias with reliability and precision. Recently, a novel model-independent method for the estimation of CMB angular power spectrum from multi-frequency observations has been proposed and implemented on the first year WMAP (WMAP-1) data by Saha et al. [Saha, R., Jain, P., Souradeep, T., 2006. ApJL, 645, L89]. We review the results from WMAP-1 and also present the new angular power spectrum based on three years of the WMAP data (WMAP-3). Previous estimates have depended on foreground templates built using extraneous observational input to remove foreground contamination. This is the first demonstration that the CMB angular spectrum can be reliably estimated with precision from a self contained analysis of the WMAP data. The primary product of WMAP are the observations of CMB in 10 independent difference assemblies (DA) distributed over five frequency bands that have uncorrelated noise. Our method utilizes maximum information available within WMAP data by linearly combining DA maps from different frequencies to remove foregrounds and estimating the power spectrum from the 24 cross-power spectra of clean maps that have independent noise. An important merit of the method is that the expected residual power from unresolved point sources is significantly tempered to a constant offset at large multipoles (in contrast to the ∼l2 contribution expected from a Poisson distribution) leading to a small correction at large multipoles. Hence, the power spectrum estimates are less susceptible to uncertainties in the model of point sources.