Cross-correlation between WMAP and 2MASS: non-Gaussianity induced by the SZ effect

We study the non-Gaussianity induced by the Sunyaev–Zel'dovich (SZ) effect in cosmic microwave background (CMB) fluctuation maps. If a CMB map is contaminated by the SZ effect of galaxies or galaxy clusters, the CMB maps should have similar non-Gaussian features to the galaxy and cluster fields. Using the WMAP data and 2MASS galaxy catalogue, we show that the non-Gaussianity of the 2MASS galaxies is imprinted on WMAP maps. The signature of non-Gaussianity can be seen with the fourth-order cross-correlation between the wavelet variables of the WMAP maps and 2MASS clusters. The intensity of the fourth-order non-Gaussian features is found to be consistent with the contamination of the SZ effect of 2MASS galaxies. We also show that this non-Gaussianity can not be seen by the high-order autocorrelation of the WMAP . This is because the SZ signals in the autocorrelations of the WMAP data generally are weaker than the WMAP –2MASS cross-correlations by a factor f ², which is the ratio between the powers of the SZ-effect map and the CMB fluctuations on the scale considered. Therefore, the ratio of high-order autocorrelations of CMB maps to cross-correlations of the CMB maps and galaxy field would be effective to constrain the powers of the SZ effect on various scales.     

Measuring statistical isotropy of CMB anisotropy

The statistical expectation values of the temperature fluctuations and polarization of cosmic microwave background (CMB) are assumed to be preserved under rotations of the sky. We investigate the statistical isotropy (SI) of the CMB maps recently measured by the Wilkinson microwave anisotropy probe (WMAP) using the bipolar spherical harmonic formalism proposed in Hajian and Souradeep [Hajian, A., Souradeep, T. (2003) Astrophys. J. Lett. 597, L5] for CMB temperature anisotropy and extended to CMB polarization in Basak, Hajian and Souradeep [Basak, S., Hajian, A., Souradeep, T. (2006) Phys. Rev. D74, 02130(R)]. The Bipolar Power Spectrum (BiPS) had been measured for the full sky CMB anisotropy maps of the first year WMAP data and now for the recently released three years of WMAP data. We also introduce and measure directional sensitive reduced Bipolar coefficients on the three year WMAP ILC map. Consistent with our published results from first year WMAP data we have no evidence for violation of statistical isotropy on large angular scales. Preliminary analysis of the recently released first WMAP polarization maps, however, indicate significant violation of SI even when the foreground contaminated regions are masked out. Further work is required to confirm a possible cosmic origin and rule out the (more likely) origin in observational artifact such as foreground residuals at high galactic latitude.     

Understanding the WMAP Results: Low-Order Multipoles and Dust in the Vicinity of the Solar System

Analyses of the cosmic microwave background (CMB) radiation maps produced by the Wilkinson Microwave Anisotropy Probe (WMAP) have revealed anomalies not predicted by the standard cosmological theory. It has been suggested that a dust cloud in the vicinity of the Solar system may be the cause for these anomalies. In this paper, the thermal emission by particles from two known interplanetary meteoroid complexes is tested against the CMB maps. Conclusions are drawn based on the geometry of cloud projections onto the WMAP sky whether these clouds are likely to explain the observed anomaly. The smooth background Zodiacal cloud and one of the Taurid meteor complex branches do not explain the WMAP anomaly.     

Foreground removal from WMAP 7 yr polarization maps using an MLP neural network

One of the fundamental problems in extracting the cosmic microwave background signal (CMB) from millimeter/submillimeter observations is the pollution by emission from the Milky Way: synchrotron, free-free, and thermal dust emission. To extract the fundamental cosmological parameters from CMB signal, it is mandatory to minimize this pollution since it will create systematic errors in the CMB power spectra. In previous investigations, it has been demonstrated that the neural network method provide high quality CMB maps from temperature data. Here the analysis is extended to polarization maps. As a concrete example, the WMAP 7-year polarization data, the most reliable determination of the polarization properties of the CMB, has been analyzed. The analysis has adopted the frequency maps, noise models, window functions and the foreground models as provided by the WMAP Team, and no auxiliary data is included. Within this framework it is demonstrated that the network can extract the CMB polarization signal with no sign of pollution by the polarized foregrounds. The errors in the derived polarization power spectra are improved compared to the errors derived by the WMAP Team.     

Angular power spectrum of CMB anisotropy from WMAP

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.     

Observation number correlation in WMAP data

A remarkable similarity between the large-scale non-Gaussian pattern of cosmic microwave background (CMB) temperatures obtained by the Wilkinson Microwave Anisotropy Probe ( WMAP ) mission and the distribution features of observation numbers is noted. Motivated by such a similarity, in this work we check the WMAP data for the correlation between pixel temperature t and observation number N . Systematic effects of imbalance in the differential observations and significant t – N correlations in magnitude, distribution of non-Gaussianity and north–south asymmetry are found. Our results indicate that, for precision cosmology studies based on WMAP observations, the observation effect on released WMAP temperature maps requires further careful study.     

Predicting the polarization of the microwave background from the WMAP temperature maps

In this paper, we study how to predict the polarization of the Cosmic Microwave Background (CMB) using knowledge of only the temperature (intensity) and the cross-correlation between temperature and polarization. We derive a “Wiener prediction” method and apply it to the Wilkinson Microwave Anisotropy Probe (WMAP) all-sky CMB temperature maps and to the MAXIMA field.     

The WMAP data and results

The Wilkinson Microwave Anisotropy Probe (WMAP) science team has released results from the first year of operation at the Earth–Sun L₂ Lagrange point. The maps are consistent with previous observations but have much better sensitivity and angular resolution than the COBE DMR maps, and much better calibration accuracy and sky coverage than ground-based and balloon-borne experiments. The angular power spectra from these ground-based and balloon-borne experiments are consistent within their systematic and statistical uncertainties with the WMAP results. WMAP detected the large angular-scale correlation between the temperature and polarization anisotropies of the CMB caused by electron scattering since the Universe became reionized after the “Dark Ages”, giving a value for the electron scattering optical depth of 0.17 ± 0.04. The simplest ΛCDM model with n=1 and Ω_tot=1 fixed provides an adequate fit to the WMAP data and gives parameters which are consistent with determinations of the Hubble constant and observations of the accelerating Universe using supernovae. The time-ordered data, maps, and power spectra from WMAP can be found at http://lambda.gsfc.nasa.gov along with 13 papers by the WMAP science team describing the results in detail.     

A comparison of anisotropic statistical properties of CMB maps based on the WMAP and planck space mission data

We compare the anisotropic properties of the cosmic microwave background (CMB) maps constructed based on the data of NASA’s WMAP (9th year of observations) and ESA’s Planck (2015 release) space missions. In our analysis, we use two two-dimensional estimators of the scatter of the signal on a sphere, which amount to algorithms of mapping the ratio of the scatter in the Northern and Southern hemispheres depending on the method of dividing (specifically, rotating and cutting) the sky into hemispheres. The scatter is computed either as a standard deviation σ, or as the difference between the minimum and maximum values on a given hemisphere. Applying both estimators to the CMB anisotropy datameasured by two spacemissions, Planck and WMAP, we compared the variations of the background at different angular scales.Maps with a resolution of l ≤ 100 show that the division into regions with different levels of statistical anisotropy lies close to the ecliptic plane, and after preliminary removal of the l ≤ 20 harmonics from the CMB data, the anisotropic signal related to the Galaxy begins to dominate.     

Non-random phases in non-trivial topologies

We present a new technique for constraining the topology of the Universe. The method exploits the existence of correlations in the phases of the spherical harmonic coefficients of the cosmic microwave background (CMB) temperature pattern associated with matched pairs of circles seen in the sky in universes with non-trivial topology. The method is computationally faster than all other statistics developed to hunt for these matched circles. We applied the method to a range of simulations with topologies of various forms and on different scales. A characteristic form of phase correlation is found in the simulations. We also applied the method to preliminary CMB maps derived from WMAP , but the separation of topological effects from e.g. foregrounds is not straightforward.     

Statistics of WMAP ILC map temperature fluctuations towards distant radio galaxies

For 2442 galaxies of the catalog, compiled based on the NED, SDSS, and CATS survey data with redshifts z, > 0.3 we conducted an analysis of the amplitude of temperature fluctuations in the cosmic microwave background (CMB) in the points, corresponding to the direction to these objects. To this end, we used the ILC map from the WMAP mission seven-year data release. We have estimated the dipole component of the background and tested the hypothesis of Kashlinsky on the existence of a “dark bulk flow”, determined for the estimated dipole component of the CMB WMAP by the value of the CMB anisotropy in the direction to the clusters of galaxies. We show that the amplitude of this dipole T _max = 0.012mK is located within the σ interval, estimated by Monte Carlo simulations for the Gaussian fluctuations of the CMB signal in the ΛCDM model. The low amplitude of the dipole indicates that it is impossible to confirm this hypothesis from the WMAP data. In addition, we studied the statistics of the fluctuation amplitude of the microwave signal in the direction to radio galaxies. A weakening of the absolute value of the mean signal in the corresponding fields was discovered.     

A low cosmic microwave background variance in the Wilkinson Microwave Anisotropy Probe data

We have estimated the cosmic microwave background (CMB) variance from the three-year Wilkinson Microwave Anisotropy Probe ( WMAP ) data, finding a value which is significantly lower than the one expected from Gaussian simulations using the WMAP best-fitting cosmological model, at a significance level of 98.7 per cent. This result is even more prominent if we consider only the North ecliptic hemisphere (99.8 per cent). Different analyses have been performed in order to identify a possible origin for this anomaly. In particular, we have studied the behaviour of single-radiometer and single-year data as well as the effect of residual foregrounds and 1/f noise, finding that none of these possibilities can explain the low value of the variance. We have also tested the effect of varying the cosmological parameters, finding that the estimated CMB variance tends to favour higher values of n _s than the one of the WMAP best-fitting model. In addition, we have also tested the consistency between the estimated CMB variance and the actual measured CMB power spectrum of the WMAP data, finding a strong discrepancy. A possible interpretation of this result could be a deviation from Gaussianity and/or isotropy of the CMB.     

Tessellated mapping of cosmic background radiation correlations and source distributions

We offer a method of correlations mapping on the full celestial sphere that allows to check the quality of reconstructed maps, their non-Gaussianity and conduct experiments in various frequency ranges. The method was evaluated on the WMAP data, both on the reconstructed maps and foreground components, and on the NRAO VLA Sky Survey (NVSS) data. We detected a significant shift in the correlation data of the dust component, which can be preconditioned by a more complex dust model than the one currently in use for component separation. While studying the NVSS correlation data, we demonstrated that the statistics of the coinciding spots in the microwave background and in the NVSS survey corresponds to the one expected in the ΛCDM model. This can testify for a chance coincidence of the spots in the NVSS and WMAP data in the CMB Cold Spot region. Our method is software-implemented in the GLESP package.     

Wilkinson Microwave Anisotropy Probe 5-yr constraints on fnl with wavelets

We present a Gaussianity analysis of the Wilkinson Microwave Anisotropy Probe ( WMAP ) 5-yr cosmic microwave background (CMB) temperature anisotropy data maps. We use several third-order estimators based on the spherical Mexican hat wavelet. We impose constraints on the local non-linear coupling parameter f _nl using well-motivated non-Gaussian simulations. We analyse the WMAP maps at resolution of 6.9 arcmin for the Q , V , and W frequency bands. We use the KQ 75 mask recommended by the WMAP team which masks out 28 per cent of the sky. The wavelet coefficients are evaluated at 10 different scales from 6.9 to 150 arcmin. With these coefficients, we compute the third order estimators which are used to perform a  χ²  analysis. The  χ²  statistic is used to test the Gaussianity of the WMAP data as well as to constrain the f _nl parameter. Our results indicate that the WMAP data are compatible with the Gaussian simulations, and the f _nl parameter is constrained to  −8 < f _nl < +111  at 95 per cent confidence level (CL) for the combined   V + W   map. This value has been corrected for the presence of undetected point sources, which add a positive contribution of  Δ f _nl= 3 ± 5  in the   V + W   map. Our results are very similar to those obtained by the WMAP team using the bispectrum.     

Understanding the WMAP Cold Spot mystery

The Cold Spot (CS) at galactic coordinates (b = −57°, l = 209°) was discovered in the Wilkinson Microwave Anisotropy Probe (WMAP)data as a cosmic background anomaly. In order to assess the cosmological significance of the Spot, we examine its properties using the cluster analysis of the local extrema in the cosmic microwave background (CMB) signal. We also check the hypothesis that the CMB signal has a non-Gaussian tail, localized in the low-multipole components. We constructed a linear filter, dividing the signal into two parts: non-Gaussian and Gaussian. Using the filter scale as a variable, we can maximize the skewness and kurtosis of the smoothed signal and minimize these statistics. We discovered that the shape of the CS is formed primarily by the components of the CMB signal represented by the multipoles between 10 ≤ ℓ ≤ 20, with a corresponding angular scale of about 5°–10°. This signal leads to the modulation of the CMB on the whole sky, clearly seen at |b| > 30° in both the ILC andWCM maps, rather than in a single localized feature. After subtraction of this modulation, the remaining part of the CMB signal appears to be consistent with statistical homogeneity and Gaussianity. We therefore infer that the mystery of the WMAP Cold Spot reflects directly the peculiarities of low multipoles of the CMB signal, rather than a single local (isolated) defect or the manifestations of a globally anisotropic cosmology.     

Testing isotropy of cosmic microwave background radiation

We introduce new symmetry-based methods to test for isotropy in cosmic microwave background (CMB) radiation. Each angular multipole is factored into unique products of power eigenvectors, related multipoles and singular values that provide two 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. The ILC– WMAP data maps show seven 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 per cent probability or lower in an isotropic distribution. Isotropy of the ILC maps is ruled out to confidence levels of better than 99.9 per cent, 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.     

Cosmology from 3 years of WMAP CMB data

The combined 3 year observations from the Wilkinson Microwave Anisotropy Probe (WMAP) have yielded full-sky temperature and polarization maps in five frequency bands (K, Ka, Q, V, W) between 23 and 94 GHz. In this article we discuss the cosmological implications of these observations. The combination of temperature and polarization data leads to a significant improvement in the measurement of the reionization optical depth τ = 0.093 ± 0.029. This, in turn, breaks a number of key degeneracies present in the constraints from temperature measurements alone allowing the WMAP CMB data on its own to offer a powerful insight into the universe’s constituents and the processes that generated the initial conditions for structure formation.     

A Faraday rotation template for the Galactic sky

Using a set of compilations of measurements for extragalactic radio sources, we construct all-sky maps of the Faraday rotation produced by the Galactic magnetic field. In order to generate the maps, we treat the radio source positions as a kind of 'mask' and construct combinations of spherical harmonic modes that are orthogonal on the masked sky. As long as relatively small multipoles are used, the resulting maps are quite stable to changes in the selection criteria for the sources, and show clearly the structure of the local Galactic magnetic field. We also suggest the use of these maps as templates for cosmic microwave background (CMB) foreground analysis, illustrating the idea with a cross-correlation analysis between the Wilkinson Microwave Anisotropy Probe ( WMAP ) data and our maps. We find a significant cross-correlation, indicating the presence of a significant residual contamination.     

Non-Gaussian foreground residuals of the WMAP first-year maps

We investigate the effect of foreground residuals in the WMAP ( Wilkinson Microwave Anisotropy Probe ) data by adding foreground contamination to Gaussian ensembles of cosmic microwave background (CMB) signal and noise maps. We evaluate a set of non-Gaussian estimators on the contaminated ensembles to determine with what accuracy any residual in the data can be constrained using higher-order statistics. We apply the estimators to the raw and cleaned Q -, V - and W -band first-year maps. The foreground subtraction method applied to clean the data in Bennett et al. appears to have induced a correlation between the power spectra and normalized bispectra of the maps which is absent in Gaussian simulations. It also appears to increase the correlation between the  Δℓ= 1  inter-ℓ bispectrum of the cleaned maps and the foreground templates. In a number of cases the significance of the effect is above the 98 per cent confidence level.     

Applications of high resolution high sensitivity observations of the CMB

With WMAP putting the phenomenological standard model of cosmology on a strong footing, one can look forward to mining the cosmic microwave background (CMB) for fundamental physics with higher sensitivity and on smaller scales. Future CMB observations have the potential to measure absolute neutrino masses, test for cosmic acceleration independent of supernova Ia observations, probe for the presence of dark energy at z2, illuminate the end of the dark ages, measure the scale-dependence of the primordial power spectrum and detect gravitational waves generated by inflation.