Probing dark energy with steerable wavelets through correlation of WMAP and NVSS local morphological measures

Using local morphological measures on the sphere defined through a steerable wavelet analysis, we examine the three-year Wilkinson Microwave Anisotropy Probe WMAP and the NRAO VLA Sky Survey (NVSS) data for correlation induced by the integrated Sachs–Wolfe (ISW) effect. The steerable wavelet constructed from the second derivative of a Gaussian allows one to define three local morphological measures, namely the signed-intensity, orientation and elongation of local features. Detections of correlation between the WMAP and NVSS data are made with each of these morphological measures. The most significant detection is obtained in the correlation of the signed-intensity of local features at a significance of 99.9 per cent. By inspecting signed-intensity sky maps, it is possible for the first time to see the correlation between the WMAP and NVSS data by eye. Foreground contamination and instrumental systematics in the WMAP data are ruled out as the source of all significant detections of correlation. Our results provide new insight on the ISW effect by probing the morphological nature of the correlation induced between the cosmic microwave background and large-scale structure of the Universe. Given the current constraints on the flatness of the Universe, our detection of the ISW effect again provides direct and independent evidence for dark energy. Moreover, this new morphological analysis may be used in future to help us to better understand the nature of dark energy.     

Correlation properties of the maps of the NVSS survey and WMAP ILC

In this paper we study one-dimensional sections of the maps of WMAP ILC and of the NVSS survey on scale lengths of 0.75, 3, 4.5, and 6.75 degrees and analyze the correlation properties of the sections. On these maps we identify the domains where the absolute value of the correlation coefficient exceeds 0.5. The catalog of such domains is presented. It is shown that the number of the domains agrees with the number of such domains on simulated maps and this fact may be indicative of just statistical agreement of the arrangement of the domains considered.     

Properties of one-dimensional sections of WMAP maps at the declination <Emphasis Type="Italic">δ</Emphasis> = 41°

One-dimensional sections of WMAP maps—ILC and background components (synchrotron, free-free radiation and dust emission) are investigated and their correlation properties on various angular scales are analyzed. Sections of the ILC map are found to correlate significantly with the maps of Galactic background components at the δ = 41° declination of RATAN-600 survey. The confidence level of the correlations found is estimated by analyzing random realizations of the Gaussian process that describes the microwave background. A method for identifying correlated intervals from maps on the sphere as a function of angular scale is proposed. This method can be used to search for non-Gaussian features (spots) found in the distribution of microwave background and radio sources in the same coordinate areas. The approach described can also be used to search for such non-Gaussian sources in observational programs performed on the radio telescope RATAN-600.     

On two low harmonics of CMB correlation maps

We have analyzed two powerful correlation harmonics (ℓ = 3and ℓ = 6) found in the correlation of the ILC WMAP signal with the submillimeter and infrared range data from the FSC IRAS and Planck catalogs. The mode phases of thesemultipoles were computed. In the spots we have found in the harmonics, the source counts were made from the NVSS, FIRST, FSC IRAS and Planck surveys. The correlation harmonic phases are close at different observational frequencies both for ℓ = 3and ℓ = 6.We do not exclude that a part of the weak signal in the ILCWMAP data, manifested in the strong correlation properties of the investigated multipoles may be due to extragalactic radiation sources.     

The Sunyaev–Zel'dovich effect contribution to WMAP: a cross-correlation between WMAP and ROSAT

We cross-correlate WMAP and ROSAT diffuse X-ray background maps and look for common features in both data sets. We use the power spectrum of the product maps and the cross-power spectrum to highlight a possible correlation. The power spectrum of the product maps does not detect any correlation and the cross-power spectrum does not show any significant deviation from zero. We explore different explanations for this lack of correlation. A universe with a low value of  σ₈  could naturally explain the lack of correlation. We also discuss the systematic effects that can affect this result, in particular the subtraction of some cluster signal from the ROSAT diffuse maps, which could significantly suppress the correlation signal. These systematic effects considerably reduce the significance of our constraints on the cosmological model. When we include the systematic effects, we find a weaker constraint on  σ₈  , allowing models with values as large as  σ₈= 1  (for  Ω_m= 0.3  ) to be consistent with the lack of correlation. To illustrate the capabilities of the method with future high-quality data, we show how from the correlation signal it should be possible to predict the level of contamination of the Sunyaev–Zel'dovich effect on the power spectrum of the cosmic microwave background. Within the systematic errors, we find evidence that this contribution is negligible for WMAP and is expected to be small in experiments like ACBAR or CBI, but can be important for future high-resolution experiments.     

The hot and cold spots in five-year WMAP data

We present an extensive frequentist analysis of the one-point statistics (number, mean, variance, skewness and kurtosis) and two-point correlation functions determined for the local extrema of the cosmic microwave background temperature field observed in five-years of Wilkinson Microwave Anisotropy Probe ( WMAP ) data. Application of a hypothesis test on the one-point statistics indicates a low variance of hot and cold spots in all frequency bands of the WMAP data. The consistency of the observations with Gaussian simulations of the best-fitting cosmological model is rejected at the 95 per cent confidence level outside the WMAP KQ75 mask and the Northern hemispheres in the Galactic and ecliptic coordinate frames. We demonstrate that it is unlikely that residual Galactic foreground emission contributes to the observed non-Gaussianities. However, the application of a high-pass filter that removes large angular scale power does improve the consistency with the best-fitting cosmological model.
Two-point correlation functions of the local extrema are calculated for both the temperature pair product [temperature–temperature (T–T)] and spatial pair-counting [point–point (P–P)]. The T–T observations demonstrate weak correlation on scales below  20°  and lie completely below the lower 3σ confidence region once various temperature thresholds are applied to the extrema determined for the KQ75 mask and northern sky partitions. The P–P correlation structure corresponds to the clustering properties of the temperature extrema, and provides evidence that it is the large angular-scale structures, and some unusual properties thereof, that are intimately connected to the properties of the hot and cold spots observed in the WMAP five-year data.     

Cross-Correlation Detection of Point Sources in the WMAP First Year Data

We apply a Cross-Correlation (CC) method developed previously for detecting gamma-ray point sources to the WMAP first year data by using the Point-Spread Function of WMAP and obtain a full sky CC coefficient map. We find that the CC method is a pow- erful tool to examine the WMAP foreground residuals which can be further cleaned accord- ingly. Evident foreground signals are found in the WMAP foreground cleaned maps and the Tegmark cleaned map. In this process 101 point sources are detected, and 26 of them are new sources additional to the originally listed WMAP 208 sources. We estimate the ?ux of these new sources and verify them by another method. As a result, a revised mask file based on the WMAP first year data is produced by including these new sources.     

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.     

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.     

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.     

A special kind of local structure in the CMB intensity maps： duel peak structure

We study the local structure of Cosmic Microwave Background (CMB) tem-perature maps released by the Wilkinson Microwave Anisotropy Probe (WMAP) team, and find a new kind of structure, which can be described as follows: a peak (or valley) of average temperature is often followed by a peak of temperature fluctuation that is 4° away. This structure is important for the following reasons: both the well known cold spot detected by Cruz et al. and the hot spot detected by Vielva et al. with the same technology (the third spot in their article) have such structure; more spots that are similar to them can be found on CMB maps and they also tend to be significant cold/hot spots; if we change the 4° characteristic into an artificial one, such as 3° or 5°, there will be less "similar spots", and the temperature peaks or valleys will be less significant. The presented "sim-ilar spots" have passed a strict consistency test which requires them to be significant on at least three different CMB temperature maps. We hope that this article could arouse some interest in the relationship of average temperature with temperature fluctuation in local areas; meanwhile, we are also trying to find an explanation for it which might be important to CMB observation and theory.     

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.     

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.     

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.     

No large-angle correlations on the non-Galactic microwave sky

We investigate the angular two-point correlation function of temperature in the Wilkinson Microwave Anisotropy Probe ( WMAP) maps. Updating and extending earlier results, we confirm the lack of correlations outside the Galaxy on angular scales greater than about 60° at a level that would occur in 0.025 per cent of realizations of the concordance model. This represents a dramatic increase in significance from the original observations by the Cosmic Background Explorer Differential Microwave Radiometer ( COBE-DMR) and a marked increase in significance from the first-year WMAP maps. Given the rest of the reported angular power spectrum   C _ℓ  , the lack of large-angle correlations that one infers outside the plane of the Galaxy requires covariance among the   C _ℓ  up to  ℓ= 5  . Alternately, it requires both the unusually small (5 per cent of realizations) full-sky large-angle correlations and an unusual coincidence of alignment of the Galaxy with the pattern of cosmological fluctuations (less than 2 per cent of those 5 per cent). We argue that unless there is some undiscovered systematic error in their collection or reduction, the data point towards a violation of statistical isotropy. The near-vanishing of the large-angle correlations in the cut-sky maps, together with their disagreement with results inferred from full-sky maps, remains open problems, and are very difficult to understand within the concordance model.     

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.     

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.     

Determination of microwave background map inhomogeneity from angular power spectrum

We present a new method for analyzing the homogeneity of the microwave background maps, based on the behavior of the angular power spectrum C(ℓ). We realize the power spectrum dispersion variation of the background signal hemisphere in the form of a new map, which characterizes the homogeneity (or inhomogeneity) of the background in the second order. Applying our method we make an analysis of the seven-year WMAP mission signal for the maps with the resolution of ℓ ≤ 100. As a result, we discover the ILC signal asymmetry, linked with the ecliptic coordinate system, also revealed in the signal of the WMAP W-channel data.     

Identification of newly discovered radio-emitting X-ray sources: results from spectroscopy

We present optical identifications for a sample of 20 previously unknown X-ray/radio sources that are present both in the source catalogue of ROSAT PSPC pointed observations ( ROSAT SRC) and in the NRAO VLA Sky Survey (NVSS). The optical spectroscopy was carried out with the 2.1-m telescope at San Pedro Martir (Mexico) during 1995 April and September. We have identified 15 active galactic nuclei [including 12 broad-emission-line (FWHM >1000 km s⁻¹) objects, one bona fide BL Lac, one BL Lac candidate and one narrow-line (FWHM < 1000 km s⁻¹) radio galaxy] and five radio galaxies. We derive the X-ray fluxes and luminosities by analysing the PSPC exposures, and show the radio morphology from the NVSS maps.  We find that the correlation between the monochromatic X-ray luminosity at 2 keV and the core radio luminosity at 5 GHz for the radio galaxies in our sample follows that found for the 3CR radio galaxies, suggesting a possible nuclear origin for the X-ray emission in these sources. This correlation is weaker in the case of broad-line objects, indicating the presence of another (unbeamed) mechanism for the X-ray emission only weakly related to the radio emission.     

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.