E. Martínez-González

Detection of Non-Gaussianity in the Wilkinson Microwave Anisotropy Probe First-Year Data Using Spherical Wavelets

A non-Gaussian detection in the Wilkinson Microwave Anisotropy Probe (WMAP) first-year data is reported. The detection has been found in the combined Q - V - W map proposed by the WMAP team after applying a wavelet technique based on the spherical Mexican hat wavelet (SMHW). The skewness and the kurtosis of the SMHW coefficients are calculated at different scales (ranging from a few arcminutes to tens of degrees). A non-Gaussian signal is detected at scales of the SMHW around 4° (size in the sky of around 10°). The right-tail probability of the detection is ≈0.4%. In addition, a study of Gaussianity is performed in each hemisphere. The northern hemisphere is compatible with Gaussianity, whereas the southern one deviates from Gaussianity with a right-tail probability of ≈0.1%. Systematics, foregrounds, and uncertainties in the estimation of the cosmological parameters are carefully studied in order to identify the possible source of non-Gaussianity. The detected deviation from Gaussianity is not found to be caused by systematic effects: (1) Each one of the Q, V, and W receivers shows the same non-Gaussianity pattern. (2) Several combinations of the different receivers at each frequency band—which highly reduce the cosmic microwave background (CMB) and the foreground emissions—do not show this non-Gaussian pattern. Similarly, Galactic foregrounds show a negligible contribution to the non-Gaussian detection: non-Gaussianity is detected in all the WMAP maps (from 23 to 94 GHz), and no frequency dependence is observed. Moreover, the expected foreground contribution to the combined WMAP map was added to CMB Gaussian simulations showing a behavior compatible with the Gaussian model. The influence of uncertainties in the CMB power spectrum estimation are also quantified. Hence, possible intrinsic temperature fluctuations (such as secondary anisotropies and primordial features) cannot be rejected as the source of this non-Gaussian detection. We remark that our result implies not only asymmetries north/south—like other previous WMAP analyses—but also a direct non-Gaussian detection.A non-Gaussian detection in the WMAP 1-year data is reported. The detection has been found in the combined Q-V-W map proposed by the WMAP team (Komatsu et al. 2003) after applying a wavelet technique based on the Spherical Mexican Hat Wavelet (SMHW). The skewness and the kurtosis of the SMHW coefficients are calculated at different scales. A non-Gaussian signal is detected at scales of the SMHW around 4 deg (size in the sky of around 10 deg). The right tail probability of the detection is approx. 0.4%. In addition, a study of Gaussianity is performed in each hemisphere. The northern hemisphere is compatible with Gaussianity, whereas the southern one deviates from Gaussianity with a right tail probability of approx. 0.1%. Systematics, foregrounds and uncertainties in the estimation of the cosmological parameters are carefully studied in order to identify the possible source of non-Gaussianity. The detected deviation from Gaussianity is not found to be caused by systematic effects: 1) each one of the Q, V and W receivers shows the same non-Gaussianity pattern, and 2) several combinations of the different receivers at each frequency band do not show this non-Gaussian pattern. Similarly, galactic foregrounds show a negligible contribution to the non-Gaussian detection: non-Gaussianity is detected in all the WMAP maps and no frequency dependence is observed. Moreover, the expected foreground contribution to the combined WMAP map was added to CMB Gaussian simulations showing a behaviour compatible with the Gaussian model. Influence of uncertainties in the CMB power spectrum estimation are also quantified. Hence, possible intrinsic temperature fluctuations (like secondary anisotropies and primordial features) can not be rejected as the source of this non-Gaussian detection.

The Non-Gaussian Cold Spot in the 3 Year Wilkinson Microwave Anisotropy Probe Data

The non-Gaussian cold spot detected in wavelet space in the WMAP 1–year data, is detected again in the coadded WMAP 3–year data at the same position (b = 57 ◦ ,l = 209 ◦ ) and size in the sky (� 10 ◦ ). The present analysis is based on several statistical methods: kurtosis, maximum absolute temperature, number of pixels below a given threshold, volume and Higher Criticism. All these methods detect deviations from Gaussianity in the 3–year data set at a slightly higher confidence level than in the WMAP 1–year data. These small differences are mainly due to the new foreground reduction technique and not to the reduction of the noise level, which is negligible at the scale of the spot. In order to avoid a posteriori analyses, we recalculate for the WMAP 3–year data the significance of the deviation in the kurtosis. The skewness and kurtosis tests were the first tests performed with wavelets for the WMAP data. We obtain that the probability of finding an at least as high deviation in Gaussian simulations is 1.85%. The frequency dependence of the spot is shown to be extremely flat. Galactic foreground emissions are not likely to be responsible for the detected deviation from Gaussianity. Subject headings: methods: data analysis – cosmic microwave background

Component separation methods for the PLANCK mission

Context. The PLANCK satellite will map the full sky at nine frequencies from 30 to 857 GHz. The CMB intensity and polarization that are its prime targets are contaminated by foreground emission. Aims. The goal of this paper is to compare proposed methods for separating CMB from foregrounds based on their different spectral and spatial characteristics, and to separate the foregrounds into “components” with different physical origins (Galactic synchrotron, free-free and dust emissions; extra-galactic and far-IR point sources; Sunyaev-Zeldovich effect, etc.) Methods. A component separation challenge has been organised, based on a set of realistically complex simulations of sky emission. Several methods including those based on internal template subtraction, maximum entropy method, parametric method, spatial and harmonic cross correlation methods, and independent component analysis have been tested. Results. Different methods proved to be effective in cleaning the CMB maps of foreground contamination, in reconstructing maps of diffuse Galactic emissions, and in detecting point sources and thermal Sunyaev-Zeldovich signals. The power spectrum of the residuals is, on the largest scales, four orders of magnitude lower than the input Galaxy power spectrum at the foreground minimum. The CMB power spectrum was accurately recovered up to the sixth acoustic peak. The point source detection limit reaches 100 mJy, and about 2300 clusters are detected via the thermal SZ effect on two thirds of the sky. We have found that no single method performs best for all scientific objectives. Conclusions. We foresee that the final component separation pipeline for PLANCK will involve a combination of methods and iterations between processing steps targeted at different objectives such as diffuse component separation, spectral estimation, and compact source extraction.

The non-Gaussian cold spot in Wilkinson Microwave Anisotropy Probe: significance, morphology and foreground contribution

The non–Gaussian cold spot in the 1–year WMAP data, described in Vielva et al. and Cruz et al., is analysed in detail in the present paper. First of all, we perform a more rigorous calculation of the significance of the non–zero kurtosis detected in WMAP maps by Vielva et al. in wavelet space, mainly generated by the Spot. We confirm the robustness of that detection, since the probability of obtaining this deviation by chance is 0.69%. Afterwards, the morphology of the Spot is studied by applying Spherical Mexican Hat Wavelets with different ellipticities. The shape of the Spot is found to be almost circular. Finally, we discuss if the observed non–Gaussianity in wavelet space can arise from bad subtracted foreground residues in the WMAP maps. We show that the flat frequency dependence of the Spot cannot be explained by a thermal Sunyaev–Zeldovich effect. Based on our present knowledge of Galactic foreground emissions, we conclude that the significance of our detection is not affected by Galactic residues in the region of the Spot. Considering different Galactic foreground estimates, the probability of finding such a big cold spot in Gaussian simulations is always below 1%.

A Cosmic Microwave Background Feature Consistent with a Cosmic Texture

The Cosmic Microwave Background provides our most ancient image of the universe and our best tool for studying its early evolution. Theories of high-energy physics predict the formation of various types of topological defects in the very early universe, including cosmic texture, which would generate hot and cold spots in the Cosmic Microwave Background. We show through a Bayesian statistical analysis that the most prominent 5°-radius cold spot observed in all-sky images, which is otherwise hard to explain, is compatible with having being caused by a texture. From this model, we constrain the fundamental symmetry-breaking energy scale to be ϕ0 ≈ 8.7 × 1015 gigaelectron volts. If confirmed, this detection of a cosmic defect will probe physics at energies exceeding any conceivable terrestrial experiment.

The performance of spherical wavelets to detect non-Gaussianity in the cosmic microwave background sky

We investigate the performance of spherical wavelets in discriminating between standard inflationary (Gaussian) and non-Gaussian models. For the latter we consider small perturbations of the Gaussian model in which an artificially specified skewness or kurtosis is introduced through the Edgeworth expansion. By combining all the information present in all the wavelet scales with the Fisher discriminant, we find that the spherical Mexican Hat wavelets are clearly superior to the spherical Haar wavelets. The former can detect levels of skewness and kurtosis of ≈1 per cent for 33-arcmin resolution, an order of magnitude smaller than the latter. Also, as expected, both wavelets are better for discriminating between the models than the direct consideration of moments of the temperature maps. The introduction of instrumental white noise in the maps, S/N = 1, does not change the main results of this paper.

Cross-correlation of the cosmic microwave background and radio galaxies in real, harmonic and wavelet spaces: detection of the integrated Sachs-Wolfe effect and dark energy constraints

We report on the first detection of the integrated Sachs-Wolfe (ISW) effect in wavelet space, at scales in the sky around 0 7° with a significance 3.3σ, by cross-correlating the Wilkinson Microwave Anisotropy Probe (WMAP) first-year data and the National Radio Astronomy Observatories (NRAO) Very Large Array (VLA) Sky Survey (NVSS). In addition, we present a detailed comparison of the capabilities of three different techniques for two different objectives: to detect the ISW effect and to put constraints on the nature of the dark energy. The three studied techniques are the cross-angular power spectrum (CAPS; harmonic space), the correlation function (CCF; real space) and the covariance of the spherical Mexican hat wavelet (SMHW) coefficients (CSMHW; wavelet space). We prove that the CSMHW is expected to provide a higher detection (in terms of the signal-to-noise ratio) of the ISW effect for a certain scale. However, the detection achieved by the CAPS is the lowest, being the signal-to-noise ratio dispersed among a wide multipole range. The CCF provides an intermediate detection level. This prediction has been corroborated by the analysis of the data. The SMHW analysis shows that the cross-correlation signal is caused neither by systematic effects nor foreground contamination. However, by taking into account the information encoded in all the multipoles/scales/angles, the CAPS provides slightly better constraints than the SMHW in the cosmological parameters that define the nature of the dark energy. The limits provided by the CCF are wider than for the other two methods, although the three of them give similar confidence levels (CLs). Two different cases have been studied: (i) a flat A cold dark matter universe; (ii) a flat universe with an equation of state parameter that, although it does not change with time, could take values different from - 1. In the first case, the CAPS provides (for a bias value of b = 1.6) Ω Λ = 0.73 +0.11 -0.14 (at la CL). Moreover, the CAPS rejects the range Ω Λ < 0.1 at 3.5σ, which is the highest detection of dark energy reported to date. In the second case, the CAPS gives Ω DE = 0.70 +0.12 -0.20 and w = -0.75 +0.32 -0.41 (at la CL). This is the first estimation of the equation of state of dark energy made through the cross-correlation of the cosmic microwave background (CMB) and the nearby galaxy density distribution. It also provides an independent estimation from that made by the WMAP team using the CMB and large-scale structure.

Point source detection using the Spherical Mexican Hat Wavelet on simulated all‐sky Planck maps

We present an estimation of the point source (PS) catalogue that could be extracted from the forthcoming ESA Planck mission data. We have applied the Spherical Mexican Hat Wavelet (SMHW) to simulated all-sky maps that include CMB, Galactic emission (thermal dust, free-free and synchrotron), thermal Sunyaev-Zel’dovich effect and PS emission, as well as instrumental white noise . This work is an extension of the one presented in Vielva et al. (2001a). We have developed an algorithm focused on a fast local optimal scale determination, that is crucial to achieve a PS catalogue with a large number of detections and a low flux limit. An important effort has been also done to reduce the CPU time processor for spherical harmonic transformation, in order to perform the PS detection in a reasonable time. The presented algorithm is able to provide a PS catalogue above fluxes: 0.48 Jy (857 GHz), 0.49 Jy (545 GHz), 0.18 Jy (353 GHz), 0.12 Jy (217 GHz), 0.13 Jy (143 GHz), 0.16 Jy (100 GHz HFI), 0.19 Jy (100 GHz LFI), 0.24 Jy (70 GHz), 0.25 Jy (44 GHz) and 0.23 Jy (30 GHz). We detect around 27700 PS at the highest frequency Planck channel and 2900 at the 30 GHz one. The completeness level are: 70% (857 GHz), 75% (545 GHz), 70% (353 GHz), 80% (217 GHz), 90% (143 GHz), 85% (100 GHz HFI), 80% (100 GHz LFI), 80% (70 GHz), 85% (44 GHz) and 80% (30 GHz). In addition, we can find several PS at different channels, allowing the study of the spectral behaviour and the physical processes acting on them. We also present the basic procedure to apply the method in maps convolved with asymmetric beams. The algorithm takes � 72 hours for the most CPU time demanding channel (857 GHz) in a Compaq HPC320 (Alpha EV68 1 GHz processor) and requires 4 GB of RAM memory; the CPU time goes as O(NRoNpix 3/2 log(Npix)), where Npix is the number of pixels in the map and NRo is the number of optimal scales needed.

The CMB cold spot: texture, cluster or void?

ABSTRACT The non-Gaussian cold spot found in the WMAP data has created controversyabout its origin. Here we calculate the Bayesian posterior probability ratios for threedifferent models that could explain the cold spot. A recent work claimed that theSpot could be caused by a cosmic texture, while other papers suggest that it couldbe due to the gravitational effect produced by an anomalously large void. Also theSunyaev-Zeldovich effect caused by a cluster is taken into account as a possible origin.We perform a template fitting on a 20 ◦ radius patch centered at Galactic coordi-nates (b = −57 ◦ ,l = 209 ◦ ) and calculate the posterior probability ratios for the voidand Sunyaev-Zeldovich models, comparing the results to those obtained with texture.Taking realistic priors for the parameters, the texture interpretation is favored, whilethe void and Sunyaev-Zeldovich hypotheses are discarded. The temperature decre-ment produced by voids or clusters is negligible considering realistic values for theparameters.Key words: methods: data analysis - cosmic microwave background

Limits on the detectability of the CMB B-mode polarization imposed by foregrounds

We investigate which practical constraints are imposed by foregrounds on the detection of the B-mode polarization generated by gravitational waves, in the case of experiments of the type currently being planned. As the B-mode signal is probably dominated by foregrounds at all frequencies, the detection of the cosmological component depends drastically on our ability to remove foregrounds. We provide an analytical expression with which to estimate the level of the residual polarization for Galactic foregrounds, according to the method employed for their subtraction. We interpret this result in terms of the lower limit of the tensor-to-scalar ratio r that allows us to disentangle the cosmological B-mode polarization from the foreground contribution. Polarized emission from extragalactic radio sources and gravitational lensing is also taken into account. As a first approach, we consider the ideal limit of an instrumental noise-free experiment: for full-sky coverage and a resolution of 1°, we obtain a limit of r ∼ 10 -4 . This value can be improved by high-resolution experiments and, in principle, there is no clear fundamental limit on the detectability of the polarization of gravitational waves. Our analysis is also applied to planned or hypothetical future polarization experiments, taking into account expected noise levels.