Wilkinson Microwave Anisotropy Probe Maps Research Articles

The cosmic shallows – I. Interaction of CMB photons in extended galaxy haloes

ABSTRACT We report and analyse a serendipitous finding of foregrounds in the cosmic microwave background (CMB) radiation associated with extended galactic haloes. Using the cross-correlation of Planck and Wilkinson Microwave Anisotropy Probe maps and the 2MRS galaxy catalogue, we find that the mean temperature radial profiles around nearby galaxies at $cz\le 4500~\rm {km~s^{-1}}$ show a statistically significant systematic decrease of $\sim 15~\mu \rm {K}$ extending up to several galaxy radii. This deficit in the temperature strongly depends on the galaxy morphological type at scales within several tens of times the galaxy size, becoming nearly independent of galaxy morphology at larger scales. The effect is significantly stronger for the more extended galaxies, with galaxy clustering having a large impact on the results. Our findings indicate the presence of statistically relevant foregrounds in the CMB maps that should be considered in detailed cosmological studies. Besides, we argue that these can be used to explore the intergalactic medium surrounding bright late-type galaxies and allow for diverse astrophysical analyses.

Test for the zero mean hypothesis in cosmology

One working hypothesis on which analyses of cosmological data are based is the zero ensemble mean hypothesis, which is related to the statistical homogeneity of cosmological perturbations. This hypothesis, however, should be tested by observational data in the current era of precision cosmology. Herein, we test the hypothesis by analyzing recent, foreground-reduced cosmic microwave background (CMB) maps, combining the spherical harmonic coefficients of the masked CMB temperature anisotropies in such a way that the combined variables can be treated as statistically independent samples. We find evidence against the zero mean hypothesis in two particular ranges of multipoles, with significance levels of $2.5\ensuremath{\sigma}$ and $3.1\ensuremath{\sigma}$ in the multipole ranges of $\ensuremath{\ell}\ensuremath{\approx}61--86$ and 213--256, respectively, for both the Planck and Wilkinson Microwave Anisotropy Probe maps. The latter signal is consistent with our previous result found by using brute-force Monte Carlo simulations. However, within the method employed in this paper we conclude that the zero mean hypothesis is consistent with the current CMB data on the basis of Stouffer's weighted $Z$ statistics, which takes multiple testing into account.

On the coherence of WMAP and Planck temperature maps

The recent data release of ESA's Planck mission together with earlier Wilkinson Microwave Anisotropy Probe (WMAP) releases provide the first opportunity to compare high-resolution full sky cosmic microwave background (CMB) temperature anisotropy maps. To quantify the coherence of these maps beyond the power spectrum, we introduce Generalized Phases in the sense of SO(3), unit vectors in the 2ℓ + 1 dimensional representation spaces. For an isotropic Gaussian distribution, Generalized Phases point to random directions and if there is non-Gaussianity, they represent most of the non-Gaussian information. The alignment of these unit vectors from two maps can be characterized by their angle, 0° expected for full coherence, and 90° for random vectors. We analyse maps from both missions with the same mask and Nside = 512 resolution, and compare both power spectra and Generalized Phases. We find excellent agreement of the Generalized Phases of Planck Spectral Matching Independent Component Analysis map with that of the WMAPQ, V, W maps, rejecting the null hypothesis of no correlations at 5σ for ℓ < 700, ℓ < 900 and ℓ < 1100, respectively, except perhaps for ℓ < 10. Using foreground reduced maps for WMAP increases the phase-coherence. The observed coherence angles can be explained with a simple assumption of Gaussianity and a WMAP noise model neglecting Planck noise, except for low-intermediate ℓ values there is a slight, but significant offset, depending on the WMAP band. On the same scales WMAP power spectrum is about 2.6 per cent higher at a very high significance, while at higher ℓ ranges there appears to be no significant bias. Using our theoretical tools, we predict the phase alignment of Planck with a hypothetical perfect noiseless CMB experiment, finding decoherence at ℓ ≃ 2900; below this value Planck can be used most efficiently to constrain non-Gaussianity.

Long-term variability of extragalactic radio sources in thePlanckEarly Release Compact Source Catalogue

Combining measurements taken using the Wilkinson Microwave Anisotropy Probe (WMAP) from 2001 to 2008 with measurements taken using Planck from 2009 to 2010, we investigate the long-term flux density variability of extragalactic radio sources selected from the Planck Early Release Compact Source Catalogue. The single-year, single-frequency WMAP maps are used to estimate yearly-averaged flux densities of the sources in the four WMAP bands: Ka (33 GHz), Q (41 GHz), V (61 GHz), and W (94 GHz). We identify 82, 67, 32, and 15 sources respectively as variable at greater than 99% confidence level in these four bands. The amplitudes of variation are comparable between bands, and are not correlated with either the flux densities or the spectral indices of the sources. The number counts of WMAP Ka-band sources are stable from year to year despite the fluctuation caused by individual source variability. Most of our sources show strong correlation in variability between bands. Almost all the sources that show variability are blazars. We have attempted to fit two simple, four-parameter models to the time-series of 32 sources showing correlated variability at multiple frequencies - a long-term flaring model and a rotating-jet model. We find that 19 sources (60%) can be fit with the simple rotating-jet model, and ten of these also fit the simple long-term flaring model. The remaining 13 sources (40%) show more complex variability behaviour that is not consistent with either model. Extended radio galaxies in our sample show no sign of variability, as expected, with the exception of Pictor A for which we report evidence for a millimetre flare lasting between 2002 and 2010.

Galactic foreground contributions to the 5-year Wilkinson Microwave Anisotropy Probe maps

We compute the cross correlation of the intensity and polarisation from the 5-year WMAP data in different sky-regions with respect to template maps for synchrotron, dust, and free-free emission. We derive the frequency dependence and polarisation fraction for all three components in 48 different sky regions of HEALPix (Nside=2) pixelisation. The anomalous emission associated with dust is clearly detected in intensity over the entire sky at the K (23 GHz) and Ka (33 GHz) WMAP bands, and is found to be the dominant foreground at low Galactic latitude, between b=-40 and b=+10. The synchrotron spectral index obtained from the K and Ka WMAP bands from an all-sky analysis is -3.32\pm 0.12 for intensity and -3.01\pm0.03 for the polarised intensity. The polarisation fraction of the synchrotron is constant in frequency and increases with latitude from ~5% near the Galactic plane up to ~40% in some regions at high latitude; the average value for |b|<20 is 8.6\pm1.7 (stat) \pm0.5 (sys) % while for |b|>20 it is 19.3\pm0.8 (stat) \pm 0.5 (sys) %. Anomalous dust and free-free emission appear to be relatively unpolarised...[Abridged]...the average polarisation fraction of dust-correlated emission at K-band is 3.2\pm0.9 (stat) \pm 1.5 (sys) %, or less than 5% at 95% confidence. When comparing real data with simulations, 8 regions show a detected polarisation above the 99th percentile of the distribution from simulations with no input foreground polarisation, 6 of which are detected at above 2sigma and display polarisation fractions between 2.6% and 7.2%, except for one anomalous region, which has 32\pm12%. The dust polarisation values are consistent with the expectation from spinning-dust emission, but polarised dust emission from magnetic-dipole radiation cannot be ruled out. Free-free emission was found to be unpolarised with an upper limit of 3.4% at 95% confidence.

Possible detection of the M 31 rotation in WMAP data

Data on the cosmic microwave background (CMB) radiation by the Wilkinson Microwave Anisotropy Probe (WMAP) had a profound impact on the understanding of a variety of physical processes in the early phases of the Universe and on the estimation of the cosmological parameters. Here, the 7-year WMAP data are used to trace the disk and the halo of the nearby giant spiral galaxy M31. We analyzed the temperature excess in three WMAP bands (W, V, and Q) by dividing the region of the sky around M31 into several concentric circular areas. We studied the robustness of the detected temperature excess by considering 500 random control fields in the real WMAP maps and simulating 500 sky maps from the best-fitted cosmological parameters. By comparing the obtained temperature contrast profiles with the real ones towards the M31 galaxy, we find that the temperature asymmetry in the M31 disk is fairly robust, while the effect in the halo is weaker. An asymmetry in the mean microwave temperature in the M31 disk along the direction of the M31 rotation is observed with a temperature contrast up to about 130 microK/pixel. We also find a temperature asymmetry in the M31 halo, which is much weaker than for the disk, up to a galactocentric distance of about 10 degrees (120 kpc) with a peak temperature contrast of about 40 microK/pixel. Although the confidence level of the signal is not high, if estimated purely statistically, which could be expected due to the weakness of the effect, the geometrical structure of the temperature asymmetry points towards a definite effect modulated by the rotation of the M31 halo. This result might open a new way to probe these relatively less studied galactic objects using high-accuracy CMB measurements, such as those with the Planck satellite or planned balloon-based experiments, which could prove or disprove our conclusions.

IMPROVED CONSTRAINTS ON PRIMORDIAL NON-GAUSSIANITY FOR THEWILKINSON MICROWAVE ANISOTROPY PROBE5-YEAR DATA

We present constraints on the nonlinear coupling parameter f nl with the Wilkinson Microwave Anisotropy Probe (WMAP) data. We use an updated method based on the spherical Mexican hat wavelet (SMHW) which provides improved constraints on the f nl parameter. This paper is a continuation of a previous work by Curto et al., where several third-order statistics based on the SMHW were considered. In this paper, we use all the possible third-order statistics computed from the wavelet coefficient maps evaluated at 12 angular scales. The scales are logarithmically distributed from 6.9 arcmin to 500 arcmin. Our analysis indicates that f nl is constrained to –18 < f nl < +80 at 95% confidence level (CL) for the combined V+W WMAP map. This value has been corrected by the presence of undetected point sources, which adds a positive contribution of Δf nl = 6 ± 5. Our result excludes at ~99% CL the best-fitting value f nl = 87 reported by Yadav & Wandelt. We have also constrained f nl for the Q, V, and W frequency bands separately, finding compatibility with zero at 95% CL for the Q and V bands but not for the W band. We have performed some further tests to understand the cause of this deviation which indicate that systematics associated with the W radiometers could be responsible for this result. Finally, we have performed a Galactic north-south analysis for f nl. We have not found any asymmetry, i.e., the best-fitting f nl for the northern pixels is compatible with the best-fitting f nl for the southern pixels.

Blind and non-blind source detection inWMAP5-yr maps

We have analysed the efficiency in source detection and flux density estimation of blind and non-blind detection techniques exploiting the MHW2 filter applied to the Wilkinson Microwave Anisotropy Probe (WMAP) 5-yr maps. A comparison with the AT20G bright source sample, with a completeness limit of 0.5 Jy and accurate flux measurements at 20 GHz, close to the lowest frequency of WMAP maps, has allowed us to assess the completeness and the reliability of the samples detected with the two approaches, as well as the accuracy of flux and error estimates, and their variations across the sky. The uncertainties on flux estimates given by our procedure turned out to be about a factor of 2 lower than the rms differences with AT20G measurements, consistent with the smoothing of the fluctuation field yielded by map filtering. Flux estimates were found to be essentially unbiased except that, close to the detection limit, a substantial fraction of fluxes are found to be inflated by the contribution of underlying positive fluctuations. This is consistent with expectations for the Eddington bias associated to the true errors on flux density estimates. The blind and non-blind approaches are found to be complementary: each of them allows the detection of sources missed by the other. Combining results of the two methods on the WMAP 5-yr maps, we have expanded the non-blindly generated New Extragalactic WMAP Point Source (NEWPS) catalogue that was based on WMAP 3-yr maps. After having removed the probably spurious objects not identified with known radio sources, the new version of the NEWPS catalogue, NEWPS_5yr comprises 484 sources detected with a signal-to-noise ratio SNR ≥ 5.

Can a primordial magnetic field originate large-scale anomalies inWMAPdata?

Several accurate analyses of the cosmic microwave background (CMB) temperature maps from the Wilkinson Microwave Anisotropy Probe (WMAP) have revealed a set of anomalous results, at large angular scales, that appears inconsistent with the statistical isotropy expected in the concordance cosmological model Λcold dark matter. Because these anomalies seem to indicate a preferred direction in the space, here we investigate the signatures that a primordial magnetic field, possibly present in the photon–baryon fluid during the decoupling era, could have produced in the large-angle modes of the observed CMB temperature fluctuations maps. To study these imprints, we simulate Monte Carlo CMB maps, which are statistically anisotropic due to the correlations between CMB multipoles induced by the magnetic field. Our analyses reveal the presence of the north–south angular correlations asymmetry phenomenon in these Monte Carlo maps, and we use these information to establish the statistical significance of such phenomenon observed in WMAP maps. Moreover, because a magnetic field produces planarity in the low-order CMB multipoles, where the planes are perpendicular to the preferred direction defined by the magnetic field, we investigate the possibility that two CMB anomalous phenomena, namely the north–south asymmetry and the quadrupole–octopole planes alignment, could have a common origin. Our results, for large angles, show that the correlations between low-order CMB multipoles introduced by a sufficiently intense magnetic field, can reproduce some of the large-angle anisotropic features mapped in WMAP data. We also reconfirm, at more than 95 per cent CL, the existence of a north–south power asymmetry in the WMAP 5-yr data.

Three‐YearWilkinson Microwave Anisotropy Probe(WMAP) Observations: Foreground Polarization

We present a full-sky model of polarized Galactic microwave emission based on 3 years of observations by the Wilkinson Microwave Anisotropy Probe (WMAP) at frequencies from 23 to 94 GHz. The model compares maps of the Stokes Q and U components from each of the five WMAP frequency bands in order to separate synchrotron from dust emission, taking into account the spatial and frequency dependence of the synchrotron and dust components. This simple two-component model of the interstellar medium accounts for at least 97% of the polarized emission in the WMAP maps of the microwave sky. Synchrotron emission dominates the polarized foregrounds at frequencies below 50 GHz, and is comparable to the dust contribution at 65 GHz. The spectral index of the synchrotron component, derived solely from polarization data, is -3.2 averaged over the full sky, with a modestly flatter index on the Galactic plane. The synchrotron emission has mean polarization fraction 2%-4% in the Galactic plane and rising to over 20% at high latitude, with prominent features such as the north Galactic spur more polarized than the diffuse component. Thermal dust emission has polarization fraction 1% near the Galactic center, rising to 6% at the anticenter. Diffuse emission from high-latitude dust is also polarized with mean fractional polarization 0.036 ± 0.011.

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

The non-Gaussian cold spot in the 1-yr Wilkinson Microwave Anisotropy Probe (WMAP) data, described by 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 per cent. 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 per cent.

No Higher Criticism of the Bianchi-corrected Wilkinson Microwave Anisotropy Probe data

Higher Criticism (HC) has been proposed by Donoho & Jin as an effective statistic to detect deviations from Gaussianity. Motivated by the success of the Bianchi VIIh model in addressing many of the anomalies observed in the Wilkinson Microwave Anisotropy Probe (WMAP) data (Jaffe et al.), we present calculations in real and in wavelet space of the HC statistic of the Bianchi-corrected WMAP first-year data. At the wavelet scale of 5°, the HC of the WMAP map drops from a value above the 99 per cent confidence level (c.l.) to a value below the 68 per cent CL when corrected by the Bianchi template. An important property of the HC statistic is its ability to locate the pixels that account for the deviation from Gaussianity. The analysis of the uncorrected WMAP data pointed to a cold spot in the Southern hemisphere, centred at l ~ 209°, b ~ −57°. The HC of the Bianchi-corrected map indicates that this spot remains prominent, albeit at a level completely consistent with Gaussian statistics. Consequently, it is debatable how much emphasis should be placed on this residual feature, but we consider the effect of modestly increasing the scaling of the template. A factor of only 1.2 renders the spot indistinguishable from the background level, with no noticeable impact on the results published in Jaffe et al. for the low-l anomalies, large-scale power asymmetry or wavelet kurtosis. A trivial interpretation would be that the Bianchi template may require a small enhancement of power on scales corresponding to the wavelet scale of 5°.

Multipole vectors: A new representation of the CMB sky and evidence for statistical anisotropy or non-Gaussianity at 2⩽l⩽8

We propose a novel representation of cosmic microwave anisotropy maps, where each multipole order $\mathcal{l}$ is represented by $\mathcal{l}$ unit vectors pointing in directions on the sky and an overall magnitude. These ``multipole vectors and scalars'' transform as vectors under rotations. Like the usual spherical harmonics, multipole vectors form an irreducible representation of the proper rotation group $\mathrm{SO}(3).$ However, they are related to the familiar spherical harmonic coefficients ${a}_{\mathcal{l}m}$ in a nonlinear way and are therefore sensitive to different aspects of the cosmic microwave background (CMB) anisotropy. Nevertheless, it is straightforward to determine the multipole vectors for a given CMB map and we present an algorithm to compute them. A code implementing this algorithm is available at http://www.phys.cwru.edu/projects/mpvectors/. Using the Wilkinson Microwave Anisotropy Probe (WMAP) full-sky maps, we perform several tests of the hypothesis that the CMB anisotropy is statistically isotropic and Gaussian random. We find that the result from comparing the oriented area of planes defined by these vectors between multipole pairs $2l~{\mathcal{l}}_{1}\ensuremath{\ne}{\mathcal{l}}_{2}l~8$ is inconsistent with the isotropic Gaussian hypothesis at the 99.4% level for the internal linear combination map and at 98.9% level for the cleaned map of Tegmark et al. A particular correlation is suggested between the $\mathcal{l}=3$ and $\mathcal{l}=8$ multipoles, as well as several other pairs. This effect is entirely different from the now familiar planarity and alignment of the quadrupole and octupole: while the aforementioned is fairly unlikely, the multipole vectors indicate correlations not expected in Gaussian random skies that make them unusually likely. The result persists after accounting for pixel noise and after assuming a residual 10% dust contamination in the cleaned WMAP map. While the definitive analysis of these results will require more work, we hope that multipole vectors will become a valuable tool for various cosmological tests, in particular those of cosmic isotropy.

Detection of Non‐Gaussianity in theWilkinson Microwave Anisotropy ProbeFirst‐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.

Exact likelihood evaluations and foreground marginalization in low resolution WMAP data

The large scale anisotropies of Wilkinson Microwave Anisotropy Probe (WMAP) data have attracted a lot of attention and have been a source of controversy, with many favorite cosmological models being apparently disfavored by the power spectrum estimates at low $\mathcal{l}.$ All the existing analyses of theoretical models are based on approximations for the likelihood function, which are likely to be inaccurate on large scales. Here we present exact evaluations of the likelihood of the low multipoles by direct inversion of the theoretical covariance matrix for low resolution WMAP maps. We project out the unwanted galactic contaminants using the WMAP derived maps of these foregrounds. This improves over the template based foreground subtraction used in the original analysis, which can remove some of the cosmological signal and may lead to a suppression of power. As a result we find an increase in power at low multipoles. For the quadrupole the maximum likelihood values are rather uncertain and vary between 140 and $220\ensuremath{\mu}{\mathrm{K}}^{2}.$ On the other hand, the probability distribution away from the peak is robust and, assuming a uniform prior between 0 and $2000\ensuremath{\mu}{\mathrm{K}}^{2},$ the probability of having the true value above $1200\ensuremath{\mu}{\mathrm{K}}^{2}$ (as predicted by the simplest cold dark matter model with a cosmological constant) is 10%, a factor of 2.5 higher than predicted by the WMAP likelihood code. We do not find the correlation function to be unusual beyond the low quadrupole value. We develop a fast likelihood evaluation routine that can be used instead of WMAP routines for low $\mathcal{l}$ values. We apply it to the Markov chain Monte Carlo analysis to compare the cosmological parameters between the two cases. The new analysis of WMAP either alone or jointly with the Sloan Digital Sky Survey (SDSS) and the Very Small Array (VSA) data reduces the evidence for running to less than $1\ensuremath{\sigma},$ giving ${\ensuremath{\alpha}}_{s}=\ensuremath{-}0.022\ifmmode\pm\else\textpm\fi{}0.033$ for the combined case. The new analysis prefers about a $1\ensuremath{\sigma}$ lower value of ${\ensuremath{\Omega}}_{m},$ a consequence of an increased integrated Sachs-Wolfe (ISW) effect contribution required by the increase in the spectrum at low $\mathcal{l}.$ These results suggest that the details of foreground removal and full likelihood analysis are important for parameter estimation from the WMAP data. They are robust in the sense that they do not change significantly with frequency, mask, or details of foreground template marginalization. The marginalization approach presented here is the most conservative method to remove the foregrounds and should be particularly useful in the analysis of polarization, where foreground contamination may be much more severe.

The Quest for Microwave Foreground X

The Wilkinson Microwave Anisotropy Probe (WMAP) team has produced a foreground map that can account for most of the low-frequency Galactic microwave emission in the WMAP maps, tentatively interpreting it as emission. Finkbeiner and collaborators have challenged these conclusions, arguing that the WMAP team's synchrotron template is in fact dominated not by radiation but by some dust-related Galactic emission process, perhaps spinning dust grains, making dramatically different predictions for its behavior at lower frequencies. By cross-correlating this template with 10 and 15 GHz cosmic microwave background observations, we find that its spectrum turns over in a manner consistent with spinning dust emission, falling about an order of magnitude below what the interpretation would predict.

Non-Gaussian signatures in the temperature fluctuation observed by the Wilkinson Microwave Anisotropy Probe

We present results from a test for the Gaussianity of the whole sky subdegree-scale cosmic microwave background (CMB) temperature anisotropy measured by the Wilkinson Microwave Anisotropy Probe (WMAP). We calculate the genus from the foreground-subtracted and Kp0-masked WMAP maps and measure the genus shift parameters defined at negative and positive threshold levels (Δν− and Δν+) and the asymmetry parameter (Δg) to quantify the deviation from the Gaussian relation. At WMAP Q, V and W bands, the genus and genus-related statistics imply that the observed CMB sky is consistent with a Gaussian random phase field. However, from the genus measurement on the Galactic northern and southern hemispheres, we have found two non-Gaussian signatures at the W-band resolution ( scale), i.e. the large difference of genus amplitudes between the north and the south and the positive genus asymmetry in the south, which are statistically significant at 2.6σ and 2.4σ levels, respectively. The large genus amplitude difference also appears in the WMAP Q- and V-band maps, deviating from the Gaussian prediction with a significance level of about 2σ. The probability that the genus curves show such a large genus amplitude difference exceeding the observed values at all Q, V and W bands in a Gaussian sky is only 1.4 per cent. Such non-Gaussian features are reduced as the higher Galactic cut is applied, but their dependence on the Galactic cut is weak. We discuss possible sources that can induce non-Gaussian features, such as the Galactic foregrounds, the integrated Sachs–Wolfe and the Sunyaev–Zel'dovich effects, and the reionization-induced low ℓ-mode non-Gaussianity that are aligned along the Galactic plane. We conclude that CMB data with higher signal-to-noise ratio and an accurate foreground model are needed to understand the non-Gaussian signatures.

Wilkinson Microwave Anisotropy Probe constraints on non-Gaussianity

The Wilkinson Microwave Anisotropy Probe ( WMAP) has made it possible to test Gaussianity of fluctuations in the cosmic microwave background with unprecedented sensitivity, thanks to its careful instrumental design minimizing systematic errors. Constraints on the CMB non-Gaussianity offer a fundamental test of inflation and general relativistic perturbation theory. On the other hand, extragalactic radio sources produce significant non-Gaussian signals, making physical interpretations of the measured non-Gaussianity complex. Applying to the WMAP 1-year data a statistical tool we have developed for separately measuring the primordial and the source non-Gaussianities, we find: (1) CMB is consistent with Gaussian fluctuations, as predicted by inflation. The r.m.s. contribution from a second order (non-linear) term is smaller than 2 × 10 −5 of the leading term. Note that the second-order perturbation theory predicts 10–100 times smaller value. (2) We have detected the source contribution at 41 GHz (Q band); thus, the WMAP map in Q band is weakly non-Gaussian at small angular scales because of the sources! This measurement has been used to determine the source contribution to the power spectrum in Q band. Our method can be applied to the Planck experiment, for which there is a chance to detect non-Gaussianity predicted by the second-order perturbation theory.