Real space tests of the statistical isotropy and Gaussianity of the Wilkinson Microwave Anisotropy Probe cosmic microwave background data

Abstract

We introduce and analyze a method for testing statistical isotropy and Gaussianity and apply it to the Wilkinson Microwave Anisotropy Probe (WMAP) cosmic microwave background (CMB) foreground reduced temperature maps. We also test cross-channel difference maps to constrain levels of residual foreground contamination and systematic uncertainties. We divide the sky into regions of varying size and shape and measure the first four moments of the one-point distribution within these regions, and using their simulated spatial distributions we test the statistical isotropy and Gaussianity hypotheses. By randomly varying orientations of these regions, we sample the underlying CMB field in a new manner, that offers a richer exploration of the data content, and avoids possible biasing due to a single choice of sky division. In our analysis we account for all two-point correlations between different regions and also show the impact on the results when these correlations are neglected. The statistical significance is assessed via comparison with realistic Monte Carlo simulations. We find the three-year WMAP maps to agree well with the isotropic, Gaussian random field simulations as probed by regions corresponding to the angular scales ranging from 6° to 30° at 68% confidence level (CL). We report a strong, anomalous (99.8% CL) dipole ‘excess’ in the V band of the three-year WMAP data and also in the V band of the WMAP five-year data (99.3% CL). Using our statistics, we notice large scale hemispherical power asymmetry, and find that it is not highly statistically significant in the WMAP three-year data () at scales . The significance is even smaller if multipoles up to are considered (∼90% CL). We give constraints on the amplitude of the previously proposed CMB dipole modulation field parameter. We find some hints of foreground contamination in the form of a locally strong, anomalous kurtosis excess in the Q+V +W co-added map, which however is not significant globally. We easily detect the residual foregrounds in cross-band difference maps at rms level (at scales ) and limit the systematical uncertainties to (at scales ).

A scale-dependent power asymmetry from isocurvature perturbations

“…If the curvaton decays while all particle species are still in thermal equilibrium with radiation, then the fluctuations in the curvaton field create only adiabatic perturbations, and the resulting asymmetry is scale invariant [39]. Recent studies have revealed that the asymmetry is not scale invariant; while ÁC ' =C ' ' 0:15 for ' & 64 [27], there are indications that this asymmetry does not extend to ' * 600 [26,50], and an analysis of quasar number counts found ÁPðkÞ=PðkÞ & 0:024 for k ' 1:3h-1:8h Mpc À1 . With the aim of explaining this scale dependence, we have considered how the asymmetry produced by a large-amplitude curvaton fluctuation changes if the curvaton decays after dark matter freezes out.…”

“…[39] predicts that the magnitude and direction of the power asymmetry are scale invariant. There are indications, however, that the asymmetry in the CMB temperature fluctuations has a smaller amplitude at ' ' 220 [28] and does not extend to ' * 600 [26,50]. Furthermore, an analysis of quasar number counts reveals that any asymmetry in the direction ð'; bÞ ¼ ð225 ; À27 Þ in the rms amplitude of primordial density fluctuations on scales that form quasars (k ' 1:3h-1:8h Mpc À1 ) must correspond to A & 0:012 at the 95% C.L., assuming that the perturbations are adiabatic [51].…”

The comptonization parameter from simulations of single-frequency, single-dish, dual-beam, cm-wave observations of galaxy clusters and mitigating CMB confusion using the Planck sky survey

“…The One Centimeter Receiver Array (OCRA) (Browne et al 2000;Peel et al 2011) is one of the experiments capable of detecting the SZ effect at 30 GHz using beam-switching radiometers installed on a 32-meter radio telescope (Lancaster et al 2011(Lancaster et al , 2007. OCRA will be mostly sensitive to SZ clusters with virial size > 3 ′ and hence to clusters at redshifts in the range 0.1 < z < 0.5 and with masses M vir > 3 × 10 14 M ⊙ /h (Lew et al 2015). However, a single frequency, beam-switching system may suffer from confusion with the primordial cosmic microwave background (CMB) or suffer from systematic error when observing extended sources.…”

“…In Lew et al (2015) the impact of CMB flux density confusion at 30 GHz was investigated, in particular for the OCRA/RT32 (32 m Radio Telescope in Toruń, Poland) experiment. It was found that the 1σ thermal SZ (tSZ) flux density uncertainty due to CMB confusion should be of the order of 10% for the range of clusters detectable with OCRA.…”

Large-Angle Non-Gaussianity in Simulated High-Resolution CMB Maps

“…[6][7][8][9][10][11][12][13][14][15][16]. In a recent paper 1 we have proposed two new large-angle non-Gaussianity indicators, based on skewness and kurtosis of large-angle patches of CMB maps, which provide measures of the departure from Gaussianity on large angular scales.…”