The two-and three-point correlation functions of the polarized five-year WMAP sky maps

We present the two- and three-point real space correlation functions of the five-year WMAP sky maps, and compare the observed functions to simulated LCDM concordance model ensembles. In agreement with previously published results, we find that the temperature correlation functions are consistent with expectations. However, the pure polarization correlation functions are acceptable only for the 33GHz band map; the 41, 61, and 94 GHz band correlation functions all exhibit significant large-scale excess structures. Further, these excess structures very closely match the correlation functions of the two (synchrotron and dust) foreground templates used to correct the WMAP data for galactic contamination, with a cross-correlation statistically significant at the 2sigma-3sigma confidence level. The correlation is slightly stronger with respect to the thermal dust template than with the synchrotron template.Comment: 10 pages, 5 figures, published in ApJ. v2: New title, minor changes to appendix, and fixed some typos. v3: Matches version published in Ap

The scalar perturbation spectral index n_s: WMAP sensitivity to unresolved point sources

Precision measurement of the scalar perturbation spectral index, n_s, from the Wilkinson Microwave Anisotropy Probe temperature angular power spectrum requires the subtraction of unresolved point source power. Here we reconsider this issue. First, we note a peculiarity in the WMAP temperature likelihood's response to the source correction: Cosmological parameters do not respond to increased source errors. An alternative and more direct method for treating this error term acts more sensibly, and also shifts n_s by ~0.3 sigma closer to unity. Second, we re-examine the source fit used to correct the power spectrum. This fit depends strongly on the galactic cut and the weighting of the map, indicating that either the source population or masking procedure is not isotropic. Jackknife tests appear inconsistent, causing us to assign large uncertainties to account for possible systematics. Third, we note that the WMAP team's spectrum was computed with two different weighting schemes: uniform weights transition to inverse noise variance weights at l = 500. The fit depends on such weighting schemes, so different corrections apply to each multipole range. For the Kp2 mask used in cosmological analysis, we prefer source corrections A = 0.012 +/- 0.005 muK^2 for uniform weighting and A = 0.015 +/- 0.005 muK^2 for N_obs weighting. Correcting WMAP's spectrum correspondingly, we compute cosmological parameters with our alternative likelihood, finding n_s = 0.970 +/- 0.017 and sigma_8 = 0.778 +/- 0.045 . This n_s is only 1.8 sigma from unity, compared to the ~2.6 sigma WMAP 3-year result. Finally, an anomalous feature in the source spectrum at l<200 remains, most strongly associated with W-band.Comment: 9 pages, 10 figures, 3 tables. Submitted to Ap

Asymmetries in the CMB anisotropy field

We report on the results from two independent but complementary statistical analyses of the WMAP first-year data, based on the power spectrum and N-point correlation functions. We focus on large and intermediate scales (larger than about 3 degrees) and compare the observed data against Monte Carlo ensembles with WMAP-like properties. In both analyses, we measure the amplitudes of the large-scale fluctuations on opposing hemispheres and study the ratio of the two amplitudes. The power-spectrum analysis shows that this ratio for WMAP, as measured along the axis of maximum asymmetry, is high at the 95%-99% level (depending on the particular multipole range included). The axis of maximum asymmetry of the WMAP data is weakly dependent on the multipole range under consideration but tends to lie close to the ecliptic axis. In the N-point correlation function analysis we focus on the northern and southern hemispheres defined in ecliptic coordinates, and we find that the ratio of the large-scale fluctuation amplitudes is high at the 98%-99% level. Furthermore, the results are stable with respect to choice of Galactic cut and also with respect to frequency band. A similar asymmetry is found in the COBE-DMR map, and the axis of maximum asymmetry is close to the one found in the WMAP data.Comment: 6 pages, 5 figures; version to appear in ApJ, textual improvements, added reference

Constraints on mode couplings and modulation of the CMB with WMAP data

We investigate a possible asymmetry in the statistical properties of the cosmic microwave background temperature field and to do so we construct an estimator aiming at detecting a dipolar modulation. Such a modulation is found to induce correlations between multipoles with $\Delta\ell=1$. Applying this estimator, to the V and W bands of the WMAP data, we found a significant detection in the V band. We argue however that foregrounds and in particular point sources are the origin of this signal.Comment: 14 pages, 14 figure

Increasing evidence for hemispherical power asymmetry in the five-year WMAP data

(Abridged)Motivated by the recent results of Hansen et al. (2008) concerning a noticeable hemispherical power asymmetry in the WMAP data on small angular scales, we revisit the dipole modulated signal model introduced by Gordon et al. (2005). This model assumes that the true CMB signal consists of a Gaussian isotropic random field modulated by a dipole, and is characterized by an overall modulation amplitude, A, and a preferred direction, p. Previous analyses of this model has been restricted to very low resolution due to computational cost. In this paper, we double the angular resolution, and compute the full corresponding posterior distribution for the 5-year WMAP data. The results from our analysis are the following: The best-fit modulation amplitude for l <= 64 and the ILC data with the WMAP KQ85 sky cut is A=0.072 +/- 0.022, non-zero at 3.3sigma, and the preferred direction points toward Galactic coordinates (l,b) = (224 degree, -22 degree) +/- 24 degree. The corresponding results for l <~ 40 from earlier analyses was A = 0.11 +/- 0.04 and (l,b) = (225 degree,-27 degree). The statistical significance of a non-zero amplitude thus increases from 2.8sigma to 3.3sigma when increasing l_max from 40 to 64, and all results are consistent to within 1sigma. Similarly, the Bayesian log-evidence difference with respect to the isotropic model increases from Delta ln E = 1.8 to Delta ln E = 2.6, ranking as "strong evidence" on the Jeffreys' scale. The raw best-fit log-likelihood difference increases from Delta ln L = 6.1 to Delta ln L = 7.3. Similar, and often slightly stronger, results are found for other data combinations. Thus, we find that the evidence for a dipole power distribution in the WMAP data increases with l in the 5-year WMAP data set, in agreement with the reports of Hansen et al. (2008).Comment: 6 pages, 2 figures; added references and minor comments. Accepted for publication in Ap

Frequentist comparison of CMB local extrema statistics in the five-year WMAP data with two anisotropic cosmological models

We present local extrema studies of two models that introduce a preferred direction into the observed cosmic microwave background (CMB) temperature field. In particular, we make a frequentist comparison of the one- and two-point statistics for the dipole modulation and ACW models with data from the five-year Wilkinson Microwave Anisotropy Probe (WMAP). This analysis is motivated by previously revealed anomalies in the WMAP data, and particularly the difference in the statistical nature of the temperature anisotropies when analysed in hemispherical partitions. The analysis of the one-point statistics indicates that the previously determined hemispherical variance difficulties can be apparently overcome by a dipole modulation field, but new inconsistencies arise if the mean and the l-dependence of the statistics are considered. The two-point correlation functions of the local extrema, the temperature pair product and the point-point spatial pair-count, demonstrate that the impact of such a modulation is to over-`asymmetrise' the temperature field on smaller scales than the wave-length of the dipole or quadrupole, and this is disfavored by the observed data.The results from the ACW model predictions, however, are consistent with the standard isotropic hypothesis. The two-point analysis confirms that the impact of this type of violation of isotropy on the temperature extrema statistics is relatively weak. From this work, we conclude that a model with more spatial structure than the dipole modulated or rotational-invariance breaking models are required to fully explain the observed large-scale anomalies in the WMAP data.Comment: 10 pages, 4 figures, 3 tables, accepted for publication in MNRA

Real space tests of the statistical isotropy and Gaussianity of the WMAP CMB data

ABRIDGED: We introduce and analyze a method for testing statistical isotropy and Gaussianity and apply it to the WMAP CMB foreground reduced, temperature maps, and cross-channel difference maps. 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. 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 deg to 30 deg at 68% confidence level. 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). We notice the large scale hemispherical power asymmetry, and find that it is not highly statistically significant in the WMAP three-year data (<~ 97%) at scales l <= 40. The significance is even smaller if multipoles up to l=1024 are considered (~90% CL). We give constraints on the amplitude of the previously-proposed CMB dipole modulation field parameter. We easily detect the residual foregrounds in cross-band difference maps at rms level <~ 7 \mu K (at scales >~ 6 deg) and limit the systematical uncertainties to <~ 1.7 \mu K (at scales >~ 30 deg).Comment: 20 pages, 20 figures; more tests added; updated to match the version to be published in JCA