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

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

Testing for Non-Gaussianity in the Wilkinson Microwave Anisotropy Probe Data: Minkowski Functionals and the Length of the Skeleton

The three Minkowski functionals and the recently defined length of the skeleton are estimated for the co-added first-year Wilkinson Microwave Anisotropy Probe (WMAP) data and compared with 5000 Monte Carlo simulations, based on Gaussian fluctuations with the a-priori best-fit running-index power spectrum and WMAP-like beam and noise properties. Several power spectrum-dependent quantities, such as the number of stationary points, the total length of the skeleton, and a spectral parameter, gamma, are also estimated. While the area and length Minkowski functionals and the length of the skeleton show no evidence for departures from the Gaussian hypothesis, the northern hemisphere genus has a chi^2 that is large at the 95% level for all scales. For the particular smoothing scale of 3.40 degrees FWHM it is larger than that found in 99.5% of the simulations. In addition, the WMAP genus for negative thresholds in the northern hemisphere has an amplitude that is larger than in the simulations with a significance of more than 3 sigma. On the smallest angular scales considered, the number of extrema in the WMAP data is high at the 3 sigma level. However, this can probably be attributed to the effect of point sources. Finally, the spectral parameter gamma is high at the 99% level in the northern Galactic hemisphere, while perfectly acceptable in the southern hemisphere. The results provide strong evidence for the presence of both non-Gaussian behavior and an unexpected power asymmetry between the northern and southern hemispheres in the WMAP data.Comment: 17 pages, 10 figures, accepted for publication in Ap

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

Bayesian Power Spectrum Analysis of the First-Year WMAP data

We present the first results from a Bayesian analysis of the WMAP first year data using a Gibbs sampling technique. Using two independent, parallel supercomputer codes we analyze the WMAP Q, V and W bands. The analysis results in a full probabilistic description of the information the WMAP data set contains about the power spectrum and the all-sky map of the cosmic microwave background anisotropies. We present the complete probability distributions for each C_l including any non-Gaussianities of the power spectrum likelihood. While we find good overall agreement with the previously published WMAP spectrum, our analysis uncovers discrepancies in the power spectrum estimates at low l multipoles. For example we claim the best-fit Lambda-CDM model is consistent with the C_2 inferred from our combined Q+V+W analysis with a 10% probability of an even larger theoretical C_2. Based on our exact analysis we can therefore attribute the "low quadrupole issue" to a statistical fluctuation.Comment: 5 pages. 4 figures. For additional information and data see http://www.astro.uiuc.edu/~iodwyer/research#wma

Probing the N=14N = 14 subshell closure: gg factor of the 26^{26}Mg(21+^+_1) state

The first-excited state $g$~factor of $^{26}$Mg has been measured relative to the $g$ factor of the $^{24}$Mg($2^+_1$) state using the high-velocity transient-field technique, giving $g=+0.86\pm0.10$. This new measurement is in strong disagreement with the currently adopted value, but in agreement with the $sd$-shell model using the USDB interaction. The newly measured $g$ factor, along with $E(2^+_1)$ and $B(E2)$ systematics, signal the closure of the $\nu d_{5/2}$ subshell at $N=14$. The possibility that precise $g$-factor measurements may indicate the onset of neutron $pf$ admixtures in first-excited state even-even magnesium isotopes below $^{32}$Mg is discussed and the importance of precise excited-state $g$-factor measurements on $sd$~shell nuclei with $N\neq Z$ to test shell-model wavefunctions is noted.Comment: 8 pages, 5 figure

Optimized Large-Scale CMB Likelihood And Quadratic Maximum Likelihood Power Spectrum Estimation

We revisit the problem of exact CMB likelihood and power spectrum estimation with the goal of minimizing computational cost through linear compression. This idea was originally proposed for CMB purposes by Tegmark et al.\ (1997), and here we develop it into a fully working computational framework for large-scale polarization analysis, adopting \WMAP\ as a worked example. We compare five different linear bases (pixel space, harmonic space, noise covariance eigenvectors, signal-to-noise covariance eigenvectors and signal-plus-noise covariance eigenvectors) in terms of compression efficiency, and find that the computationally most efficient basis is the signal-to-noise eigenvector basis, which is closely related to the Karhunen-Loeve and Principal Component transforms, in agreement with previous suggestions. For this basis, the information in 6836 unmasked \WMAP\ sky map pixels can be compressed into a smaller set of 3102 modes, with a maximum error increase of any single multipole of 3.8\% at $\ell\le32$, and a maximum shift in the mean values of a joint distribution of an amplitude--tilt model of 0.006$\sigma$. This compression reduces the computational cost of a single likelihood evaluation by a factor of 5, from 38 to 7.5 CPU seconds, and it also results in a more robust likelihood by implicitly regularizing nearly degenerate modes. Finally, we use the same compression framework to formulate a numerically stable and computationally efficient variation of the Quadratic Maximum Likelihood implementation that requires less than 3 GB of memory and 2 CPU minutes per iteration for $\ell \le 32$, rendering low-$\ell$ QML CMB power spectrum analysis fully tractable on a standard laptop.Comment: 13 pages, 13 figures, accepted by ApJ