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

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

Marginal distributions for cosmic variance limited CMB polarization data

We provide computationally convenient expressions for all marginal distributions of the polarization CMB power spectrum distribution P(C_l|sigma_l), where C_l = {C_l^TT, C_l^TE, C_l^EE, C_l^BB} denotes the set of ensemble averaged polarization CMB power spectra, and sigma_l = {sigma_l^TT, sigma_l^TE, sigma_l^EE, sigma_l^BB} the set of the realization specific polarization CMB power spectra. This distribution describes the CMB power spectrum posterior for cosmic variance limited data. The expressions derived here are general, and may be useful in a wide range of applications. Two specific applications are described in this paper. First, we employ the derived distributions within the CMB Gibbs sampling framework, and demonstrate a new conditional CMB power spectrum sampling algorithm that allows for different binning schemes for each power spectrum. This is useful because most CMB experiments have very different signal-to-noise ratios for temperature and polarization. Second, we provide new Blackwell-Rao estimators for each of the marginal polarization distributions, which are relevant to power spectrum and likelihood estimation. Because these estimators represent marginals, they are not affected by the exponential behaviour of the corresponding joint expression, but converge quickly.Comment: 8 pages, 3 figures; minor adjustment, accepted for publication in ApJ

CMB likelihood approximation by a Gaussianized Blackwell-Rao estimator

We introduce a new CMB temperature likelihood approximation called the Gaussianized Blackwell-Rao (GBR) estimator. This estimator is derived by transforming the observed marginal power spectrum distributions obtained by the CMB Gibbs sampler into standard univariate Gaussians, and then approximate their joint transformed distribution by a multivariate Gaussian. The method is exact for full-sky coverage and uniform noise, and an excellent approximation for sky cuts and scanning patterns relevant for modern satellite experiments such as WMAP and Planck. A single evaluation of this estimator between l=2 and 200 takes ~0.2 CPU milliseconds, while for comparison, a single pixel space likelihood evaluation between l=2 and 30 for a map with ~2500 pixels requires ~20 seconds. We apply this tool to the 5-year WMAP temperature data, and re-estimate the angular temperature power spectrum, $C_{\ell}$, and likelihood, L(C_l), for l<=200, and derive new cosmological parameters for the standard six-parameter LambdaCDM model. Our spectrum is in excellent agreement with the official WMAP spectrum, but we find slight differences in the derived cosmological parameters. Most importantly, the spectral index of scalar perturbations is n_s=0.973 +/- 0.014, 1.9 sigma away from unity and 0.6 sigma higher than the official WMAP result, n_s = 0.965 +/- 0.014. This suggests that an exact likelihood treatment is required to higher l's than previously believed, reinforcing and extending our conclusions from the 3-year WMAP analysis. In that case, we found that the sub-optimal likelihood approximation adopted between l=12 and 30 by the WMAP team biased n_s low by 0.4 sigma, while here we find that the same approximation between l=30 and 200 introduces a bias of 0.6 sigma in n_s.Comment: 10 pages, 7 figures, submitted to Ap

Gender and Attorney Negotiation Ethics

Few studies of gender differences and legal ethics exist, and of these only a handful focus on gender and negotiation ethics. In light of the paucity of evidence on this topic, we decided to include gender as a component of a broader study of attorney negotiation ethics. This Essay sets forth and discusses our findings and hypotheses regarding gender and negotiation ethics. In Part II we explain the requirements of the professional rules of attorney conduct governing negotiation, and in Part III we discuss the study’s methodology and findings from the larger study. Part IV offers a detailed review of the literature related to the influence of gender on ethical decision-making. The data resulting from this study is presented in Part V, and in Part VI, we discuss potential explanations for our findings in addition to addressing our study’s limitations. In conclusion, Part VII makes several suggestions for further studies on this topic

Systematic Distortion in Cosmic Microwave Background Maps

To minimize instrumentally induced systematic errors, cosmic microwave background (CMB) anisotropy experiments measure temperature differences across the sky using paires of horn antennas, temperature map is recovered from temperature differences obtained in sky survey through a map-making procedure. To inspect and calibrate residual systematic errors in recovered temperature maps is important as most previous studies of cosmology are based on these maps. By analyzing pixel-ring couping and latitude dependence of CMB temperatures, we find notable systematic deviation from CMB Gaussianity in released Wilkinson Microwave Anisotropy Probe (WMAP) maps. The detected deviation is hard to explain by any process in the early universe and can not be ignored for a precision cosmology study.Comment: accepted for publication in Sci China G-Phy Mech Astro

A Markov Chain Monte Carlo Algorithm for analysis of low signal-to-noise CMB data

We present a new Monte Carlo Markov Chain algorithm for CMB analysis in the low signal-to-noise regime. This method builds on and complements the previously described CMB Gibbs sampler, and effectively solves the low signal-to-noise inefficiency problem of the direct Gibbs sampler. The new algorithm is a simple Metropolis-Hastings sampler with a general proposal rule for the power spectrum, C_l, followed by a particular deterministic rescaling operation of the sky signal. The acceptance probability for this joint move depends on the sky map only through the difference of chi-squared between the original and proposed sky sample, which is close to unity in the low signal-to-noise regime. The algorithm is completed by alternating this move with a standard Gibbs move. Together, these two proposals constitute a computationally efficient algorithm for mapping out the full joint CMB posterior, both in the high and low signal-to-noise regimes.Comment: Submitted to Ap