A close examination of cosmic microwave background mirror-parity after Planck

Previous claims of significant evidence for mirror-parity in the large-scale cosmic microwave background (CMB) data from the Wilkinson Microwave Anisotropy Probe (WMAP) experiment have been recently echoed in the first study of isotropy and statistics of CMB data from Planck. We revisit these claims with a careful analysis of the latest data available. We construct statistical estimators in both harmonic and pixel space, test them on simulated data with and without mirror-parity symmetry, apply different Galactic masks, and study the dependence of the results on arbitrary choices of free parameters. We confirm that the data exhibit evidence for odd mirror-parity at a significance which reaches as high as ~ 99 per cent C.L., under some circumstances. However, given the inherent biases in the pixel-based statistic and the dependence of both pixel and harmonic space statistics on the particular form of Galactic masking and other a-posteriori choices, we conclude that these results are not in significant tension with the predictions of the concordance cosmological model.Comment: 9 pages, 5 figures, minor changes, as published in MNRA

The Kullback-Leibler Divergence as an Estimator of the Statistical Properties of CMB Maps

The identification of unsubtracted foreground residuals in the cosmic microwave background maps on large scales is of crucial importance for the analysis of polarization signals. These residuals add a non-Gaussian contribution to the data. We propose the Kullback-Leibler (KL) divergence as an effective, non-parametric test on the one-point probability distribution function of the data. With motivation in information theory, the KL divergence takes into account the entire range of the distribution and is highly non-local. We demonstrate its use by analyzing the large scales of the Planck 2013 SMICA temperature fluctuation map and find it consistent with the expected distribution at a level of 6%. Comparing the results to those obtained using the more popular Kolmogorov-Smirnov test, we find the two methods to be in general agreement.Comment: 12 pages, 5 figures, minor change, as published in JCA

Skewness and Kurtosis as Indicators of Non-Gaussianity in Galactic Foreground Maps

Observational cosmology is entering an era in which high precision will be required in both measurement and data analysis. Accuracy, however, can only be achieved with a thorough understanding of potential sources of contamination from foreground effects. Our primary focus will be on non- Gaussian effects in foregrounds. This issue will be crucial for coming experiments to determine B-mode polarization. We propose a novel method for investigating a data set in terms of skewness and kurtosis in locally defined regions that collectively cover the entire sky. The method is demonstrated on two sky maps: (i) the SMICA map of Cosmic Microwave Background fluctuations provided by the Planck Collaboration and (ii) a version of the Haslam map at 408 MHz that describes synchrotron radiation. We find that skewness and kurtosis can be evaluated in combination to reveal local physical information. In the present case, we demonstrate that the local properties of both maps are predominantly Gaussian. This result was expected for the SMICA map; that it also applies for the Haslam map is surprising. The approach described here has a generality and flexibility that should make it useful in a variety of astrophysical and cosmological contexts.Comment: 15 pages, 7 figures, minor change, as published in JCA

The 43GHz SiO maser in the circumstellar envelope of the AGB star R Cassiopeiae

We present multi-epoch, total intensity, high-resolution images of 43GHz, v=1, J=1-0 SiO maser emission toward the Mira variable R Cas. In total we have 23 epochs of data for R Cas at approximate monthly intervals over an optical pulsation phase range from 0.158 to 1.78. These maps show a ring-like distribution of the maser features in a shell, which is assumed to be centred on the star at a radius of 1.6 to 2.3 times the stellar radii. It is clear from these images that the maser emission is significantly extended around the star. At some epochs a faint outer arc can be seen at 2.2 stellar radii. The intensity of the emission waxes and wanes during the stellar phase. Some maser features are seen infalling as well as outflowing. We have made initial comparisons of our data with models by Gray et. al. (2009).Comment: 12 pages, 14 figure

Stochastic inequalities for single-server loss queueing systems

The present paper provides some new stochastic inequalities for the characteristics of the $M/GI/1/n$ and $GI/M/1/n$ loss queueing systems. These stochastic inequalities are based on substantially deepen up- and down-crossings analysis, and they are stronger than the known stochastic inequalities obtained earlier. Specifically, for a class of $GI/M/1/n$ queueing system, two-side stochastic inequalities are obtained.Comment: 17 pages, 11pt To appear in Stochastic Analysis and Application