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

Reactivity difference between protolytic forms of some macrocyclic chromium(III) complexes in ligand substitution and electron transfer processes

The review provides insight into the mechanism of ligand substitution and electron transfer (from chromium( III) to iron(III)) by comparison of the reactivity of some tetraazamacrocyclic chromium(III) complexes in the conjugate acid-base forms. Use of two geometrical isomers made possible to estimate the influence of geometry and protolytic reactions in trans and cis position towards the leaving group on the rate enhancement. Studies on the reaction rates in different media demonstrated the role played by outer sphere interactions in a monodentate ligand substitution

Highly productive forage legume stands show no positive biodiversity effect on yield and N2-fixation

Background and aims While N2-fixation in diversified grasslands including forage legumes and non-legumes has been widely studied, N2-fixation in swards containing only forage legumes remains unclear. In this study, we investigated N2-fixation in pure stands and mixtures of three forage legumes. Methodology N2-fixation, dry matter (DM) and nitrogen (N) yields were quantified in a field experiment for red clover (Trifolium pratense L.), white clover (Trifolium repens L.) and lucerne (Medicago sativa L.) pure stands and mixtures using the isotope dilution method. Results All three forage legume species derived most (around 85%) of their N from atmospheric N2-fixation (%Ndfa). However, no positive effect of species diversity was found in any of the mixtures. Species composition of the forage legume mixtures affected the amount of N from N2-fixation by affecting DM production and N accumulation of the species, where the seasonal amount of N2-fixation ranged from 370 to 500 kg N ha−1; which was highest in the presence of red clover. Conclusions We found thatmixturesof thethree forage legumes were highly productive, but did not show positive advantages compared to the red clover pure stands in terms of DM, N yield and %Ndfa

Nitrogen fixation in red clover grown in multi-species mixtures with ryegrass, chicory, plantain and caraway

While many studies have investigated effects of species composition and management on N2-fixation dynamics in simple clover-grass mixtures, there is a lack of knowledge about the performance of legumes and their N2-fixation in more species-rich grassland including non-legume forbs. This study investigated N2-fixation and total N yield in grassland mixtures including different combinations of red clover, perennial ryegrass and three deep rooted forbs: chicory, ribwort plantain and caraway, managed without and with slurry application. The percentage of clover N derived from atmosphere (%Ndfa) increased in mixtures, but was unaffected by inclusion of forbs. However, forbs affected the quantity of N2-fixation and total N yield by affecting the red clover proportion in the mixtures. Mixtures composed of grass,clover and plantain or caraway showed higher N2-fixation and N yield than with chicory included. Slurry application reduced N2-fixation due to decreasing clover contents in the sampled biomass. The study highlighted differences among forbs in their influence on legume N2-fixation and total N yield showing that forbs can be included in grasslands without negative effects on red clover performance

Effecs of including forbs on N2-fixation and N yield in red clover-ryegrass mixtures

Background: Legume biological nitrogen (N2)-fixation is stimulated by neighboring non-fixing species, but studies of legume N2-fixation in temporary grasslands including non-leguminous forage herb (forb) species are rare. Methodology: We investigated N2-fixation and N yield in a range of species mixtures consisting of three forb species chicory (Cichorium intybus L.), ribwort plantain (Plantago lanceolata L.) and caraway (Carum carvi L.) mixed into a traditional perennial ryegrass (Lolium perenne L.) and red clover(Trifolium pratense L.) mixture at two fertilisation levels. Results: The percentage of red clover N derived from the atmosphere (%Ndfa) was higher in mixtures than in pure stand, but did not increase with inclusion of forbs. Red clover in all the mixtures derived over 90% of its N from fixation even when fertilised with 216 kg total N ha-1. Forbs affected the amount of N2-fixation by affecting the red clover proportion in the harvested biomass. Conclusions: We conclude that forbs can be included in temporary grasslands with no negative effect on total herbage production and percentage of legume N2-fixation. However, mixtures should not include a high seeding proportion of chicory for a balance between legume and non-legume biomass proportions

Short-term residual N unaffected by forbs in grass-clover mixtures

We determined the effect on residual nitrogen (N) of including forbs (chicory, ribwort plantain and caraway) in perennial ryegrass-red clover mixtures. Although soil N inputs during the grassland phase differed markedly between mixtures, in a pot experiment we found no differences in the potentially mineralizable N of the soil or in the dry matter production and N content of the spring barley test crop. The fertilizer value of the grassland mixtures corresponded to 10 g N/m2, irrespective of forb inclusion. Thus, the inclusion of nonlegume forbs did not negatively affect short-term residual N fertility of legume-based grasslands

Joint Bayesian component separation and CMB power spectrum estimation

We describe and implement an exact, flexible, and computationally efficient algorithm for joint component separation and CMB power spectrum estimation, building on a Gibbs sampling framework. Two essential new features are 1) conditional sampling of foreground spectral parameters, and 2) joint sampling of all amplitude-type degrees of freedom (e.g., CMB, foreground pixel amplitudes, and global template amplitudes) given spectral parameters. Given a parametric model of the foreground signals, we estimate efficiently and accurately the exact joint foreground-CMB posterior distribution, and therefore all marginal distributions such as the CMB power spectrum or foreground spectral index posteriors. The main limitation of the current implementation is the requirement of identical beam responses at all frequencies, which restricts the analysis to the lowest resolution of a given experiment. We outline a future generalization to multi-resolution observations. To verify the method, we analyse simple models and compare the results to analytical predictions. We then analyze a realistic simulation with properties similar to the 3-yr WMAP data, downgraded to a common resolution of 3 degree FWHM. The results from the actual 3-yr WMAP temperature analysis are presented in a companion Letter.Comment: 23 pages, 16 figures; version accepted for publication in ApJ -- only minor changes, all clarifications. More information about the WMAP3 analysis available at http://www.astro.uio.no/~hke under the Research ta

Exact Foldy-Wouthuysen transformation for gravitational waves and magnetic field background

We consider an exact Foldy-Wouthuysen transformation for the Dirac spinor field on the combined background of a gravitational wave and constant uniform magnetic field. By taking the classical limit of the spinor field Hamiltonian we arrive at the equations of motion for the non-relativistic spinning particle. Two different kinds of the gravitational fields are considered and in both cases the effect of the gravitational wave on the spinor field and on the corresponding spinning particle may be enforced by the sufficiently strong magnetic field. This result can be relevant for the astrophysical applications and, in principle, useful for creating the gravitational wave detectors based on atomic physics and precise interferometry

Instability of reconstruction of the low CMB multipoles

We discuss the problem of the bias of the Internal Linear Combination (ILC) CMB map and show that it is closely related to the coefficient of cross-correlation K(l) of the true CMB and the foreground for each multipole l. We present analysis of the cross-correlation for the WMAP ILC quadrupole and octupole from the first (ILC(I)) and the third (ILC(III)) year data releases and show that these correlations are about -0.52-0.6. Analysing 10^4 Monte Carlo simulations of the random Gaussian CMB signals, we show that the distribution function for the corresponding coefficient of the cross-correlation has a polynomial shape P(K,l)\propto(1-K^2)^(l-1). We show that the most probable value of the cross-correlation coefficient of the ILC and foreground quadrupole has two extrema at K ~= +/-0.58$. Thus, the ILC(III) quadrupole represents the most probable value of the coefficient K. We analyze the problem of debiasing of the ILC CMB and pointed out that reconstruction of the bias seems to be very problematic due to statistical uncertainties. In addition, instability of the debiasing illuminates itself for the quadrupole and octupole components through the flip-effect, when the even (l+m) modes can be reconstructed with significant error. This error manifests itself as opposite, in respect to the true sign of even low multipole modes, and leads to significant changes of the coefficient of cross-correlation with the foreground. We show that the CMB realizations, whose the sign of quadrupole (2,0) component is negative (and the same, as for all the foregrounds), the corresponding probability to get the positive sign after implementation of the ILC method is about 40%.Comment: 11 pages, 5 figure