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

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

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

Management affects nitrate leaching from organic farms

Management decisions significantly affect nitrate-N leaching (N-leaching) from comparable organic fields. The main concern is field management during autumn and themanagement of grass leys. After ploughing-in fertility building crops, like grass-clover leys, effective catch crops are important during autumn and winter for at least two years on sandy soils. On farms with grazing animals the occurrence of “hot spots” should be avoided. These hot spots develop with uneven concentrations of animal manure combined with limited N-uptake in the ley. Management measures to minimize N-leachingmay conflicts with the farmers aim to produce high quality feed and/or to combat yield limiting perennial weeds. It may also conflict with the organic regulations for the grazing period of cows