Measuring Planck beams with planets

Aims. Accurate measurement of the cosmic microwave background (CMB) anisotropy requires precise knowledge of the instrument beam. We explore how well the Planck beams will be determined from observations of planets, developing techniques that are also appropriate for other experiments. Methods. We simulate planet observations with a Planck-like scanning strategy, telescope beams, noise, and detector properties. Then we employ both parametric and non-parametric techniques, reconstructing beams directly from the time-ordered data. With a faithful parameterization of the beam shape, we can constrain certain detector properties, such as the time constants of the detectors, to high precision. Alternatively, we decompose the beam using an orthogonal basis. For both techniques, we characterize the errors in the beam reconstruction with Monte Carlo realizations. For a simplified scanning strategy, we study the impact on estimation of the CMB power spectrum. Finally, we explore the consequences for measuring cosmological parameters, focusing on the spectral index of primordial scalar perturbations, n_s. Results. The quality of the power spectrum measurement will be significantly influenced by the optical modeling of the telescope. In our most conservative case, using no information about the optics except the measurement of planets, we find that a single transit of Jupiter across the focal plane will measure the beam window functions to better than 0.3% for the channels at 100–217 GHz that are the most sensitive to the CMB. Constraining the beam with optical modeling can lead to much higher quality reconstruction. Conclusions. Depending on the optical modeling, the beam errors may be a significant contribution to the measurement systematics for n_s

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

Relevance of Ion-Channeling for Direct DM Detection

The channeling of the recoiling nucleus in crystalline detectors after a WIMP collision would produce a larger scintillation or ionization signal in direct detection experiments than otherwise expected. I present estimates of the importance of this effect for the total direct detection rate and the daily modulation of the signal using analytic models produced in the 1960's and 70's to describe the effects of channeling and blocking in crystals.Comment: Talk given at the TAUP 2009 conference, Rome, Italy, July 1-5 2009. 3 pages, 4 figures. jpconf.cls and jpconf11.clo files need to typeset the tex fil

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

Testing the Gaussianity of the COBE-DMR data with spherical wavelets

We investigate the Gaussianity of the 4-year COBE-DMR data (in HEALPix pixelisation) using an analysis based on spherical Haar wavelets. We use all the pixels lying outside the Galactic cut and compute the skewness, kurtosis and scale-scale correlation spectra for the wavelet coefficients at each scale. We also take into account the sensitivity of the method to the orientation of the input signal. We find a detection of non-Gaussianity at $> 99$ per cent level in just one of our statistics. Taking into account the total number of statistics computed, we estimate that the probability of obtaining such a detection by chance for an underlying Gaussian field is 0.69. Therefore, we conclude that the spherical wavelet technique shows no strong evidence of non-Gaussianity in the COBE-DMR data.Comment: latex file 7 pages, 6 figures, submitted to MNRA

A common missense variant in BRCA2 predisposes to early onset breast cancer

INTRODUCTION: Mutations in the BRCA2 gene are one of the two major causes of hereditary breast cancer. Protein-truncating mutations of BRCA2 are usually deleterious and increase the risk of breast cancer up to 80% over a lifetime. A few missense mutations in BRCA2 are believed to have a similarly high penetrance, apart from more common neutral polymorphisms. It is often difficult to classify a particular sequence variant as a mutation or a polymorphism. For a deleterious variant, one would expect a greater allele frequency in breast cancer cases than in ethnic-matched controls. In contrast, neutral polymorphic variants should be equally frequent in the two groups. METHODS: We genotyped 3,241 cases of breast cancer diagnosed at under 51 years of age, unselected for family history, from 18 hospitals throughout Poland and 2,791 ethnic-matched controls for a single BRCA2 C5972T variant. RESULTS: The variant was present in approximately 6% of the Polish population. In the study, 13 women (11 cases and two controls (OR = 4.7; p = 0.02)) were homozygous for the variant allele. The overall odds ratio for breast cancer in women with a single copy of the BRCA2 C5972T variant was 1.1 (p = 0.7); however, the effect was significant for patients diagnosed at or before age 40 (OR = 1.4; p = 0.04). We reviewed the association between the BRCA2 variant in different histologic subgroups and found the effect most pronounced in women who had ductal carcinoma in situ (DCIS) with micro-invasion (OR = 2.8; p < 0.0001). CONCLUSION: The BRCA2 C5972T allele is a common variant in Poland that increases the risk of DCIS with micro-invasion. The homozygous state is rare but increases the risk of breast cancer five-fold

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

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

Angular Power Spectrum of the Microwave Background Anisotropy seen by the COBE Differential Microwave Radiometer

The angular power spectrum estimator developed by Peebles (1973) and Hauser & Peebles (1973) has been modified and applied to the 4 year maps produced by the COBE DMR. The power spectrum of the observed sky has been compared to the power spectra of a large number of simulated random skies produced with noise equal to the observed noise and primordial density fluctuation power spectra of power law form, with $P(k) \propto k^n$. The best fitting value of the spectral index in the range of spatial scales corresponding to spherical harmonic indices $3 \leq \ell \lesssim 30$ is an apparent spectral index $n_{app}$ = 1.13 (+0.3) (-0.4) which is consistent with the Harrison-Zel'dovich primordial spectral index $n_{pri} = 1$ The best fitting amplitude for $n_{app} = 1$ is $\langle Q_{RMS}^2\rangle^{0.5}$ = 18 uK.Comment: 17 pages including 3 PostScript figures. Submitted to The Astrophysical Journal (Letters