Efficient data structures for masks on 2D grids

This article discusses various methods of representing and manipulating arbitrary coverage information in two dimensions, with a focus on space- and time-efficiency when processing such coverages, storing them on disk, and transmitting them between computers. While these considerations were originally motivated by the specific tasks of representing sky coverage and cross-matching catalogues of astronomical surveys, they can be profitably applied in many other situations as well.Comment: accepted by A&

CMB Polarization Systematics Due to Beam Asymmetry: Impact on Inflationary Science

CMB polarization provides a unique window into cosmological inflation; the amplitude of the B-mode polarization from last scattering is uniquely sensitive to the energetics of inflation. However, numerous systematic effects arising from optical imperfections can contaminate the observed B-mode power spectrum. In particular, systematic effects due to the coupling of the underlying temperature and polarization fields with elliptical or otherwise asymmetric beams yield spurious systematic signals. This paper presents a non-perturbative analytic calculation of some of these signals. We show that results previously derived in real space can be generalized, formally, by including infinitely many higher-order corrections to the leading order effects. These corrections can be summed and represented as analytic functions when a fully Fourier-space approach is adopted from the outset. The formalism and results presented in this paper were created to determine the susceptibility of CMB polarization probes of the primary gravitational wave signal but can be easily extended to the analysis of gravitational lensing of the CMB.Comment: 14 pages, 11 figures, 6 tables. Minor corrections included to match published versio

CMB Polarization Systematics Due to Beam Asymmetry: Impact on Inflationary Science

CMB polarization provides a unique window into cosmological inflation; the amplitude of the B-mode polarization from last scattering is uniquely sensitive to the energetics of inflation. However, numerous systematic effects arising from optical imperfections can contaminate the observed B-mode power spectrum. In particular, systematic effects due to the coupling of the underlying temperature and polarization fields with elliptical or otherwise asymmetric beams yield spurious systematic signals. This paper presents a non-perturbative analytic calculation of some of these signals. We show that results previously derived in real space can be generalized, formally, by including infinitely many higher-order corrections to the leading order effects. These corrections can be summed and represented as analytic functions when a fully Fourier-space approach is adopted from the outset. The formalism and results presented in this paper were created to determine the susceptibility of CMB polarization probes of the primary gravitational wave signal but can be easily extended to the analysis of gravitational lensing of the CMB.Comment: 14 pages, 11 figures, 6 tables. Minor corrections included to match published versio

Gabor Transforms on the Sphere with Applications to CMB Power Spectrum Estimation

The Fourier transform of a dataset apodised with a window function is known as the Gabor transform. In this paper we extend the Gabor transform formalism to the sphere with the intention of applying it to CMB data analysis. The Gabor coefficients on the sphere known as the pseudo power spectrum is studied for windows of different size. By assuming that the pseudo power spectrum coefficients are Gaussian distributed, we formulate a likelihood ansatz using these as input parameters to estimate the full sky power spectrum from a patch on the sky. Since this likelihood can be calculated quickly without having to invert huge matrices, this allows for fast power spectrum estimation. By using the pseudo power spectrum from several patches on the sky together, the full sky power spectrum can be estimated from full-sky or nearly full-sky observations.Comment: 37 pages, 31 figures, accepted for publication in MNRA

Previrialization: Perturbative and N-Body Results

We present a series of N-body experiments which confirm the reality of the previrialization effect. We also use weakly nonlinear perturbative approach to study the phenomenon. These two approaches agree when the rms density contrast, $\sigma$, is small; more surprisingly, they remain in agreement when $\sigma \approx 1$. When the slope of the initial power spectrum is $n>-1$, nonlinear tidal interactions slow down the growth of density fluctuations and the magnitude of the suppression increases when $n$ (i.e. the relative amount of small scale power) is increased. For $n<-1$ we see an opposite effect: the fluctuations grow more rapidly than in linear theory. The transition occurs at $n=-1$ when the weakly nonlinear correction to $\sigma$ is close to zero and the growth rate is close to linear. Our results resolve recent controversy between two N-body studies of previrialization. Peebles (1990) assumed $n=0$ and found strong evidence in support of previrialization, while Evrard \& Crone (1992), who assumed $n=-1$, reached opposite conclusions. As we show here, the initial conditions with $n=-1$ are rather special because the nonlinear effects nearly cancel out for that particular spectrum. In addition to our calculations for scale-free initial spectra, we show results for a more realistic spectrum of Peacock \& Dodds (1994). Its slope near the scale usually adopted for normalization is close to $-1$, so $\sigma$ is close to linear. Our results retroactively justify linear normalization at 8$h^{-1}$ Mpc, while also demonstrating the danger and limitations of this practice.Comment: Significantly revised, 25 pages, uuencoded compressed postscript, figures included, to appear in Ap