arXiv subjects

Eric Hivon

Publications and source records attributed to Eric Hivon.

28 records · Page 2Linked to original sources

arXiv2004

Fast estimation of polarization power spectra using correlation functions

We present a fast method for estimating the cosmic microwave background polarization power spectra using unbiased estimates of heuristically-weighted correlation functions. This extends the O(N_pix^(3/2)) method of Szapudi et al. (2001) to polarized data. If the sky coverage allows the correlation functions to be estimated over the full range of angular separations, they can be inverted directly with integral transforms and clean separation of the electric (E) and magnetic (B) modes of polarization is obtained exactly in the mean. We assess the level of E-B mixing that arises from apodized integral transforms when the correlation function can only be estimated for a subset of angular scales, and show that it is significant for small-area observations. We introduce new estimators to deal with this case on the spherical sky that preserve E-B separation; their construction requires an additional integration of the correlation functions but the computational cost is negligible. We illustrate our methods with application to a large-area survey with parameters similar to PLANCK, and the small-area Background Imaging of Cosmic Extragalactic Polarization experiment. In both cases we show that the errors on the recovered power spectra are close to theoretical expectations.

astro-ph↗

arXiv2002

Opening A New Window to the Early Universe

DASI has ended a 34-year quest to detect the CMB polarization, sounding the starting gun for a new race to peer further back in time, with more precision than ever before. Many more CMB polarization experiments are in progress or planned. NASA's recently launched Microwave Anisotropy Probe (MAP) should detect the large-angle polarization induced by early star formation. This should be followed by increasingly precise ground and balloon experiments leading to the Launch of the European Space Agency's Planck satellite in 2007. If the recent past is any indication, studies of the CMB will continue to advance cosmology, even after Planck.

astro-ph↗

arXiv2002

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.

astro-ph↗

arXiv2000

The Pseudo-$C_l$ method: Cosmic microwave background anisotropy power spectrum statistics for high precision cosmology

As the era of high precision cosmology approaches, the empirically determined power spectrum of the microwave background anisotropy $C_l$ will provide a crucial test for cosmological theories. We present an exact semi-analytic framework for the study of the ampling statistics of the $C_l$ resulting from observations with partial sky coverage and anisotropic noise distributions. This includes space-borne, air-borne and ground-based experiments. We apply this theory to demonstrate its power for constructing fast but unbiased approximate methods for the joint estimation of cosmological parameters. Further applications, such as a test for possible non-Gaussianity of the underlying theory and a ``poor man's power spectrum estimator'' are suggested. An appendix derives recursion relations for the efficient computation of the couplings between spherical harmonics on the cut sky.

astro-ph↗

arXiv2000

Multiparameter estimation with the Pseudo-C_l method

We apply the Pseudo-C_l formalism to obtain an unbiased, approximate method for efficient simultaneous estimation of several cosmological parameters from large, almost full-sky cosmic microwave background data sets.

astro-ph↗

arXiv1999

The HEALPix Primer

HEALPix is a Hierarchical, Equal Area, and iso-Latitude Pixelisation of the sphere designed to support efficiently - local operations on the pixel set, - a hierarchical tree structure for multi-resolution applications, and - the global Fast Spherical Harmonic transform. The HEALPix concept and the mathematical software based on it introduced in this primer meet the challenges which future high resolution and large volume CMB data sets including the MAP and Planck mission products will present.

astro-ph↗

arXiv1998

CMB anisotropy power spectrum statistics

Much attention has been given to the problem of estimating cosmological parameters from the $C_l$ measured by future experiments. Many of the approaches which are being used either invoke poorly controlled approximations or are computationally expensive. We derive exact results as well as fast and highly accurate approximations for mapping a theoretical model onto the observed power spectrum coefficients and computing their statistical properties. These results obtain from an analytic framework which applies for any azimuthally symmetric sky coverage regardless of the fraction of the sky observed by the experiment.

astro-ph↗

arXiv1998

Topological Analysis of High-Resolution CMB Maps

We report the development of numerical tools for the topological analysis of sub--degree resolution, all--sky maps. Software to be released in the HEALFAST (V0.9) package defines neighbour relationships for the HEALPIX tessellation of the sphere. We apply this routine to a fast extrema search which scales strictly linearly in the number of pixels, $N_{p}$. We also present a highly efficient algorithm for simulating the gradient vector and curvature tensor fields ``on--the--fly'' with the temperature map, needing only of order $N_{p} \log_2 N_{p}$ more operations.

astro-ph↗

arXiv1997

Non-Linear Evolution of the Bispectrum of Cosmological Perturbations

The bispectrum, the three-point function of density fluctuations in Fourier space, is the lowest order statistic that carries information about the spatial coherence of large-scale structures. For Gaussian initial conditions, when the density fluctuation amplitude is small, tree-level (leading order) perturbation theory predicts a characteristic dependence of the bispectrum on the shape of the triangle formed by the three wave vectors. This configuration dependence provides a signature of gravitational instability, and departures from it in galaxy catalogs can be interpreted as due to bias, that is, non-gravitational effects. On the other hand, N-body simulations indicate that the reduced three-point function becomes relatively shape-independent in the strongly non-linear regime. In order to understand this non-linear transition and assess the domain of reliability of shape-dependence as a probe of bias, we calculate the one-loop (next-to-leading order) corrections to the bispectrum in perturbation theory. We compare these results with measurements in numerical simulations with scale-free and CDM initial power spectra. We find that the one-loop corrections account very well for the departures from the tree-level results measured in numerical simulations on weakly non-linear scales. In this regime, the reduced bispectrum qualitatively retains its tree-level shape, but the amplitude can change significantly. At smaller scales, the reduced bispectrum in the simulations starts to flatten, an effect which can be partially understood from the one-loop results. In the strong clustering regime, where perturbation theory breaks down entirely, the simulation results confirm that the reduced bispectrum has almost no dependence on triangle shape, in rough agreement with the hierarchical ansatz.

astro-ph↗

arXiv1996

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, $σ$, is small; more surprisingly, they remain in agreement when $σ\approx 1$. 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 $σ$ 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 $σ$ 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.

astro-ph↗