Benjamin D. Wandelt

HEALPIX : A framework for high-resolution discretization and fast analysis of data distributed on the sphere

HEALPix—the Hierarchical Equal Area isoLatitude Pixelization—is a versatile structure for the pixelization of data on the sphere. An associated library of computational algorithms and visualization software supports fast scientific applications executable directly on discretized spherical maps generated from very large volumes of astronomical data. Originally developed to address the data processing and analysis needs of the present generation of cosmic microwave background experiments (e.g., BOOMERANG, WMAP), HEALPix can be expanded to meet many of the profound challenges that will arise in confrontation with the observational output of future missions and experiments, including, e.g., Planck, Herschel, SAFIR, and the Beyond Einstein inflation probe. In this paper we consider the requirements and implementation constraints on a framework that simultaneously enables an efficient discretization with associated hierarchical indexation and fast analysis/synthesis of functions defined on the sphere. We demonstrate how these are explicitly satisfied by HEALPix.

Evidence of Primordial Non-Gaussianity (f(NL)) in the Wilkinson Microwave Anisotropy Probe 3-Year Data at 2.8sigma

We present evidence for the detection of primordial non-Gaussianity of the local type (fNL), using the temperature information of the Cosmic Microwave Background (CMB) from the WMAP 3-year data. We employ the bispectrum estimator of non-Gaussianity described in [1] which allows us to analyze the entirety of the WMAP data without an arbitrary cut-off in angular scale. Using the combined information from WMAP’s two main science channels up to lmax = 750 and the conservative Kp0 foreground mask we find 27 < fNL < 147 at 95% C.L., with a central value of fNL = 87. This corresponds to a rejection of fNL = 0 at more than 99.5% significance. We find that this detection is robust to variations in lmax, frequency and masks, and that no known foreground, instrument systematic, or secondary anisotropy explains our signal while passing our suite of tests. We explore the impact of several analysis choices on the stated significance and find 2.5 σ for the most conservative view. We conclude that the WMAP 3-year data disfavors canonical single field slow-roll inflation.

Halo Properties in Cosmological Simulations of Self-interacting Cold Dark Matter

We present a comparison of halo properties in cosmological simulations of collisionless cold dark matter (CDM) and self-interacting dark matter (SIDM) for a range of dark matter cross sections. We find, in agreement with various authors, that CDM yields cuspy halos that are too centrally concentrated as compared to observations. Conversely, SIDM simulations using a Monte Carlo N-body technique produce halos with significantly reduced central densities and flatter cores. We introduce a concentration parameter based on enclosed mass that we expect will be straightforward to determine observationally and present predictions for SIDM and CDM. SIDM also produces more spherical halos than CDM, providing possibly the strongest observational constraint on SIDM. In our simulations with SIDM cross sections ?DM ? 10-23 to 10-25 cm2 GeV-1, collisions reduce the central density in galaxy halos, with larger cross sections producing lower densities. Simulations in the upper end of this range best match current observations of galaxy properties but are disfavored by cluster simulations of Yoshida and colleagues. This problem would be alleviated in models in which the cross section is velocity dependent.

Measuring Primordial Non-Gaussianity in the Cosmic Microwave Background

We derive a fast way for measuring primordial non-Gaussianity in a nearly full-sky map of the cosmic microwave background. We find a cubic combination of sky maps combining bispectrum configurations to capture a quadratic term in primordial fluctuations. Our method takes only N3/2 operations rather than N5/2, as taken by the bispectrum analysis (1000 times faster for l = 512), retaining the same sensitivity. A key component is a map of the underlying primordial fluctuations, which can be more sensitive to the primordial non-Gaussianity than a temperature map. We also derive a fast and accurate statistic for measuring non-Gaussian signals from foreground point sources. The statistic is 106 times faster than the full bispectrum analysis and can be used to estimate contamination from the sources. Our algorithm has been successfully applied to the Wilkinson Microwave Anisotropy Probe sky maps by Komatsu and coworkers.

Global, exact cosmic microwave background data analysis using Gibbs sampling

We describe an efficient and exact method that enables global Bayesian analysis of cosmic microwave background (CMB) data. The method reveals the joint posterior density (or likelihood for flat priors) of the power spectrum

Adaptive ray tracing for radiative transfer around point sources

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Power Spectrum Estimation from High-Resolution Maps by Gibbs Sampling

and the CMB signal. Foregrounds and instrumental parameters can be simultaneously inferred from the data. The method allows the specification of a wide range of foreground priors. We explicitly show how to propagate the non-Gaussian dependency structure of the

Measurement of the cosmic microwave background bispectrum on the COBE DMR sky maps

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PRECISION COSMOGRAPHY WITH STACKED VOIDS

posterior through to the posterior density of the parameters. If desired, the analysis can be coupled to theoretical (cosmological) priors and can yield the posterior density of cosmological parameter estimates directly from the time-ordered data. The method does not hinge on special assumptions about the survey geometry or noise properties, etc., It is based on a Monte Carlo approach and hence parallelizes trivially. No trace or determinant evaluations are necessary. The feasibility of this approach rests on the ability to solve the systems of linear equations which arise. These are of the same size and computational complexity as the map-making equations. We describe a preconditioned conjugate gradient technique that solves this problem and demonstrate in a numerical example that the computational time required for each Monte Carlo sample scales as

Fast Estimator of Primordial Non-Gaussianity from Temperature and Polarization Anisotropies in the Cosmic Microwave Background

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