General CMB and Primordial Bispectrum Estimation I: Mode Expansion, Map-Making and Measures of f_NL

TL;DR

This paper introduces versatile bispectrum estimation techniques for CMB data, enabling efficient analysis of non-Gaussian features across various models and datasets, including high-resolution maps and secondary anisotropies.

Contribution

It presents a novel mode expansion approach for bispectrum estimation that works with non-separable shapes and provides practical tools for analyzing CMB non-Gaussianity.

Findings

Validated estimators with WMAP data consistent with previous results

Demonstrated rapid convergence of mode expansions for known bispectra

Enabled extraction of full bispectrum from observational maps

Abstract

We present a detailed implementation of two bispectrum estimation methods which can be applied to general non-separable primordial and CMB bispectra. The method exploits bispectrum mode decompositions on the domain of allowed wavenumber or multipole values. Concrete mode examples constructed from symmetrised tetrahedral polynomials are given, demonstrating rapid convergence for known bispectra. We use these modes to generate simulated CMB maps of high resolution (l > 2000) given an arbitrary primordial power spectrum and bispectrum or an arbitrary late-time CMB angular power spectrum and bispectrum. By extracting coefficients for the same separable basis functions from an observational map, we are able to present an efficient and general f_NL estimator for a given theoretical model. The estimator has two versions comparing theoretical and observed coefficients at either primordial or late times, thus encompassing a wider range of models, including secondary anisotropies, lensing and cosmic strings. We provide examples and validation of both f_NL estimation methods by direct comparison with simulations in a WMAP-realistic context. In addition, we show how the full bispectrum can be extracted from observational maps using these mode expansions, irrespective of the theoretical model under study. We also propose a universal definition of the bispectrum parameter F_NL for more consistent comparison between theoretical models. We obtain WMAP5 estimates of f_NL for the equilateral model from both our primordial and late-time estimators which are consistent with each other, as well as with results already published in the literature. These general bispectrum estimation methods should prove useful for the analysis of nonGaussianity in the Planck satellite data, as well as in other contexts.