Secondary non-Gaussianity and Cross-Correlation Analysis

TL;DR

This paper develops optimized estimators for cross-power and skew spectra on the sky, enabling detailed analysis of secondary effects like ISW and SZ, and non-Gaussianity in the CMB with partial sky coverage.

Contribution

It introduces a formalism for the skew spectrum of three fields, enhancing the study of non-Gaussianity and secondary anisotropies in the CMB.

Findings

Effective estimators for cross-power and skew spectra are developed.

The formalism improves detection prospects for ISW, SZ, and CMB lensing effects.

Analysis indicates high significance of secondary effects in CMB data.

Abstract

We develop optimised estimators of two sorts of power spectra for fields defined on the sky, in the presence of partial sky coverage. The first is the cross-power spectrum of two fields on the sky; the second is the skew spectrum of three fields. These can probe the Integrated Sachs Wolfe Effect (ISW) at large angular scales and the Sunyaev Z\'eldovich (SZ) effect from hot gas in clusters at small angular scales. The skew spectrum, recently introduced by Munshi & Heavens (2009), is an optimised statistic which can be tuned to study a particular form of non-Gaussianity, such as may arise in the early Universe, but which retains information on the nature of non-Gaussianity. In this paper we develop the mathematical formalism for the skew spectrum of 3 different fields. When applied to the CMB, this allows us to explore the contamination of the skew spectrum by secondary sources of CMB fluctuations. Considering the three-point function, the study of the bispectrum provides valuable information regarding cross-correlation of secondaries with lensing of CMB with much higher significance compared to just the study involving CMB sky alone. We use our analytical models to study specific cases of cosmological interest which include cross-correlating CMB with various large scale tracers to probe ISW and SZ effects for cross spectral analysis and use the formalism to study the signal-to-noise ratio for detection of the weak lensing of the CMB by cross-correlating it with different tracers as well as point sources for CMB experiments such as Planck (abridged).