A CMB Gibbs sampler for localized secondary anisotropies

TL;DR

This paper presents a Bayesian Gibbs sampling method to accurately characterize localized secondary anisotropies in CMB maps, such as SZ effects, by efficiently sampling from complex joint posterior distributions.

Contribution

It introduces a novel Bayesian formalism and Gibbs sampling scheme for analyzing localized secondary anisotropies in CMB data, enabling exact marginalization over correlated parameters.

Findings

Efficient sampling from joint posterior of multi-component sky models.

Exact marginalization of secondary anisotropy properties.

Computational feasibility demonstrated with existing code.

Abstract

As well as primary fluctuations, CMB temperature maps contain a wealth of additional information in the form of secondary anisotropies. Secondary effects that can be identified with individual objects, such as the thermal and kinetic Sunyaev-Zel'dovich (SZ) effects due to galaxy clusters, are difficult to unambiguously disentangle from foreground contamination and the primary CMB however. We develop a Bayesian formalism for rigorously characterising anisotropies that are localised on the sky, taking the TSZ and KSZ effects as an example. Using a Gibbs sampling scheme, we are able to efficiently sample from the joint posterior distribution for a multi-component model of the sky with many thousands of correlated physical parameters. The posterior can then be exactly marginalised to estimate properties of the secondary anisotropies, fully taking into account degeneracies with the other signals in the CMB map. We show that this method is computationally tractable using a simple implementation based on the existing Commander component separation code, and also discuss how other types of secondary anisotropy can be accommodated within our framework.