A CMB GIBBS SAMPLER for LOCALIZED SECONDARY ANISOTROPIES

Abstract

In addition to primary fluctuations, cosmic microwave background (CMB) temperature maps contain a wealth of additional information in the form of secondary anisotropies. However, secondary effects that can be identified with individual objects, such as the thermal and kinetic Sunyaev–Zel'dovich (TSZ–KSZ) effects due to galaxy clusters, are difficult to unambiguously disentangle from foreground contamination and the primary CMB. We develop a Bayesian formalism to rigorously characterize anisotropies that are localized 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 marginalized to estimate the 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 discuss how other types of secondary anisotropy can be accommodated within our framework. © American Astronomical Society. All rights reserved.