A Simulation-Based Method for Correcting Mode Coupling in CMB Angular Power Spectra

TL;DR

This paper introduces a simulation-based spectral correction method using a transfer matrix to accurately account for mode coupling effects in CMB angular power spectra analysis, improving upon traditional transfer function approaches.

Contribution

The paper presents a novel 2D transfer matrix method for correcting mode coupling in CMB power spectra, addressing limitations of existing transfer function techniques.

Findings

The method effectively captures mode mixing in CMB data.

Application to SPIDER data demonstrates improved spectral correction.

The approach enhances the accuracy of power spectrum estimation.

Abstract

Modern CMB analysis pipelines regularly employ complex time-domain filters, beam models, masking, and other techniques during the production of sky maps and their corresponding angular power spectra. However, these processes can generate couplings between multipoles from the same spectrum and from different spectra, in addition to the typical power attenuation. Within the context of pseudo-$C_\ell$ based, MASTER-style analyses, the net effect of the time-domain filtering is commonly approximated by a multiplicative transfer function, $F_{\ell}$, that can fail to capture mode mixing and is dependent on the spectrum of the signal. To address these shortcomings, we have developed a simulation-based spectral correction approach that constructs a two-dimensional transfer matrix, $J_{\ell\ell'}$, which contains information about mode mixing in addition to mode attenuation. We demonstrate the application of this approach on data from the first flight of the SPIDER balloon-borne CMB experiment.