Bias in low-multipole CMB reconstructions

TL;DR

This paper critically examines the biases in low-multipole CMB reconstructions, revealing that common reconstruction techniques can introduce biases due to foreground leakage, and suggests more robust methods for analyzing the true CMB sky.

Contribution

The study identifies biases in standard CMB reconstruction methods caused by foreground leakage and proposes more robust approaches for analyzing large-scale CMB data.

Findings

Reconstruction is biased by foreground leakage.

Using unobscured regions without reconstruction is more robust.

Optimal estimators can be used without smoothing in noise-free data.

Abstract

The large-angle, low multipole cosmic microwave background (CMB) provides a unique view of the largest angular scales in the Universe. Study of these scales is hampered by the facts that we have only one Universe to observe, only a few independent samples of the underlying statistical distribution of these modes, and an incomplete sky to observe due to the interposing Galaxy. Techniques for reconstructing a full sky from partial sky data are well known and have been applied to the large angular scales. In this work we critically study the reconstruction process and show that, in practise, the reconstruction is biased due to leakage of information from the region obscured by foregrounds to the region used for the reconstruction. We conclude that, despite being suboptimal in a technical sense, using the unobscured region without reconstructing is the most robust measure of the true CMB sky. We also show that for noise free data reconstructing using the usual optimal, unbiased estimator may be employed without smoothing thus avoiding the leakage problem. Unfortunately, directly applying this to real data with noise and residual, unmasked foregrounds yields highly biased reconstructions requiring further care to apply this method successfully to real-world CMB.