Maximum likelihood analysis of systematic errors in interferometric observations of the cosmic microwave background

TL;DR

This paper assesses how instrumental systematic errors, especially differential pointing errors, affect interferometric measurements of the CMB, providing guidelines for error control to ensure accurate detection of B-modes and tensor-to-scalar ratio.

Contribution

It introduces a maximum likelihood analysis pipeline to quantify systematic error impacts on CMB interferometry, focusing on differential pointing errors and their effect on key cosmological parameters.

Findings

Pointing errors must be controlled to 0.7° rms to recover B-modes at r=0.01

Pointing errors slightly bias the tensor-to-scalar ratio r by ~10%

Impact on TB and EB measurements is negligible

Abstract

We investigate the impact of instrumental systematic errors in interferometric measurements of the cosmic microwave background (CMB) temperature and polarization power spectra. We simulate interferometric CMB observations to generate mock visibilities and estimate power spectra using the statistically optimal maximum likelihood technique. We define a quadratic error measure to determine allowable levels of systematic error that do not induce power spectrum errors beyond a given tolerance. As an example, in this study we focus on differential pointing errors. The effects of other systematics can be simulated by this pipeline in a straightforward manner. We find that, in order to accurately recover the underlying B-modes for r=0.01 at 28<l<384, Gaussian-distributed pointing errors must be controlled to 0.7^\circ rms for an interferometer with an antenna configuration similar to QUBIC, in agreement with analytical estimates. Only the statistical uncertainty for 28<l<88 would be changed at ~10% level. With the same instrumental configuration, we find the pointing errors would slightly bias the 2-\sigma upper limit of the tensor-to-scalar ratio r by ~10%. We also show that the impact of pointing errors on the TB and EB measurements is negligibly small.