Foreground-Induced Biases in CMB Polarimeter Self-Calibration

TL;DR

This paper investigates how polarized Galactic foregrounds can bias the self-calibration of CMB polarimeters, potentially leading to false B-mode signals, and proposes an expanded calibration method to mitigate this effect.

Contribution

It introduces a formalism to account for foreground-induced biases in self-calibration, improving accuracy in CMB polarization measurements.

Findings

Bias is negligible for high-resolution experiments with CMB-dominated modes.

Low-resolution, dusty sky observations can have biases up to 0.5 degrees.

A 0.5-degree bias can mimic a tensor-to-scalar ratio of about 2×10⁻³.

Abstract

Precise polarisation measurements of the cosmic microwave background (CMB) require accurate knowledge of the instrument orientation relative to the sky frame used to define the cosmological Stokes parameters. Suitable celestial calibration sources that could be used to measure the polarimeter orientation angle are limited, so current experiments commonly `self-calibrate.' The self-calibration method exploits the theoretical fact that the $EB$ and $TB$ cross-spectra of the CMB vanish in the standard cosmological model, so any detected $EB$ and $TB$ signals must be due to systematic errors. However, this assumption neglects the fact that polarized Galactic foregrounds in a given portion of the sky may have non-zero $EB$ and $TB$ cross-spectra. If these foreground signals remain in the observations, then they will bias the self-calibrated telescope polarisation angle and produce a spurious $B$-mode signal. In this paper we estimate the foreground-induced bias for various instrument configurations and then expand the self-calibration formalism to account for polarized foreground signals. Assuming the $EB$ correlation signal for dust is in the range constrained by angular power spectrum measurements from Planck at 353 GHz (scaled down to 150 GHz), then the bias is negligible for high angular resolution experiments, which have access to CMB-dominated high $\ell$ modes with which to self-calibrate. Low-resolution experiments observing particularly dusty sky patches can have a bias as large as $0.5^\circ$. A miscalibration of this magnitude generates a spurious $BB$ signal corresponding to a tensor-to-scalar ratio of approximately $r\sim2\times10^{-3}$, within the targeted range of planned experiments.