Recovering unbiased CMB polarization maps using modern ground-based experiments with minimal assumptions about atmospheric emission

TL;DR

This paper addresses unbiased reconstruction of CMB polarization maps from ground-based data in the presence of atmospheric noise. It develops and compares two mapmaking approaches: pair differencing (PD), derived from a maximum-likelihood perspective under minimal atmospheric assumptions, and statistical downweighting (DW), which relies on an expanded noise model including atmospheric contributions. The authors show that PD delivers near-ideal polarization maps with modest losses in sensitivity, especially when a continuously rotating half-wave plate (HWP) is used, and remains robust to realistic detector-noise variations; DW, by contrast, requires symmetric pair weights or accurate atmospheric modeling to reach comparable performance. The work demonstrates that PD offers a practical, model-independent path to robust polarization reconstruction for current and future ground-based CMB polarization experiments, with important implications for constraining the tensor-to-scalar ratio $r$ and probing primordial $B$-modes.

Abstract

We present a study of unbiased reconstruction of cosmic microwave background (CMB) polarization maps from data collected by modern ground-based observatories. Atmospheric emission is a major source of correlated noise in such experiments, complicating the recovery of faint cosmological signals. We consider estimators that require minimal assumptions about unpolarized atmospheric emission properties, instead exploiting hardware solutions commonly implemented in modern instruments, such as pairs of orthogonal antennas in each focal plane pixel, and polarization signal modulation via a continuously rotating half-wave plate (HWP). We focus on two techniques: (i) statistical down-weighting of low-frequency atmospheric signals, and (ii) pair-differencing (PD), which involves differencing signals collected by two detectors in the same focal plane pixel. We compare their performance against the idealized case where the atmospheric signal is perfectly known and cleanly subtracted. We show that PD can be derived from maximum likelihood principles under general assumptions about the atmospheric signal, optimizing map sensitivity. In the absence of instrumental systematics but with reasonable detector noise variations, PD yields polarized sky maps with noise levels only slightly worse than the ideal case. While down-weighting could match this performance, it requires highly accurate atmospheric models that are not readily available. PD performance is affected by instrumental systematics, particularly those leaking atmospheric signal to the difference time stream. However, effects like gain mismatch are efficiently mitigated by a rotating HWP, making PD a competitive, robust, and efficient solution for CMB polarization mapmaking without atmospheric modeling.

Figures (8)

• Figure 1: Reference $BB$ noise power spectra obtained from the ideal reconstruction (atmosphere-free, only instrumental noise).
• Figure 2: Comparison of white noise covariance block values for DW/PD and HWP/no-HWP cases. Nominal values of the instrumental noise parameters are used. Noise weights are fitted to the data independently for each detector. Each panel of this $3\times3$ histogram matrix shows the distribution of values of the white noise covariance blocks \ref{['eq:cov-block']} across the map. These blocks are normalized by the variance of the best constrained pixel, such that their smallest values across the map are 1 for $II$ and 2 for $QQ$ and $UU$.
• Figure 3: Comparison of $BB$ noise power spectra using pair differencing, with (left) vs. without (right) HWP rotation. Different setups are represented with combinations of markers and colors. "Nominal" (blue) corresponds to the nominal instrumental noise model. "Perturbed" (orange) has instrumental noise parameters drawn with a dispersion of $\qty{10}{\percent}$ around nominal values. "Perturbed pairs" (red) is a case where perturbations are applied in such a way that detectors of one pair always have the same parameters, i.e., any variations are only between different detector pairs. For each case, we plot the ratio of the noise power spectrum over that of the corresponding ideal (reference) case.
• Figure 4: Comparison of $BB$ noise power spectra using downweighting, with (left) vs without (right) HWP rotation. Different setups are represented with combinations of markers and colors. "Nominal" and "Perturbed" cases are the same as in Fig. \ref{['fig:pd-spectra']}. "Nominal + symmetric weights" is a case where instrumental noise parameters are nominal, and moreover the assumed noise weights are forced to be symmetric, i.e., the same for both detectors of a pair. "Perturbed + symmetric weights" is the same idea but with the perturbed noise parameters. "Nominal + instrumental weights" has both nominal instrumental parameters and noise weights following that model (not fitted to the data which contains atmosphere). For each case, we plot the ratio of the noise power spectrum over that of the corresponding ideal (reference) case.
• Figure 5: Normalized hit map of the extended simulation (10 days of observation) in equatorial coordinates. The corresponding sky fraction is about $\qty{20}{\percent}$.