Characterization of the Polarization Beam Response of SPT-3G Using Point Sources

Precise measurements of cosmic microwave background polarization require rigorous control of instrumental systematics. For the South Pole Telescope’s third-generation camera (SPT-3G), accurate characterization of the beam is critical for understanding the polarized mm-wave sky. Here, we present direct measurements of SPT-3G’s polarized beam response using observations of 100 polarized extragalactic point sources. Previous SPT-3G CMB power spectrum analyses introduced a phenomenological parameter $β_\mathrm{pol}$ to describe the degree of polarization preserved in beam sidelobes. These analyses found evidence for significant depolarization driven by the requirement of polarization power spectrum consistency between different frequency bands. Our direct measurements yield $β_\mathrm{pol}=0.90\pm0.10$ at 95 GHz, $1.01\pm0.12$ at 150 GHz, and $0.81\pm0.29$ at 220 GHz, indicating minimal sidelobe depolarization. We validate these results through extensive systematic tests including Bayesian posterior sampling versus frequentist bootstrap resampling, real-space versus Fourier-space analysis, and variations on temperature-to-polarization leakage handling, covariance determination, and source selection. When compared to values inferred from previous cosmological analyses, which favored significant depolarization to resolve inter-frequency power spectrum inconsistencies, we find a mild tension of $1.9σ$. However, this apparent discrepancy is dependent on the beam modeling, as our point source-based analysis derives much of its constraining power on $β_\mathrm{pol}$ from higher multipoles than the power spectrum analysis. These measurements therefore admit three explanations for the frequency-dependent residuals observed in the power spectrum analysis: a statistical fluctuation, the need for more sophisticated polarized beam models, or systematics other than beam depolarization.

💡 Research Summary

This paper presents a direct measurement of the polarized beam response of the South Pole Telescope’s third‑generation camera (SPT‑3G) using a sample of 100 bright, polarized extragalactic point sources observed between 2019 and 2023. The motivation stems from earlier cosmological analyses of SPT‑3G data (notably the “C25” study) that introduced a phenomenological parameter β_pol to describe how much of the beam’s sidelobes preserve polarization. Those analyses inferred β_pol ≈ 0.5–0.6 in each of the three observing bands (95, 150, 220 GHz), implying substantial depolarization in the sidelobes and a >5σ preference for β_pol < 1 to achieve consistency among auto‑ and cross‑spectra across frequencies.

The authors adopt a fundamentally different approach: they fit the radial polarization profiles of individual point sources directly, thereby measuring β_pol independently of any CMB power‑spectrum likelihood. Key methodological advances include (i) deconvolution of detector time‑constant effects at the time‑ordered‑data level, which cleanly separates optical beam properties from detector response; (ii) construction of empirical temperature‑to‑polarization leakage templates from the data themselves, iteratively refined to remove true astrophysical polarization; and (iii) a joint Bayesian inference framework (implemented with JAX and GPU acceleration) that simultaneously solves for the main‑lobe beam parameters, sidelobe structure, source polarization amplitudes, and the global β_pol for each frequency band. The analysis is cross‑validated using both real‑space radial profiles and Fourier‑space (ℓ‑mode) power spectra, and systematic robustness is tested through bootstrap resampling, alternative leakage‑template weightings, varied source selection cuts, and different covariance estimators.

The resulting β_pol values are β_95 = 0.90 ± 0.10, β_150 = 1.01 ± 0.12, and β_220 = 0.81 ± 0.29. These numbers indicate that, contrary to the earlier indirect constraints, the SPT‑3G beam preserves polarization almost perfectly, with only a modest hint of depolarization at 220 GHz. The discrepancy with the C25 results corresponds to a 1.9σ tension. The authors argue that this tension is largely driven by the different multipole ranges that dominate each analysis: the point‑source method draws most of its constraining power from high‑ℓ (ℓ ≈ 3000–5000) where the beam’s fine structure matters, whereas the power‑spectrum analysis is sensitive primarily to lower ℓ (ℓ ≲ 2000). Consequently, the simple single‑parameter β_pol model may be insufficient; a more sophisticated, ℓ‑dependent polarized beam model could reconcile the two measurements.

Systematic tests show that the β_pol estimates are stable under variations of leakage‑template construction (linear, median, flat, quadratic weighting), source flux cuts, exclusion of extended sources, and the choice of covariance matrix (data‑driven vs. theoretical noise model). The Bayesian posterior distributions agree closely with frequentist bootstrap confidence intervals, reinforcing the robustness of the result.

In the discussion, the authors outline three possible explanations for the residual frequency‑dependent discrepancies observed in the CMB power‑spectrum analysis: (1) a statistical fluctuation; (2) inadequacy of the current single‑parameter polarized beam model; or (3) other, non‑beam systematics affecting the spectra. They suggest that future work should incorporate an ℓ‑dependent beam model, expand the point‑source sample, and integrate the directly measured β_pol priors into cosmological likelihoods. The findings imply that, for SPT‑3G, beam‑induced depolarization is not a dominant systematic, thereby strengthening confidence in upcoming CMB polarization measurements, including searches for primordial B‑modes.