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

TL;DR

This work directly measures the polarized beam response of SPT-3G by fitting beam models to 100 polarized extragalactic point sources, focusing on the depolarization parameter $\beta_{\mathrm{pol}}$. Using two complementary beam models (a flexible B-spline representation and the physically motivated $\beta_{\mathrm{pol}}$ parameterization) and a rigorous Fourier-domain covariance approach with bootstrap uncertainties, the authors find $\beta_{\mathrm{pol}}=0.90\pm0.10$ at 95 GHz, $1.01\pm0.12$ at 150 GHz, and $0.81\pm0.29$ at 220 GHz, consistent with fully polarized sidelobes ($\beta_{\mathrm{pol}}=1$) at high significance. A mild $1.9\sigma$ tension with previous CMB-power-spectrum-inferred constraints is explored and attributed to the different angular scales probed and potential modeling limitations, suggesting future work to refine beam models or account for other systematics. The study demonstrates that bright polarized point sources can constrain beam-induced polarization systematics with ~10% precision, enabling tighter priors for cosmological analyses and guiding future instrument upgrades such as SPT-3G+. The robust methodology, including GPU-accelerated fitting, extensive systematic tests, and cross-validation across analysis choices, provides a template for beam characterization in high-resolution CMB polarimetry.

Abstract

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.

Figures (6)

• Figure 1: Empirical temperature-to-polarization leakage templates for the main field. These templates represent the spurious $Q$ and $U$ signal induced by a temperature point source, constructed by averaging source maps after subtracting the best-fit astrophysical polarization models. The structure of these templates is consistent with the leakage patterns identified in the cosmological analysis camphuis25. These patterns are scaled by the source peak temperature and subtracted from each source prior to beam analysis.
• Figure 2: Visualization of Table \ref{['tab:hyperparameters']}. Points indicate the maximum-likelihood values (or posterior means for the Bayesian case), and error bars denote $1\sigma$ uncertainties (bootstrap or posterior standard deviation). The results are consistent across all variations, with the real-space and white-noise analyses yielding larger uncertainties as expected due to their suboptimal weighting of atmospheric noise. The tight agreement across leakage template methods and data subsets confirms that the measurement is not driven by specific analysis choices or source sub-populations.
• Figure 3: Example of a typical bright polarized point source in SPT-3G observations at 95 GHz. Rows show Stokes $T$, $Q$, and $U$ parameters. Columns display the observed data, best-fit $\beta_{\mathrm{pol}}$ model, and residuals. The color scales are in units of $\mathrm{mK}_\mathrm{CMB}$, where one unit corresponds to the flux density needed to make the CMB appear 1 mK brighter at 95 GHz. The azimuthally symmetric model leaves residuals in Stokes $T$ due to the asymmetric nature of the beam. Stokes $Q$ and $U$ do not show any residuals at the source location.
• Figure 4: Temperature (top) and polarization (bottom) radial beam profiles reconstructed using the B-spline basis. These profiles are peak-normalized such that $B(r=0)=1$. Thick colored curves show the best-fit profiles for 95 GHz (red), 150 GHz (gold), and 220 GHz (blue). Thin colored lines show a subset of the 200 bootstrap realizations, illustrating the measurement uncertainty. The polarization beam uncertainties are approximately 50 times larger than temperature beam uncertainties due to the $\sim2\%$ intrinsic polarization fraction of most sources. Overlaid on the polarization beams are predictions from the $\beta_{\mathrm{pol}}$ model for two limiting cases: fully depolarized sidelobes ($\beta_{\mathrm{pol}}=0$, dot-dashed black) and fully polarized sidelobes ($\beta_{\mathrm{pol}}=1$, dotted black). The model-independent B-spline fits closely track the $\beta_{\mathrm{pol}}=1$ prediction, showing no evidence of significant depolarization.
• Figure 5: Harmonic domain representation of the beam profiles shown in Figure \ref{['fig:bspline_beams']}. The curves are obtained via Hankel transformation of the real-space B-spline fits and contain equivalent information. The profiles retain the real-space peak normalization $B(r=0)=1$, corresponding to $\int \ell B(\ell) d\ell = 2\pi$.