A Measurement of the Largest-Scale CMB E-mode Polarization with CLASS
Yunyang Li, Joseph Eimer, John Appel, Charles Bennett, Michael Brewer, Sarah Marie Bruno, Ricardo Bustos, Carol Chan, David Chuss, Joseph Cleary, Sumit Dahal, Rahul Datta, Jullianna Denes Couto, Kevin Denis, Rolando Dunner, Thomas Essinger-Hileman, Kathleen Harrington, Kyle Helson, Johannes Hubmayr, Jeffrey Iuliano, John Karakla, Tobias Marriage, Nathan Miller, Carolina Morales Perez, Lucas Parker, Matthew Petroff, Rodrigo Reeves, Karwan Rostem, Caleigh Ryan, Rui Shi, Koji Shukawa, Deniz Valle, Duncan Watts, J. Weiland, Edward Wollack, Zhilei Xu, Lingzhen Zeng
We present measurements of large-scale cosmic microwave background (CMB) E-mode polarization from the Cosmology Large Angular Scale Surveyor (CLASS) 90 GHz data. Using 115 det-yr of observations collected through 2024 with a variable-delay polarization modulator, we achieved a polarization sensitivity of 78μKarcmin, comparable to Planck at similar frequencies (100 and 143 GHz). The analysis demonstrates effective mitigation of systematic errors and addresses challenges to large-angular-scale power recovery posed by time-domain filtering in maximum-likelihood map-making. A novel implementation of the pixel-space transfer matrix is introduced, which enables efficient filtering simulations and bias correction in the power spectrum using the quadratic cross-spectrum estimator. Overall, we achieved an unbiased time-domain filtering correction to recover the largest angular scale polarization, with the only power deficit, arising from map-making non-linearity, being characterized as less than 3%. Through cross-correlation with Planck, we detected the cosmic reionization at 99.4% significance and measured the reionization optical depth τ=0.053+0.018−0.019, marking the first ground-based attempt at such a measurement. At intermediate angular scales (ℓ>30), our results, both independently and in cross-correlation with Planck, remain fully consistent with Planck’s measurements.

Sensitivity-Improved Polarization Maps at 40 GHz with CLASS and WMAP data
Rui Shi, John W. Appel, Charles L. Bennett, Ricardo Bustos, David T. Chuss, Sumit Dahal, Jullianna Denes Couto, Joseph R. Eimer, Thomas Essinger-Hileman, Kathleen Harrington, Jeffrey Iuliano, Yunyang Li, Tobias A. Marriage, Matthew A. Petroff, Karwan Rostem, Zeya Song, Deniz A. N. Valle, Duncan J. Watts, Janet L. Weiland, Edward J. Wollack, Zhilei Xu
Improved polarization measurements at frequencies below 70 GHz with degree-level angular resolution are crucial for advancing our understanding of the Galactic synchrotron radiation and the potential polarized anomalous microwave emission and ultimately benefiting the detection of primordial B modes. In this study, we present sensitivity-improved 40 GHz polarization maps obtained by combining the CLASS 40 GHz and WMAP Q-band data through a weighted average in the harmonic domain. The decision to include WMAP Q-band data stems from similarities in the bandpasses. Leveraging the accurate large-scale measurements from WMAP Q band and the high-sensitivity information from CLASS 40 GHz band at intermediate scales, the noise level at ℓ∈[30,100] is reduced by a factor of 2−3 in the map space. A pixel domain analysis of the polarized synchrotron spectral index (βs) using WMAP K band and the combined maps (mean and 16/84th percentile across the βs map: −3.08+0.20−0.20) reveals a stronger preference for spatial variation (PTE for a uniform βs hypothesis smaller than 0.001) than the results obtained using WMAP K and Ka bands (−3.08+0.14−0.14). The cross-power spectra of the combined maps follow the same trend as other low-frequency data, and validation through simulations indicates negligible bias introduced by the combination method (sub-percent level in the power spectra). The products of this work are publicly available on 𝙻𝙰𝙼𝙱𝙳𝙰.

CLASS Angular Power Spectra and Map-Component Analysis for 40 GHz Observations through 2022
Joseph R. Eimer, Yunyang Li, Michael K. Brewer, Rui Shi, Aamir Ali, John W. Appel, Charles L. Bennett, Ricardo Bustos, David T. Chuss, Joseph Cleary, Sumit Dahal, Rahul Datta, Jullianna Denes Couto, Kevin L. Denis, Rolando Dünner, Thomas Essinger-Hileman, Pedro Fluxá, Johannes Hubmayer, Kathleen Harrington, Jeffrey Iuliano, John Karakla, Tobias A. Marriage, Carolina Núñez, Lucas Parker, Matthew A. Petroff, Rodrigo A. Reeves, Karwan Rostem, Deniz A. N. Valle, Duncan J. Watts, Janet L. Weiland, Edward J. Wollack, Zhilei Xu, Lingzhen Zeng
Measurement of the largest angular scale (ℓ<30) features of the cosmic microwave background (CMB) polarization is a powerful way to constrain the optical depth to reionization, τ, and search for the signature of inflation through the detection of primordial B-modes. We present an analysis of maps covering nearly 75% of the sky made from the ground-based 40GHz channel of the Cosmology Large Angular Scale Surveyor (CLASS) from August 2016 to May 2022. Using fast front-end polarization modulation from the Atacama Desert in Chile, we show this channel achieves higher sensitivity than the analogous frequencies from satellite measurements in the range 10<ℓ<100. After a final calibration adjustment, noise simulations show the CLASS linear (circular) polarization maps have a white noise level of 125(130)μKarcmin. We measure the Galaxy-masked EE and BB spectra of diffuse synchrotron radiation and compare to space-based measurements at similar frequencies. In combination with external data, we expand measurements of the spatial variations of the synchrotron spectral energy density (SED) to include new regions of the sky and measure the faint diffuse SED in the harmonic domain. We place a new upper limit on a background of circular polarization in the range 5<ℓ<125 with the first bin showing Dℓ<0.023 μK2CMB at 95% confidence. These results establish a new standard for recovery of the largest-scale CMB polarization from the ground and signal exciting possibilities when the higher sensitivity and higher frequency CLASS channels are included in the analysis.

CLASS Observations of Atmospheric Cloud Polarization at Millimeter Wavelengths
Yunyang Li, John W. Appel, Charles L. Bennett, Ricardo Bustos, David T. Chuss, Joseph Cleary, Jullianna Denes Couto, Sumit Dahal, Rahul Datta, Rolando Dünner, Joseph R. Eimer, Thomas Essinger-Hileman, Kathleen Harrington, Jeffrey Iuliano, Tobias A. Marriage, Matthew A. Petroff, Rodrigo A. Reeves, Karwan Rostem, Rui Shi, Deniz A. N. Valle, Duncan J. Watts, Oliver F. Wolff, Edward J. Wollack, Zhilei Xu
The dynamic atmosphere imposes challenges to ground-based cosmic microwave background observation, especially for measurements on large angular scales. The hydrometeors in the atmosphere, mostly in the form of clouds, scatter the ambient thermal radiation and are known to be the main linearly polarized source in the atmosphere. This scattering-induced polarization is significantly enhanced for ice clouds due to the alignment of ice crystals under gravity, which are also the most common clouds seen at the millimeter-astronomy sites at high altitudes. This work presents a multifrequency study of cloud polarization observed by the Cosmology Large Angular Scale Surveyor (CLASS) experiment on Cerro Toco in the Atacama Desert of northern Chile, from 2016 to 2022, at the frequency bands centered around 40, 90, 150, and 220 GHz. Using a machine-learning-assisted cloud classifier, we made connections between the transient polarized emission found in all four frequencies with the clouds imaged by monitoring cameras at the observing site. The polarization angles of the cloud events are found to be mostly 90∘ from the local meridian, which is consistent with the presence of horizontally aligned ice crystals. The 90 and 150 GHz polarization data are consistent with a power law with a spectral index of 3.90±0.06, while an excess/deficit of polarization amplitude is found at 40/220 GHz compared with a Rayleigh scattering spectrum. These results are consistent with Rayleigh-scattering-dominated cloud polarization, with possible effects from supercooled water absorption and/or Mie scattering from a population of large cloud particles that contribute to the 220 GHz polarization.

CLASS Data Pipeline and Maps for 40 GHz Observations through 2022
Yunyang Li, Joseph Eimer, Keisuke Osumi, John Appel, Michael Brewer, Aamir Ali, Charles Bennett, Sarah Marie Bruno, Ricardo Bustos, David Chuss, Joseph Cleary, Jullianna Couto, Sumit Dahal, Rahul Datta, Kevin Denis, Rolando Dunner, Francisco Raul Espinoza Inostroza, Thomas Essinger-Hileman, Pedro Fluxa, Kathleen Harrington, Jeffrey Iuliano, John Karakla, Tobias Marriage, Nathan Miller, Sasha Novack, Carolina Núñez, Matthew Petroff, Rodrigo Reeves, Karwan Rostem, Rui Shi, Deniz Valle, Duncan Watts, J. Weiland, Edward Wollack, Zhilei Xu, Lingzhen Zeng
The Cosmology Large Angular Scale Surveyor (CLASS) is a telescope array that observes the cosmic microwave background over 75\% of the sky from the Atacama Desert, Chile, at frequency bands centered near 40, 90, 150, and 220 GHz. This paper describes the CLASS data pipeline and maps for 40~GHz observations conducted from August 2016 to May 2022. We demonstrate how well the CLASS survey strategy, with rapid (10Hz) front-end modulation, recovers the large-scale Galactic polarization signal from the ground: the mapping transfer function recovers 75\% of EE, BB, and VV power at ℓ=20 and 45\% at ℓ=10. We present linear and circular polarization maps over 75\% of the sky. Simulations based on the data imply the maps have a white noise level of 110μKarcmin and correlated noise component rising at low-ℓ as ℓ−2.2. The transfer-function-corrected low-ℓ component is comparable to the white noise at the angular knee frequencies of ℓ≈16 (linear polarization) and ℓ≈12 (circular polarization). Finally, we present simulations of the level at which expected sources of systematic error bias the measurements, finding sub-percent bias for the ΛCDM EE power spectra. Bias from E-to-B leakage due to the data reduction pipeline and polarization angle uncertainty approaches the expected level for an r=0.01 BB power spectrum. Improvements to the instrument calibration and the data pipeline will decrease this bias.

Microwave Observations of Venus with CLASS
Sumit Dahal, Michael K. Brewer, Alex B. Akins, John W. Appel, Charles L. Bennett, Ricardo Bustos, Joseph Cleary, Jullianna D. Couto, Thomas Essinger-Hileman, Jeffrey Iuliano, Yunyang Li, Tobias A. Marriage, Carolina Núñez, Matthew A. Petroff, Rodrigo Reeves, Karwan Rostem, Rui Shi, Deniz A. N. Valle, Duncan J. Watts, Edward J. Wollack, Zhilei Xu
We report on the disk-averaged absolute brightness temperatures of Venus measured at four microwave frequency bands with the Cosmology Large Angular Scale Surveyor (CLASS). We measure temperatures of 432.3 ± 2.8 K, 355.6 ± 1.3 K, 317.9 ± 1.7 K, and 294.7 ± 1.9 K for frequency bands centered at 38.8, 93.7, 147.9, and 217.5 GHz, respectively. We do not observe any dependence of the measured brightness temperatures on solar illumination for all four frequency bands. A joint analysis of our measurements with lower frequency Very Large Array (VLA) observations suggests relatively warmer (∼ 7 K higher) mean atmospheric temperatures and lower abundances of microwave continuum absorbers than those inferred from prior radio occultation measurements.

Venus Observations at 40 and 90 GHz with CLASS
Sumit Dahal, Michael K. Brewer, John W. Appel, Aamir Ali, Charles L. Bennett, Ricardo Bustos, Manwei Chan, David T. Chuss, Joseph Cleary, Jullianna D. Couto, Rahul Datta, Kevin L. Denis, Joseph Eimer, Francisco Espinoza, Thomas Essinger-Hileman, Dominik Gothe, Kathleen Harrington, Jeffrey Iuliano, John Karakla, Tobias A. Marriage, Sasha Novack, Carolina Núñez, Ivan L. Padilla, Lucas Parker, Matthew A. Petroff, Rodrigo Reeves, Gary Rhoades, Karwan Rostem, Deniz A. N. Valle, Duncan J. Watts, Janet L. Weiland, Edward J. Wollack, Zhilei Xu
Using the Cosmology Large Angular Scale Surveyor (CLASS), we measure the disk-averaged absolute Venus brightness temperature to be 432.3 ± 2.8 K and 355.6 ± 1.3 K in the Q and W frequency bands centered at 38.8 and 93.7 GHz, respectively. At both frequency bands, these are the most precise measurements to date. Furthermore, we observe no phase dependence of the measured temperature in either band. Our measurements are consistent with a CO₂-dominant atmospheric model that includes trace amounts of additional absorbers like SO₂ and H₂SO₄.

Two-year Cosmology Large Angular Scale Surveyor (CLASS) Observations: A First Detection of Atmospheric Circular Polarization at Q Band
Matthew A. Petroff, Joseph R. Eimer, Kathleen Harrington, Aamir Ali, John W. Appel, Charles L. Bennett, Michael K. Brewer, Ricardo Bustos, Manwei Chan, David T. Chuss, Joseph Cleary, Jullianna Denes Couto, Sumit Dahal, Rolando Dünner, Thomas Essinger-Hileman, Pedro Fluxá Rojas, Jeffrey Iuliano, Tobias A. Marriage, Nathan J. Miller, Carolina Núñez, Ivan L. Padilla, Lucas Parker, Rodrigo Reeves, Karwan Rostem, Deniz Augusto Nunes Valle, Duncan J. Watts, Janet L. Weiland, Edward J. Wollack, Zhilei Xu
The Earth’s magnetic field induces Zeeman splitting of the magnetic dipole transitions of molecular oxygen in the atmosphere, which produces polarized emission in the millimeter-wave regime. This polarized emission is primarily circularly polarized and manifests as a foreground with a dipole-shaped sky pattern for polarization-sensitive ground-based cosmic microwave background (CMB) experiments, such as the Cosmology Large Angular Scale Surveyor (CLASS), which is uniquely capable of measuring large angular scale circular polarization. Using atmospheric emission theory and radiative transfer formalisms, we model the expected amplitude and spatial distribution of this signal and evaluate the model for the CLASS observing site in the Atacama Desert of northern Chile. Then, using two years of observations near 40 GHz from the CLASS Q-band telescope, we present a detection of this signal and compare the observed signal to that predicted by the model. We recover an angle between magnetic north and true north of (−5.5±0.6)∘, which is consistent with the expectation of −5.9∘ for the CLASS observing site. When comparing dipole sky patterns fit to both simulated and data-derived sky maps, the dipole directions match to within a degree, and the measured amplitudes match to within ∼20%.

Two-year Cosmology Large Angular Scale Surveyor (CLASS) Observations: A Measurement of Circular Polarization at 40 GHz
Ivan L. Padilla, Joseph R. Eimer, Yunyang Li, Graeme E. Addison, Aamir Ali, John W. Appel, Charles L. Bennett, Ricardo Bustos, Michael K. Brewer, Manwei Chan, David T. Chuss, Joseph Cleary, Jullianna Couto, Sumit Dahal, Kevin Denis, Rolando Dünner, Thomas Essinger-Hileman, Pedro Fluxá, Saianeesh K. Haridas, Kathleen Harrington, Jeffrey Iuliano, John Karakla, Tobias A. Marriage, Nathan J. Miller, Carolina Núñez, Lucas Parker, Matthew A. Petroff, Rodrigo Reeves, Karwan Rostem, Robert W. Stevens, Deniz Augusto Nunes Valle, Duncan J. Watts, Janet L. Weiland, Edward J. Wollack, Zhilei Xu
We report circular polarization measurements from the first two years of observation with the 40 GHz polarimeter of the Cosmology Large Angular Scale Surveyor (CLASS). CLASS is conducting a multi-frequency survey covering 75% of the sky from the Atacama Desert designed to measure the cosmic microwave background (CMB) linear E and B polarization on angular scales 1∘≲θ≤90∘, corresponding to a multipole range of 2≤ℓ≲200. The modulation technology enabling measurements of linear polarization at the largest angular scales from the ground, the Variable-delay Polarization Modulator, is uniquely designed to provide explicit sensitivity to circular polarization (Stokes V). We present a first detection of circularly polarized atmospheric emission at 40 GHz that is well described by a dipole with an amplitude of 124±4μK when observed at an elevation of 45∘, and discuss its potential impact as a foreground to CMB experiments. Filtering the atmospheric component, CLASS places a 95% C.L. upper limit of 0.4μK2 to 13.5μK2 on ℓ(ℓ+1)CVVℓ/(2π) between 1≤ℓ≤120, representing a two-orders-of-magnitude improvement over previous limits.