A novel CMB polarization likelihood package for large angular scales built from combined WMAP and Planck LFI legacy maps

Abstract

We present a cosmic microwave background (CMB) large-scale polarization dataset obtained by combining Wilkinson Microwave Anisotropy Probe (WMAP) in the K, Q, and V bands with the Planck 70 GHz maps. We employed the legacy frequency maps released by the WMAP and Planck collaborations and performed our own Galactic foreground mitigation technique, relying on Planck 353 GHz for polarized dust and on Planck 30 GHz and WMAP K for polarized synchrotron. We derived a single, optimally noise-weighted, low residual foreground map and the accompanying noise covariance matrix. These are shown through χ2 analysis to be robust over an ample collection of Galactic masks. We used this dataset, along with the Planck legacy Commander temperature solution, to build a pixel-based low-resolution CMB likelihood package, whose robustness we tested extensively with the aid of simulations, finding an excellent level of consistency. Using this likelihood package alone, we are able to constrain the optical depth to reionization, τ = 0.069−0.012+0.011 at 68% confidence level, on 54% of the sky. Adding the Planck high-ℓ temperature and polarization legacy likelihood, the Planck lensing likelihood, and BAO observations, we find τ = 0.0714−0.0096+0.0087 in a full ΛCDM exploration. The latter bounds are slightly less constraining than those obtained by employing the Planck High Frequency Instrument’s (HFI) CMB data for large-angle polarization, which only include EE correlations. Our bounds are based on a largely independent dataset that includes TE correlations. They are generally compatible with Planck HFI, but lean towards slightly higher values for τ. We have made the low-resolution Planck and WMAP joint dataset publicly available, along with the accompanying likelihood code.

BeyondPlanck XII. Cosmological parameter constraints with end-to-end error propagation

“…In the left panel of Fig. 4 we show the marginal posterior distribution for τ as derived from the low-BeyondPlanck likelihood alone (black curve), and compare this with corresponding previous estimates from the literature (Hinshaw et al 2013;Planck Collaboration VI 2020;Natale et al 2020;Pagano et al 2020). We note, however, that making head-to-head comparisons between all of these is non-trivial, as the reported parameters depend on different assumptions and data combinations.…”

“…From top to bottom, the three panels show 1) posterior τ estimate; 2) posterior r estimate, expressed in terms of a detection level with respect to a signal with vanishing B-modes in units of σ; and 3) χ 2 PTE evaluated for the best-fit power spectrum in each case. only low-polarization and marginalizes over only a small set of strongly correlated parameters, i.e., A s and/or r. Taking into account the fact that Natale et al (2020) analyzes the official LFI and WMAP products jointly, we choose to tune our analysis configuration to them, to facilitate a head-to-head comparison for the most relevant case. Corresponding numerical values are summarized in Table 3.…”

“…For comparison, the actual Natale et al (2020) uncertainty is 0.011, or about 30 % smaller. We interpret our larger uncertainty as being due to marginalizing over a more complete set of statistical uncertainties in the BeyondPlanck analysis framework than is possible with the frequentist-style and official LFI and WMAP data products.…”

Measurements of the E -mode polarization and temperature- E -mode correlation of the CMB from SPT-3G 2018 data

“…For the range of angular multipoles considered here, τ is degenerate with A s ; we therefore use large-scale polarization information from Planck [26] to inform a Gaussian prior of τ ¼ 0.0543AE 0.0073, and we report constraints on the combined amplitude parameter 10 9 A s e −2τ in this work. Widening the prior to [61] has no significant effect on cosmological parameter constraints. We account for aberration in a manner similar to Ref.…”

High $H_0$ Values from CMB E-mode Data: A Clue for Resolving the Hubble Tension?

“…In recent years, a number of other studies have constrained τ using different combinations of Planck and WMAP data, including alternative processing and mapmaking for the Planck polarization (e.g., Weiland et al 2018;Planck Collaboration Int. LVII 2020;BeyondPlanck Collaboration I 2020;Natale et al 2020). These analyses give a spread in mean values of τ from 0.05 to 0.07, and 1σ uncertainties from 0.006 to 0.2.…”