Spatial variations in the spectral index of polarized synchrotron emission in the 9 yr WMAP sky maps

We estimate the spectral index, beta, of polarized synchrotron emission as observed in the 9 yr WMAP sky maps using two methods, linear regression ("T-T plot") and maximum likelihood. We partition the sky into 24 disjoint sky regions, and evaluate the spectral index for all polarization angles between 0 deg and 85 deg in steps of 5. Averaging over polarization angles, we derive a mean spectral index of beta_all-sky=-2.99+-0.01 in the frequency range of 23-33 GHz. We find that the synchrotron spectral index steepens by 0.14 from low to high Galactic latitudes, in agreement with previous studies, with mean spectral indices of beta_plane=-2.98+-0.01 and beta_high-lat=-3.12+-0.04. In addition, we find a significant longitudinal variation along the Galactic plane with a steeper spectral index toward the Galactic center and anticenter than toward the Galactic spiral arms. This can be well modeled by an offset sinusoidal, beta(l)=-2.85+0.17sin(2l-90). Finally, we study synchrotron emission in the BICEP2 field, in an attempt to understand whether the claimed detection of large-scale B-mode polarization could be explained in terms of synchrotron contamination. Adopting a spectral index of beta=-3.12, typical for high Galactic latitudes, we find that the most likely bias corresponds to about 2% of the reported signal (r=0.003). The flattest index allowed by the data in this region is beta=-2.5, and under the assumption of a straight power-law frequency spectrum, we find that synchrotron emission can account for at most 20% of the reported BICEP2 signal.Comment: 11 pages, 9 figures, updated to match version published in Ap

The effect of systematics on polarized spectral indices

We study four particularly bright polarized compact objects (Tau A, Virgo A, 3C273 and Fornax A) in the 7-year WMAP sky maps, with the goal of understanding potential systematics involved in estimation of foreground spectral indices. We estimate the spectral index, the polarization angle, the polarization fraction and apparent size and shape of these objects when smoothed to a nominal resolution of 1 degree FWHM. Second, we compute the spectral index as a function of polarization orientation, alpha. Because these objects are approximately point sources with constant polarization angle, this function should be constant in the absence of systematics. However, computing it for the K- and Ka-band WMAP data we find strong index variations for all four sources. For Tau A, we find a spectral index beta=-2.59+-0.03 for alpha=30 degrees, and beta=-2.03+-0.01 for alpha=50 degrees. On the other hand, the spectral index between Ka and Q band is found to be stable. A simple elliptical Gaussian toy model with parameters matching those observed in Tau A reproduces the observed signal, and shows that the spectral index is in particular sensitive to the detector polarization angle. Based on these findings, we first conclude that estimation of spectral indices with the WMAP K-band polarization data at 1 degree scales is not robust. Second, we note that these issues may be of concern for ground-based and sub-orbital experiments that use the WMAP polarization measurements of Tau A for calibration of gain and polarization angles.Comment: 5 pages, 6 figures, submitted to ApJ; new figure and expanded conclusio

Constraints on the spectral index of polarized synchrotron emission from WMAP and Faraday-corrected S-PASS data

We constrain the spectral index of polarized synchrotron emission, $\beta_s$, by correlating the recently released 2.3 GHz S-Band Polarization All Sky Survey (S-PASS) data with the 23 GHz 9-year Wilkinson Microwave Anisotropy Probe (WMAP) sky maps. We sub-divide the S-PASS field, which covers the Southern Ecliptic hemisphere, into $15^{\circ}\times 15^{\circ}$ regions, and estimate the spectral index of polarized synchrotron emission within each region using a simple but robust T-T plot technique. Three different versions of the S-PASS data are considered, corresponding to either no correction for Faraday rotation; Faraday correction based on the rotation measure model presented by the S-PASS team; or Faraday correction based on a rotation measure model presented by Hutschenreuter and En{\ss}lin. We find that the correlation between S-PASS and WMAP is strongest when applying the S-PASS model. Adopting this correction model, we find that the mean spectral index of polarized synchrotron emission gradually steepens from $\beta_s\approx-2.8$ at low Galactic latitudes to $\beta_s\approx-3.2$ at high Galactic latitudes, in good agreement with previously published results. Finally, we consider two special cases defined by the BICEP2 and SPIDER fields, and obtain mean estimates of $\beta_{BICEP2}=-3.22\pm0.06$ and $\beta_{SPIDER}=-3.21\pm0.03$, respectively. Adopting the WMAP 23 GHz sky map bandpass filtered to including angular scales only between $2^{\circ}$ and $10^{\circ}$ as a spatial template, we constrain the root-mean-square synchrotron polarization amplitude to be less than $0.03\mu K$ ($0.009\mu K$) at 90 GHz (150 GHz) for the BICEP2 field, corresponding roughly to a tensor-to-scalar ratio of $r\lesssim0.02$ ($r\lesssim0.005$), respectively. Very similar constraints are obtained for the SPIDER field.Comment: 14 pages, 13 Figures, to be submitted to A&

A Monte Carlo comparison between template-based and Wiener-filter CMB dipole estimators

We review and compare two different CMB dipole estimators discussed in the literature, and assess their performances through Monte Carlo simulations. The first method amounts to simple template regression with partial sky data, while the second method is an optimal Wiener filter (or Gibbs sampling) implementation. The main difference between the two methods is that the latter approach takes into account correlations with higher-order CMB temperature fluctuations that arise from non-orthogonal spherical harmonics on an incomplete sky, which for recent CMB data sets (such as Planck) is the dominant source of uncertainty. For an accepted sky fraction of 81% and an angular CMB power spectrum corresponding to the best-fit Planck 2018 $\Lambda$CDM model, we find that the uncertainty on the recovered dipole amplitude is about six times smaller for the Wiener filter approach than for the template approach, corresponding to 0.5 and 3$~\mu$K, respectively. Similar relative differences are found for the corresponding directional parameters and other sky fractions. We note that the Wiener filter algorithm is generally applicable to any dipole estimation problem on an incomplete sky, as long as a statistical and computationally tractable model is available for the unmasked higher-order fluctuations. The methodology described in this paper forms the numerical basis for the most recent determination of the CMB solar dipole from Planck, as summarized by arXiv:2007.04997.Comment: 8 pages, 10 figures, submitted to A&

B-mode polarization forecasts for GreenPol

We present tensor-to-scalar ratio forecasts for GreenPol, a hypothetical ground-based B-mode experiment aiming to survey the cleanest regions of the Northern Galactic hemisphere at five frequencies between 10 and 44 GHz. Its primary science goal would be to measure large-scale CMB polarization fluctuations at multipoles $\ell \lesssim 500$, and thereby constrain the primordial tensor-to-scalar ratio. The observations for the suggested experiment would take place at the Summit Station (72deg N, 38deg W) on Greenland, at an altitude of 3216 meters above sea level. In this paper we simulate various experimental setups, and derive limits on the tensor-to-scalar ratio after CMB component separation using a Bayesian component separation implementation called Commander. When combining the proposed experiment with Planck HFI observations for constraining polarized thermal dust emission, we find a projected limit of r<0.02 at 95 % confidence for the baseline configuration. This limit is very robust with respect to a range of important experimental parameters, including sky coverage, detector weighting, foreground priors etc. Overall, GreenPol would have the possibility to provide deep CMB polarization measurements of the Northern Galactic hemisphere at low frequencies.Comment: 10 pages, 8 figures. To be submitted to A&

Tensor-to-scalar ratio forecasts for extended LiteBIRD frequency configurations

LiteBIRD is a planned JAXA-led cosmic microwave background (CMB) B-mode satellite experiment aiming for launch in the late 2020s, with a primary goal of detecting the imprint of primordial inflationary gravitational waves. Its current baseline focal-plane configuration includes 15 frequency bands between 40 and 402 GHz, fulfilling the mission requirements to detect the amplitude of gravitational waves with the total uncertainty on the tensor-to-scalar ratio, δr, down to δr < 0.001. A key aspect of this performance is accurate astrophysical component separation, and the ability to remove polarized thermal dust emission is particularly important. In this paper we note that the CMB frequency spectrum falls off nearly exponentially above 300 GHz relative to the thermal dust spectral energy distribution, and a relatively minor high frequency extension can therefore result in even lower uncertainties and better model reconstructions. Specifically, we compared the baseline design with five extended configurations, while varying the underlying dust modeling, in each of which the High-Frequency Telescope (HFT) frequency range was shifted logarithmically toward higher frequencies, with an upper cutoff ranging between 400 and 600 GHz. In each case, we measured the tensor-to-scalar ratio r uncertainty and bias using both parametric and minimum-variance component-separation algorithms. When the thermal dust sky model includes a spatially varying spectral index and temperature, we find that the statistical uncertainty on r after foreground cleaning may be reduced by as much as 30–50% by extending the upper limit of the frequency range from 400 to 600 GHz, with most of the improvement already gained at 500 GHz. We also note that a broader frequency range leads to higher residuals when fitting an incorrect dust model, but also it is easier to discriminate between models through higher χ² sensitivity. Even in the case in which the fitting procedure does not correspond to the underlying dust model in the sky, and when the highest frequency data cannot be modeled with sufficient fidelity and must be excluded from the analysis, the uncertainty on r increases by only about 5% for a 500 GHz configuration compared to the baseline.This work is supported in Japan by ISAS/JAXA for Pre-Phase A2 studies, by the acceleration program of JAXA research and development directorate, by the World Premier International Research Center Initiative (WPI) of MEXT, by the JSPS Core-to-Core Program of A. Advanced Research Networks, and by JSPS KAKENHI Grant Numbers JP15H05891, JP17H01115, and JP17H01125. The Canadian contribution is supported by the Canadian Space Agency. The French LiteBIRD phase A contribution is supported by the Centre National d’Études Spatiales (CNES), by the Centre National de la Recherche Scientifique (CNRS), and by the Commissariat à l’Énergie Atomique (CEA). The German participation in LiteBIRD is supported in part by the Excellence Cluster ORIGINS, which is funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy (Grant No. EXC-2094 – 390783311). The Italian LiteBIRD phase A contribution is supported by the Italian Space Agency (ASI Grants No. 2020-9-HH.0 and 2016-24-H.1-2018), the National Institute for Nuclear Physics (INFN) and the National Institute for Astrophysics (INAF). Norwegian participation in LiteBIRD is supported by the Research Council of Norway (Grant No. 263011) and has received funding from the European Research Council (ERC) under the Horizon 2020 Research and Innovation Programme (Grant agreement No. 772253 and 819478). The Spanish LiteBIRD phase A contribution is supported by the Spanish Agencia Estatal de Investigación (AEI), project refs. PID2019-110610RB-C21, PID2020-120514GB-I00, ProID2020010108 and ICTP20210008. Funds that support contributions from Sweden come from the Swedish National Space Agency (SNSA/Rymdstyrelsen) and the Swedish Research Council (Reg. no. 2019-03959). The US contribution is supported by NASA grant no. 80NSSC18K0132. We also acknowledge funding from the European Research Council (ERC) under the Horizon 2020 Research and Innovation Programme (Grant agreement No. 725456 and 849169) and The Royal Society (Grant No. URF/R/191023)

Cosmoglobe DR1. III. First full-sky model of polarized synchrotron emission from all WMAP and Planck LFI data

We present the first model of full-sky polarized synchrotron emission that is derived from all WMAP and Planck LFI frequency maps. The basis of this analysis is the set of end-to-end reprocessed Cosmoglobe Data Release 1 sky maps presented in a companion paper, which have significantly lower instrumental systematics than the legacy products from each experiment. We find that the resulting polarized synchrotron amplitude map has an average noise rms of $3.2\,\mathrm{\mu K}$ at 30 GHz and $2^{\circ}$ FWHM, which is 30% lower than the recently released BeyondPlanck model that included only LFI+WMAP Ka-V data, and 29% lower than the WMAP K-band map alone. The mean $B$-to-$E$ power spectrum ratio is $0.40\pm0.02$, with amplitudes consistent with those measured previously by Planck and QUIJOTE. Assuming a power law model for the synchrotron spectral energy distribution, and using the $T$--$T$ plot method, we find a full-sky inverse noise-variance weighted mean of $\beta_{\mathrm{s}}=-3.07\pm0.07$ between Cosmoglobe DR1 K-band and 30 GHz, in good agreement with previous estimates. In summary, the novel Cosmoglobe DR1 synchrotron model is both more sensitive and systematically cleaner than similar previous models, and it has a more complete error description that is defined by a set of Monte Carlo posterior samples. We believe that these products are preferable over previous Planck and WMAP products for all synchrotron-related scientific applications, including simulation, forecasting and component separation.Comment: 15 pages, 15 figures, submitted to A&

Cosmoglobe: Towards end-to-end CMB cosmological parameter estimation without likelihood approximations

We implement support for a cosmological parameter estimation algorithm as proposed by Racine et al. (2016) in Commander, and quantify its computational efficiency and cost. For a semi-realistic simulation similar to Planck LFI 70 GHz, we find that the computational cost of producing one single sample is about 60 CPU-hours and that the typical Markov chain correlation length is $\sim$100 samples. The net effective cost per independent sample is $\sim$6 000 CPU-hours, in comparison with all low-level processing costs of 812 CPU-hours for Planck LFI and WMAP in Cosmoglobe Data Release 1. Thus, although technically possible to run already in its current state, future work should aim to reduce the effective cost per independent sample by at least one order of magnitude to avoid excessive runtimes, for instance through multi-grid preconditioners and/or derivative-based Markov chain sampling schemes. This work demonstrates the computational feasibility of true Bayesian cosmological parameter estimation with end-to-end error propagation for high-precision CMB experiments without likelihood approximations, but it also highlights the need for additional optimizations before it is ready for full production-level analysis.Comment: 10 pages, 8 figures. Submitted to A&

Cosmoglobe DR1 results. II. Constraints on isotropic cosmic birefringence from reprocessed WMAP and Planck LFI data

Cosmic birefringence is a parity-violating effect that might have rotated the plane of linearly polarized light of the cosmic microwave background (CMB) by an angle $\beta$ since its emission. This has recently been measured to be non-zero at a statistical significance of $3.6\sigma$ in the official Planck PR4 and 9-year WMAP data. In this work, we constrain $\beta$ using the reprocessed BeyondPlanck LFI and Cosmoglobe DR1 WMAP polarization maps. These novel maps have both lower systematic residuals and a more complete error description than the corresponding official products. Foreground $EB$ correlations could bias measurements of $\beta$, and while thermal dust $EB$ emission has been argued to be statistically non-zero, no evidence for synchrotron $EB$ power has been reported. Unlike the dust-dominated Planck HFI maps, the majority of the LFI and WMAP polarization maps are instead dominated by synchrotron emission. Simultaneously constraining $\beta$ and the polarization miscalibration angle, $\alpha$, of each channel, we find a best-fit value of $\beta=0.35^{\circ}\pm0.70^{\circ}$ with LFI and WMAP data only. When including the Planck HFI PR4 maps, but fitting $\beta$ separately for dust-dominated, $\beta_{>70\,\mathrm{GHz}}$, and synchrotron-dominated channels, $\beta_{\leq 70\,\mathrm{GHz}}$, we find $\beta_{\leq 70\,\mathrm{GHz}}=0.53^{\circ}\pm0.28^\circ$. This differs from zero with a statistical significance of $1.9\sigma$, and the main contribution to this value comes from the LFI 70 GHz channel. While the statistical significances of these results are low on their own, the measurement derived from the LFI and WMAP synchrotron-dominated maps agrees with the previously reported HFI-dominated constraints, despite the very different astrophysical and instrumental systematics involved in all these experiments.Comment: 10 pages, 7 figures, 2 tables. Submitted to A&

Cosmoglobe DR1 results. I. Improved Wilkinson Microwave Anisotropy Probe maps through Bayesian end-to-end analysis

We present Cosmoglobe Data Release 1, which implements the first joint analysis of WMAP and Planck LFI time-ordered data, processed within a single Bayesian end-to-end framework. This framework builds directly on a similar analysis of the LFI measurements by the BeyondPlanck collaboration, and approaches the CMB analysis challenge through Gibbs sampling of a global posterior distribution, simultaneously accounting for calibration, mapmaking, and component separation. The computational cost of producing one complete WMAP+LFI Gibbs sample is 812 CPU-hr, of which 603 CPU-hrs are spent on WMAP low-level processing; this demonstrates that end-to-end Bayesian analysis of the WMAP data is computationally feasible. We find that our WMAP posterior mean temperature sky maps and CMB temperature power spectrum are largely consistent with the official WMAP9 results. Perhaps the most notable difference is that our CMB dipole amplitude is $3366.2 \pm 1.4\ \mathrm{\mu K}$, which is $11\ \mathrm{\mu K}$higher than the WMAP9 estimate and$2.5\ {\sigma}$ higher than BeyondPlanck; however, it is in perfect agreement with the HFI-dominated Planck PR4 result. In contrast, our WMAP polarization maps differ more notably from the WMAP9 results, and in general exhibit significantly lower large-scale residuals. We attribute this to a better constrained gain and transmission imbalance model. It is particularly noteworthy that the W-band polarization sky map, which was excluded from the official WMAP cosmological analysis, for the first time appears visually consistent with the V-band sky map. Similarly, the long standing discrepancy between the WMAP K-band and LFI 30 GHz maps is finally resolved, and the difference between the two maps appears consistent with instrumental noise at high Galactic latitudes. All maps and the associated code are made publicly available through the Cosmoglobe web page.Comment: 65 pages, 61 figures. Data available at cosmoglobe.uio.no. Submitted to A&