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  • 1
    In: Astronomy & Astrophysics, EDP Sciences, Vol. 675 ( 2023-07), p. A12-
    Abstract: We present cosmological parameter constraints estimated using the Bayesian B EYOND P LANCK analysis framework. This method supports seamless end-to-end error propagation from raw time-ordered data onto final cosmological parameters. As a first demonstration of the method, we analyzed time-ordered Planck LFI observations, combined with selected external data (WMAP 33–61 GHz, Planck HFI DR4 353 and 857 GHz, and Haslam 408 MHz) in the form of pixelized maps that are used to break critical astrophysical degeneracies. Overall, all the results are generally in good agreement with previously reported values from Planck 2018 and WMAP, with the largest relative difference for any parameter amounting about 1 σ when considering only temperature multipoles between 30 ≤  ℓ  ≤ 600. In cases where there are differences, we note that the B EYOND P LANCK results are generally slightly closer to the high- ℓ HFI-dominated Planck 2018 results than previous analyses, suggesting slightly less tension between low and high multipoles. Using low- ℓ polarization information from LFI and WMAP, we find a best-fit value of τ  = 0.066 ± 0.013, which is higher than the low value of τ  = 0.052 ± 0.008 derived from Planck 2018 and slightly lower than the value of 0.069 ± 0.011 derived from the joint analysis of official LFI and WMAP products. Most importantly, however, we find that the uncertainty derived in the B EYOND P LANCK processing is about 30 % greater than when analyzing the official products, after taking into account the different sky coverage. We argue that this uncertainty is due to a marginalization over a more complete model of instrumental and astrophysical parameters, which results in more reliable and more rigorously defined uncertainties. We find that about 2000 Monte Carlo samples are required to achieve a robust convergence for a low-resolution cosmic microwave background (CMB) covariance matrix with 225 independent modes, and producing these samples takes about eight weeks on a modest computing cluster with 256 cores.
    Type of Medium: Online Resource
    ISSN: 0004-6361 , 1432-0746
    RVK:
    RVK:
    Language: English
    Publisher: EDP Sciences
    Publication Date: 2023
    detail.hit.zdb_id: 1458466-9
    SSG: 16,12
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  • 2
    In: Astronomy & Astrophysics, EDP Sciences, Vol. 675 ( 2023-07), p. A10-
    Abstract: We present Planck Low Frequency Instrument (LFI) frequency sky maps derived within the B EYOND P LANCK framework. This framework draws samples from a global posterior distribution that includes instrumental, astrophysical, and cosmological parameters, and the main product is an entire ensemble of frequency sky map samples, each of which corresponds to one possible realization of the various modeled instrumental systematic corrections, including correlated noise, time-variable gain, as well as far sidelobe and bandpass corrections. This ensemble allows for computationally convenient end-to-end propagation of low-level instrumental uncertainties into higher-level science products, including astrophysical component maps, angular power spectra, and cosmological parameters. We show that the two dominant sources of LFI instrumental systematic uncertainties are correlated noise and gain fluctuations, and the products presented here support – for the first time – full Bayesian error propagation for these effects at full angular resolution. We compared our posterior mean maps with traditional frequency maps delivered by the Planck Collaboration, and find generally good agreement. The most important quality improvement is due to significantly lower calibration uncertainties in the new processing, as we find a fractional absolute calibration uncertainty at 70 GHz of Δ g 0 / g 0  = 5 × 10 −5 , which is nominally 40 times smaller than that reported by Planck 2018. However, we also note that the original Planck 2018 estimate has a nontrivial statistical interpretation, and this further illustrates the advantage of the new framework in terms of producing self-consistent and well-defined error estimates of all involved quantities without the need of ad hoc uncertainty contributions. We describe how low-resolution data products, including dense pixel-pixel covariance matrices, may be produced from the posterior samples directly, without the need for computationally expensive analytic calculations or simulations. We conclude that posterior-based frequency map sampling provides unique capabilities in terms of low-level systematics modeling and error propagation, and may play an important role for future Cosmic Microwave Background (CMB) B -mode experiments aiming at nanokelvin precision.
    Type of Medium: Online Resource
    ISSN: 0004-6361 , 1432-0746
    RVK:
    RVK:
    Language: English
    Publisher: EDP Sciences
    Publication Date: 2023
    detail.hit.zdb_id: 1458466-9
    SSG: 16,12
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  • 3
    In: Astronomy & Astrophysics, EDP Sciences, Vol. 675 ( 2023-07), p. A4-
    Abstract: End-to-end simulations play a key role in the analysis of any high-sensitivity cosmic microwave background (CMB) experiment, providing high-fidelity systematic error propagation capabilities that are unmatched by any other means. In this paper, we address an important issue regarding such simulations, namely, how to define the inputs in terms of sky model and instrument parameters. These may either be taken as a constrained realization derived from the data or as a random realization independent from the data. We refer to these as posterior and prior simulations, respectively. We show that the two options lead to significantly different correlation structures, as prior simulations (contrary to posterior simulations) effectively include cosmic variance, but they exclude realization-specific correlations from non-linear degeneracies. Consequently, they quantify fundamentally different types of uncertainties. We argue that as a result, they also have different and complementary scientific uses, even if this dichotomy is not absolute. In particular, posterior simulations are in general more convenient for parameter estimation studies, while prior simulations are generally more convenient for model testing. Before B EYOND P LANCK , most pipelines used a mix of constrained and random inputs and applied the same hybrid simulations for all applications, even though the statistical justification for this is not always evident. B EYOND P LANCK represents the first end-to-end CMB simulation framework that is able to generate both types of simulations and these new capabilities have brought this topic to the forefront. The B EYOND P LANCK posterior simulations and their uses are described extensively in a suite of companion papers. In this work, we consider one important applications of the corresponding prior simulations, namely, code validation. Specifically, we generated a set of one-year LFI 30 GHz prior simulations with known inputs and we used these to validate the core low-level B EYOND P LANCK algorithms dealing with gain estimation, correlated noise estimation, and mapmaking.
    Type of Medium: Online Resource
    ISSN: 0004-6361 , 1432-0746
    RVK:
    RVK:
    Language: English
    Publisher: EDP Sciences
    Publication Date: 2023
    detail.hit.zdb_id: 1458466-9
    SSG: 16,12
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  • 4
    In: Astronomy & Astrophysics, EDP Sciences, Vol. 675 ( 2023-07), p. A1-
    Abstract: We describe the B EYOND P LANCK project in terms of our motivation, methodology, and main products, and provide a guide to a set of companion papers that describe each result in more detail. Building directly on experience from ESA’s Planck mission, we implemented a complete end-to-end Bayesian analysis framework for the Planck Low Frequency Instrument (LFI) observations. The primary product is a full joint posterior distribution P ( ω  ∣  d ), where ω represents the set of all free instrumental (gain, correlated noise, bandpass, etc.), astrophysical (synchrotron, free-free, thermal dust emission, etc.), and cosmological (cosmic microwave background – CMB – map, power spectrum, etc.) parameters. Some notable advantages of this approach compared to a traditional pipeline procedure are seamless end-to-end propagation of uncertainties; accurate modeling of both astrophysical and instrumental effects in the most natural basis for each uncertain quantity; optimized computational costs with little or no need for intermediate human interaction between various analysis steps; and a complete overview of the entire analysis process within one single framework. As a practical demonstration of this framework, we focus in particular on low- ℓ CMB polarization reconstruction with Planck LFI. In this process, we identify several important new effects that have not been accounted for in previous pipelines, including gain over-smoothing and time-variable and non-1/ f correlated noise in the 30 and 44 GHz channels. Modeling and mitigating both previously known and newly discovered systematic effects, we find that all results are consistent with the ΛCDM model, and we constrained the reionization optical depth to τ  = 0.066 ± 0.013, with a low-resolution CMB-based χ 2 probability to exceed of 32%. This uncertainty is about 30% larger than the official pipelines, arising from taking a more complete instrumental model into account. The marginal CMB solar dipole amplitude is 3362.7 ± 1.4 μK, where the error bar was derived directly from the posterior distribution without the need of any ad hoc instrumental corrections. We are currently not aware of any significant unmodeled systematic effects remaining in the Planck LFI data, and, for the first time, the 44 GHz channel is fully exploited in the current analysis. We argue that this framework can play a central role in the analysis of many current and future high-sensitivity CMB experiments, including LiteBIRD, and it will serve as the computational foundation of the emerging community-wide C OSMOGLOBE effort, which aims to combine state-of-the-art radio, microwave, and submillimeter data sets into one global astrophysical model.
    Type of Medium: Online Resource
    ISSN: 0004-6361 , 1432-0746
    RVK:
    RVK:
    Language: English
    Publisher: EDP Sciences
    Publication Date: 2023
    detail.hit.zdb_id: 1458466-9
    SSG: 16,12
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  • 5
    In: Astronomy & Astrophysics, EDP Sciences, Vol. 675 ( 2023-07), p. A3-
    Abstract: We describe the computational infrastructure for end-to-end Bayesian cosmic microwave background (CMB) analysis implemented by the BeyondPlanck Collaboration. The code is called Commander3 . It provides a statistically consistent framework for global analysis of CMB and microwave observations and may be useful for a wide range of legacy, current, and future experiments. The paper has three main goals. Firstly, we provide a high-level overview of the existing code base, aiming to guide readers who wish to extend and adapt the code according to their own needs or re-implement it from scratch in a different programming language. Secondly, we discuss some critical computational challenges that arise within any global CMB analysis framework, for instance in-memory compression of time-ordered data, fast Fourier transform optimization, and parallelization and load-balancing. Thirdly, we quantify the CPU and RAM requirements for the current B EYOND P LANCK analysis, finding that a total of 1.5 TB of RAM is required for efficient analysis and that the total cost of a full Gibbs sample for LFI is 170 CPU-hrs, including both low-level processing and high-level component separation, which is well within the capabilities of current low-cost computing facilities. The existing code base is made publicly available under a GNU General Public Library (GPL) license.
    Type of Medium: Online Resource
    ISSN: 0004-6361 , 1432-0746
    RVK:
    RVK:
    Language: English
    Publisher: EDP Sciences
    Publication Date: 2023
    detail.hit.zdb_id: 1458466-9
    SSG: 16,12
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  • 6
    In: Astronomy & Astrophysics, EDP Sciences, Vol. 675 ( 2023-07), p. A6-
    Abstract: We present a Bayesian method for estimating instrumental noise parameters and propagating noise uncertainties within the global B EYOND P LANCK Gibbs sampling framework, which we applied to Planck Low Frequency Instrument (LFI) time-ordered data. Following previous works in the literature, we initially adopted a 1/ f model for the noise power spectral density (PSD), but we found the need for an additional lognormal component in the noise model in the 30 and 44 GHz bands. We implemented an optimal Wiener-filter (or constrained realization) gap-filling procedure to account for masked data. We then used this procedure to both estimate the gapless correlated noise in the time-domain, n corr , and to sample the noise PSD parameters, ξ n  = { σ 0 ,  f knee ,  α ,  A p }. In contrast to previous Planck analyses, we assumed piecewise stationary noise only within each pointing period (PID), and not throughout the full mission, but we adopted the LFI Data Processing Center results as priors on α and f knee . We generally found best-fit correlated noise parameters that are mostly consistent with previous results, with a few notable exceptions. However, a detailed inspection of the time-dependent results has revealed many important findings. First and foremost, we find strong evidence for statistically significant temporal variations in all noise PSD parameters, many of which are directly correlated with satellite housekeeping data. Second, while the simple 1/ f model appears to be an excellent fit for the LFI 70 GHz channel, there is evidence for additional correlated noise that is not described by a 1/ f model in the 30 and 44 GHz channels, including within the primary science frequency range of 0.1–1 Hz. In general, most 30 and 44 GHz channels exhibit deviations from 1/ f at the 2–3 σ level in each one-hour pointing period, motivating the addition of the lognormal noise component for these bands. For certain periods of time, we also find evidence of strong common mode noise fluctuations across the entire focal plane. Overall, we conclude that a simple 1/ f profile is not adequate for obtaining a full characterization of the Planck LFI noise, even when fitted hour-by-hour, and a more general model is required. These findings have important implications for large-scale CMB polarization reconstruction with the Planck LFI data and the current work is a first attempt at understanding and mitigating these issues.
    Type of Medium: Online Resource
    ISSN: 0004-6361 , 1432-0746
    RVK:
    RVK:
    Language: English
    Publisher: EDP Sciences
    Publication Date: 2023
    detail.hit.zdb_id: 1458466-9
    SSG: 16,12
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  • 7
    In: Astronomy & Astrophysics, EDP Sciences, Vol. 675 ( 2023-07), p. A11-
    Abstract: We present posterior sample-based cosmic microwave background (CMB) constraints from Planck LFI and WMAP observations as derived through global end-to-end Bayesian processing within the B EYOND P LANCK framework. We first used these samples to study correlations between CMB, foreground, and instrumental parameters. We identified a particularly strong degeneracy between CMB temperature fluctuations and free-free emission on intermediate angular scales (400 ≲  ℓ  ≲ 600), mitigated through model reduction, masking, and resampling. We compared our posterior-based CMB results with previous Planck products and found a generally good agreement, however, with notably higher noise due to our exclusion of Planck HFI data. We found a best-fit CMB dipole amplitude of 3362.7 ± 1.4 μK, which is in excellent agreement with previous Planck results. The quoted dipole uncertainty is derived directly from the sampled posterior distribution and does not involve any ad hoc contributions for Planck instrumental systematic effects. Similarly, we find a temperature quadrupole amplitude of $ \sigma^{TT}_2=229\pm97\,\muup{\rm K}^2 $ , which is in good agreement with previous results in terms of the amplitude, but the uncertainty is one order of magnitude greater than the naive diagonal Fisher uncertainty. Concurrently, we find less evidence of a possible alignment between the quadrupole and octopole than previously reported, due to a much larger scatter in the individual quadrupole coefficients that is caused both by marginalizing over a more complete set of systematic effects – as well as by requiring a more conservative analysis mask to mitigate the free-free degeneracy. For higher multipoles, we find that the angular temperature power spectrum is generally in good agreement with both Planck and WMAP. At the same time, we note that this is the first time that the sample-based, asymptotically exact Blackwell-Rao estimator has been successfully established for multipoles up to ℓ  ≤ 600. It now accounts for the majority of the cosmologically important information. Overall, this analysis demonstrates the unique capabilities of the Bayesian approach with respect to end-to-end systematic uncertainty propagation and we believe it can and should play an important role in the analysis of future CMB experiments. Cosmological parameter constraints are presented in a companion paper.
    Type of Medium: Online Resource
    ISSN: 0004-6361 , 1432-0746
    RVK:
    RVK:
    Language: English
    Publisher: EDP Sciences
    Publication Date: 2023
    detail.hit.zdb_id: 1458466-9
    SSG: 16,12
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  • 8
    In: Astronomy & Astrophysics, EDP Sciences, Vol. 675 ( 2023-07), p. A8-
    Abstract: We introduce a new formulation of the Conviqt convolution algorithm in terms of spin harmonics, and apply this to the problem of sidelobe correction for B EYOND P LANCK , the first end-to-end Bayesian Gibbs sampling framework for CMB analysis. We compare our implementation to the previous Planck LevelS implementation, and find good agreement between the two codes in terms of accuracy, but with a speed-up reaching a factor of 3–10, depending on the frequency bandlimits, l max and m max . The new algorithm is significantly simpler to implement and maintain, since all low-level calculations are handled through an external spherical harmonic transform library. We find that our mean sidelobe estimates for Planck LFI are in good agreement with previous efforts. Additionally, we present novel sidelobe rms maps that quantify the uncertainty in the sidelobe corrections due to variations in the sky model.
    Type of Medium: Online Resource
    ISSN: 0004-6361 , 1432-0746
    RVK:
    RVK:
    Language: English
    Publisher: EDP Sciences
    Publication Date: 2023
    detail.hit.zdb_id: 1458466-9
    SSG: 16,12
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  • 9
    In: The Open Journal of Astrophysics, The Open Journal, Vol. 6 ( 2023-03-16)
    Type of Medium: Online Resource
    ISSN: 2565-6120
    Language: Unknown
    Publisher: The Open Journal
    Publication Date: 2023
    detail.hit.zdb_id: 3001843-2
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  • 10
    In: Astronomy & Astrophysics, EDP Sciences, Vol. 675 ( 2023-07), p. A13-
    Abstract: We present the intensity foreground algorithms and model employed within the B EYOND P LANCK analysis framework. The B EYOND P LANCK analysis is aimed at integrating component separation and instrumental parameter sampling within a global framework, leading to complete end-to-end error propagation in the Planck Low Frequency Instrument (LFI) data analysis. Given the scope of the B EYOND P LANCK analysis, a limited set of data is included in the component separation process, leading to foreground parameter degeneracies. In order to properly constrain the Galactic foreground parameters, we improve upon the previous Commander component separation implementation by adding a suite of algorithmic techniques. These algorithms are designed to improve the stability and computational efficiency for weakly constrained posterior distributions. These are: (1) joint foreground spectral parameter and amplitude sampling, building on ideas from M IRAMARE ; (2) component-based monopole determination; (3) joint spectral parameter and monopole sampling; and (4) application of informative spatial priors for component amplitude maps. We find that the only spectral parameter with a significant signal-to-noise ratio using the current B EYOND P LANCK data set is the peak frequency of the anomalous microwave emission component, for which we find ν p  = 25.3 ± 0.5 GHz; all others must be constrained through external priors. Future works will be aimed at integrating many more data sets into this analysis, both map and time-ordered based, thereby gradually eliminating the currently observed degeneracies in a controlled manner with respect to both instrumental systematic effects and astrophysical degeneracies. When this happens, the simple LFI-oriented data model employed in the current work will need to be generalized to account for both a richer astrophysical model and additional instrumental effects. This work will be organized within the Open Science-based C OSMOGLOBE community effort.
    Type of Medium: Online Resource
    ISSN: 0004-6361 , 1432-0746
    RVK:
    RVK:
    Language: English
    Publisher: EDP Sciences
    Publication Date: 2023
    detail.hit.zdb_id: 1458466-9
    SSG: 16,12
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