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DOE OSTI2023

BEYONDPLANCK X. Planck Low Frequency Instrument frequency maps with sample-based error propagation

We present Planck Low Frequency Instrument (LFI) frequency sky maps derived within the BEYONDPLANCK 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 Δg 0 /g 0 = 5 x 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.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

BeyondPlanck: I. Global Bayesian analysis of the Planck Low Frequency Instrument data

We describe the BEYONDPLANCK 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 COSMOGLOBE effort, which aims to combine state-of-the-art radio, microwave, and submillimeter data sets into one global astrophysical model.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Inference of the optical depth to reionization τ from Planck CMB maps with convolutional neural networks

The optical depth to reionization, τ, is the least constrained parameter of the cosmological Λ cold dark matter (ΛCDM) model. To date, its most precise value is inferred from large-scale polarized cosmic microwave background (CMB) power spectra from the High Frequency Instrument (HFI) aboard the Planck satellite. These maps are known to contain significant contamination by residual non-Gaussian systematic effects, which are hard to model analytically. Therefore, robust constraints on τ are currently obtained through an empirical cross-spectrum likelihood built from simulations. In this paper, we present a likelihood-free inference of τ from polarized Planck HFI maps which, for the first time, is fully based on neural networks (NNs). NNs have the advantage of not requiring an analytical description of the data and can be trained on state-of-the-art simulations, combining the information from multiple channels. By using Gaussian sky simulations and Planck SRoll2 simulations, including CMB, noise, and residual instrumental systematic effects, we trained, tested, and validated NN models considering different setups. We inferred the value of τ directly from Stokes Q and U maps at ~4° pixel resolution, without computing angular power spectra. On Planck data, we obtained τ NN = 0.0579 ± 0.0082, which is compatible with current EE cross-spectrum results but with a ~30% larger uncertainty, which can be assigned to the inherent nonoptimality of our estimator and to the retraining procedure applied to avoid biases. While this paper does not improve on current cosmological constraints on τ, our analysis represents a first robust application of NN-based inference on real data, and highlights its potential as a promising tool for complementary analysis of near-future CMB experiments, also in view of the ongoing challenge to achieve the first detection of primordial gravitational waves.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

An extended Vlasov–Fokker–Planck approach for kinetic simulations of laser plasmas

Vlasov–Fokker–Planck simulation codes occupy an important niche in modeling laser-produced plasmas, since they are well suited to studying the effect of collisions on electron kinetic phenomena, especially energy transport. One of the most important elements of energy transport is the absorption of laser light by the plasma; however, simulating this in detail requires resolving oscillations of the laser light, whose characteristic timescale is orders of magnitude shorter than the simulation time needed to study transport physics. For this reason, most Vlasov–Fokker–Planck codes used to study electron transport in laser plasmas rely on simplified models of the laser–plasma coupling. Their underlying assumptions nominally preclude their use for modeling laser light having short-scale structure in space or time, such as broadband lasers. In this work, we derive a more general computational framework suitable for arbitrarily structured laser fields. Furthermore, our approach is based on an extended set of Vlasov–Fokker–Planck equations that separately solve for the low- and high-frequency plasma response. We implement these extended Vlasov–Fokker–Planck equations in the spherical harmonic code K2 and demonstrate the performance of the method on several laser absorption test problems, with particular attention to the judicious selection of time steps, time integrators, and spherical harmonic truncation, according to the intensity and spectrum of the laser light under consideration. Comparison with the widely used Langdon absorption operator shows the Langdon operator performs remarkably well for predicting laser heating in the simple cases considered here, even in situations that would seem to violate its underlying assumptions.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2013

Axion hot dark matter bounds after Planck

We use cosmological observations in the post-Planck era to derive limits on thermally produced cosmological axions. In the early universe such axions contribute to the radiation density and later to the hot dark matter fraction. We find an upper limit m{sub a} < 0.67 eV at 95% C.L. after marginalising over the unknown neutrino masses, using CMB temperature and polarisation data from Planck and WMAP respectively, the halo matter power spectrum extracted from SDSS-DR7, and the local Hubble expansion rate H{sub 0} released by the Carnegie Hubble Program based on a recalibration of the Hubble Space Telescope Key Project sample. Leaving out the local H{sub 0} measurement relaxes the limit somewhat to 0.86 eV, while Planck+WMAP alone constrain the axion mass to 1.01 eV, the first time an upper limit on m{sub a} has been obtained from CMB data alone. Our axion limit is therefore not very sensitive to the tension between the Planck-inferred H{sub 0} and the locally measured value. This is in contrast with the upper limit on the neutrino mass sum, which we find here to range from Σ m{sub ν} < 0.27 eV at 95% C.L. combining all of the aforementioned observations, to 0.84 eV from CMB data alone.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

The Atacama Cosmology Telescope: cross correlation with Planck maps

We present the temperature power spectrum of the Cosmic Microwave Background obtained by cross-correlating maps from the Atacama Cosmology Telescope (ACT) at 148 and 218 GHz with maps from the Planck satellite at 143 and 217 GHz, in two overlapping regions covering 592 square degrees. We find excellent agreement between the two datasets at both frequencies, quantified using the variance of the residuals between the ACT power spectra and the ACT × Planck cross-spectra. We use these cross-correlations to measure the calibration of the ACT data at 148 and 218 GHz relative to Planck, to 0.7% and 2% precision respectively. We find no evidence for anisotropy in the calibration parameter. We compare the Planck 353 GHz power spectrum with the measured amplitudes of dust and cosmic infrared background (CIB) of ACT data at 148 and 218 GHz. We also compare planet and point source measurements from the two experiments.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

North-South non-Gaussian asymmetry in Planck CMB maps

We report the results of a statistical analysis performed with the four foreground-cleaned Planck maps by means of a suitably defined local-variance estimator. Our analysis shows a clear dipolar structure in Planck's variance map pointing in the direction (l,b) ≅ (220°,-32°), thus consistent with the North-South asymmetry phenomenon. Surprisingly, and contrary to previous findings, removing the CMB quadrupole and octopole makes the asymmetry stronger. Our results show a maximal statistical significance, of 98.1% CL, in the scales ranging from ℓ=4 to ℓ=500. Additionally, through exhaustive analyses of the four foreground-cleaned and individual frequency Planck maps, we find unlikely that residual foregrounds could be causing this dipole variance asymmetry. Moreover, we find that the dipole gets lower amplitudes for larger masks, evidencing that most of the contribution to the variance dipole comes from a region near the galactic plane. Finally, our results are robust against different foreground cleaning procedures, different Planck masks, pixelization parameters, and the addition of inhomogeneous real noise.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Brans-Dicke inflation in light of the Planck 2015 data

We study inflation in the Brans-Dicke gravity as a special model of the scalar-tensor gravity. We obtain the inflationary observables containing the scalar spectral index, the tensor-to-scalar ratio, the running of the scalar spectral index and the equilateral non-Gaussianity parameter in terms of the general form of the potential in the Jordan frame. Then, we compare the results for various inflationary potentials in light of the Planck 2015 data. Our study shows that in the Brans-Dicke gravity, the power-law, inverse power-law and exponential potentials are ruled out by the Planck 2015 data. But, the hilltop, Higgs, Coleman-Weinberg and natural potentials can be compatible with Planck 2015 TT,TE,EE+lowP data at 95% CL. Moreover, the D-brane, SB SUSY and displaced quadratic potentials can be in well agreement with the observational data since their results can lie inside the 68% CL region of Planck 2015 TT,TE,EE+lowP data.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Big-Bang Nucleosynthesis after Planck

We assess the status of big-bang nucleosynthesis (BBN) in light of the final Planck data release and other recent developments, and in anticipation of future measurements. Planck data from the recombination era fix the cosmic baryon density to 0.9% precision, and now damping tail measurements determine the helium abundance and effective number of neutrinos with precision approaching that of astronomical and BBN determinations respectively. All three parameters are related by BBN. In addition, new high-redshift measurements give D/H to better precision than theoretical predictions, and new Li/H data reconfirm the lithium problem. We present new 7 Be(n, p) 7 Li rates using new neutron capture measurements; we have also examined the effect of proposed changes in the d(p, γ) 3 He rates. Using these results we perform a series of likelihood analyses. We assess BBN/CMB consistency, with attention to how our results depend on the choice of Planck data, as well as how the results depend on the choice of non-BBN, non-Planck data sets. Most importantly the lithium problem remains, and indeed is more acute given the very tight D/H observational constraints; new neutron capture data reveals systematics that somewhat increases uncertainty and thus slightly reduces but does not essentially change the problem. We confirm that d(p, γ) 3 He theoretical rates brings D/H out of agreement and slightly increases 7 Li; new experimental data are needed at BBN energies. Setting the lithium problem aside, we find the effective number of neutrino species at BBN is Nν = 2.86±0.15. Future CMB Stage-4 measurements promise substantial improvements in BBN parameters: helium abundance determinations will be competitive with the best astronomical determinations, and Neff will approach sensitivities capable of detecting the effects of Standard Model neutrino heating of the primordial plasma.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

POWER ASYMMETRY IN WMAP AND PLANCK TEMPERATURE SKY MAPS AS MEASURED BY A LOCAL VARIANCE ESTIMATOR

We revisit the question of hemispherical power asymmetry in the WMAP and Planck temperature sky maps by measuring the local variance over the sky and on disks of various sizes. For the 2013 Planck sky map we find that none of the 1000 available isotropic Planck ''Full Focal Plane'' simulations have a larger variance asymmetry than that estimated from the data, suggesting the presence of an anisotropic signature formally significant at least at the 3.3σ level. For the WMAP 9 year data we find that 5 out of 1000 simulations have a larger asymmetry. The preferred direction for the asymmetry from the Planck data is (l, b) = (212°, –13°), in good agreement with previous reports of the same hemispherical power asymmetry.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

COSMOLOGY FROM GRAVITATIONAL LENS TIME DELAYS AND PLANCK DATA

Under the assumption of a flat ΛCDM cosmology, recent data from the Planck satellite point toward a Hubble constant that is in tension with that measured by gravitational lens time delays and by the local distance ladder. Prosaically, this difference could arise from unknown systematic uncertainties in some of the measurements. More interestingly—if systematics were ruled out—resolving the tension would require a departure from the flat ΛCDM cosmology, introducing, for example, a modest amount of spatial curvature, or a non-trivial dark energy equation of state. To begin to address these issues, we present an analysis of the gravitational lens RXJ1131–1231 that is improved in one particular regard: we examine the issue of systematic error introduced by an assumed lens model density profile. We use more flexible gravitational lens models with baryonic and dark matter components, and find that the exquisite Hubble Space Telescope image with thousands of intensity pixels in the Einstein ring and the stellar velocity dispersion of the lens contain sufficient information to constrain these more flexible models. The total uncertainty on the time-delay distance is 6.6% for a single system. We proceed to combine our improved time-delay distance measurement with the WMAP9 and Planck posteriors. In an open ΛCDM model, the data for RXJ1131–1231 in combination with Planck favor a flat universe with Ω{sub k}=0.00{sub −0.02}{sup +0.01} (68% credible interval (CI)). In a flat wCDM model, the combination of RXJ1131–1231 and Planck yields w=−1.52{sub −0.20}{sup +0.19} (68% CI)

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

CMB signatures of metal-free star formation and Planck 2015 polarization data

Standard analyses of the reionization history of the Universe from Planck cosmic microwave background (CMB) polarization measurements consider only the overall optical depth to electron scattering (τ), and further assume a step-like reionization history. However, the polarization data contain information beyond the overall optical depth, and the assumption of a step-like function may miss high redshift contributions to the optical depth and leads to biased τ constraints. Accounting for its full reionization information content, we reconsider the interpretation of Planck 2015 Low-Frequency Instrument (LFI) polarization data using simple, yet physically motivated reionization models. We show that these measurements still, in fact, allow a non-negligible contribution from metal-free (Pop-III) stars forming in mini-haloes of mass M ~ 10 5 –10 6 M ⊙ at z ≳ 15, provided this mode of star formation is fairly inefficient. We find that an early, self-regulated phase of Pop-III star formation with a gradual, plateau feature in the ionization history provides a good match to the Planck LFI measurements. In this case, as much as 20 percent of the volume of the Universe is ionized by z ~ 20. Although preferred when the full information content of the data is incorporated, this model would spuriously be disfavoured in the standard analysis. This preference is driven mostly by excess power from E-mode polarization at multipoles of 10 ≲ ℓ ≲ 20, which may reflect remaining systematic errors in the data, a statistical fluctuation or signatures of the first stars. Measurements from the Planck High-Frequency Instrument should be able to confirm or refute this hint and future cosmic-variance-limited E-mode polarization surveys can provide substantially more information on these signatures.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Reionization effective likelihood from Planck 2018 data

We release relike (reionization effective likelihood), a fast and accurate effective likelihood code based on the latest Planck 2018 data that allows one to constrain any model for reionization between 6 < z < 30 using five constraints from the CMB reionization principal components (PC). We tested the code on two example models which showed excellent agreement with sampling the exact Planck likelihoods using either a simple Gaussian PC likelihood or its full kernel density estimate. This code enables a fast and consistent means for combining Planck constraints with other reionization data sets, such as kinetic Sunyaev-Zeldovich effects, line-intensity mapping, luminosity function, star formation history, quasar spectra, etc., where the redshift dependence of the ionization history is important. Since the PC technique tests any reionization history in the given range, we also derive model-independent constraints for the total Thomson optical depth τ PC = $0.0619$$^{+0.0056}_{–0.0068}$ and its 15 ≤ z ≤ 30 high redshift component τ PC (15,30) < 0.020 (95% C.L.). Furthermore, the upper limits on the high-redshift optical depth is a factor of ~3 larger than those reported in the Planck 2018 cosmological parameter paper using the FlexKnot method and we validate our results with a direct analysis of a two-step model which permits this small high-z component.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Planck integrated Sachs-Wolfe-lensing likelihood and the CMB temperature

Here we present a new Planck CMB lensing-CMB temperature cross-correlation likelihood that can be used to constrain cosmology via the integrated Sachs-Wolfe (ISW) effect. CMB lensing is an excellent tracer of ISW, and we use the latest PR4 Planck data maps and lensing reconstruction to produce the first public Planck likelihood to constrain this signal. We demonstrate the likelihood by constraining the CMB background temperature from Planck data alone, where the ISW-lensing cross-correlation is a powerful way to break the geometric degeneracy, substantially improving constraints from the CMB and lensing power spectra alone.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2018

No evidence for dust B -mode decorrelation in Planck data

Constraints on inflationary B modes using cosmic microwave background polarization data commonly rely on either template cleaning or cross-spectra between maps at different frequencies to disentangle Galactic foregrounds from the cosmological signal. Assumptions about how the foregrounds scale with frequency are therefore crucial to interpreting the data. Recent results from the Planck satellite collaboration claim significant evidence for a decorrelation in the polarization signal of the spatial pattern of Galactic dust between 217 and 353 GHz. Such a decorrelation would suppress power in the cross-spectrum between high-frequency maps, where the dust is strong, and lower-frequency maps, where the sensitivity to cosmological B modes is strongest. Alternatively, it would leave residuals in lower-frequency maps cleaned with a template derived from the higher-frequency maps. If not accounted for, both situations would result in an underestimate of the dust contribution and thus an upward bias on measurements of the tensor-to-scalar ratio, r. In this paper, we revisit this measurement and find that the no-decorrelation hypothesis cannot be excluded with the Planck data. There are three main reasons for this: (i) There is significant noise bias in cross-spectra between Planck data splits that needs to be accounted for. (ii) There is strong evidence for unknown instrumental systematics, the amplitude of which we estimate using alternative Planck data splits. (iii) There are significant correlations between measurements in different sky patches that need to be taken into account when assessing the statistical significance. Finally, between ℓ = 55-90 and over 72% of the sky, the dust BB correlation between 217 and 353 GHz is 1.001 +.004/.021 -.004/.000 (68% stat/syst.) and shows no significant trend with the sky fraction.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2026

Fokker-Planck Equation Governing the Distribution of Walkers in Auxiliary-Field Quantum Monte Carlo

Auxiliary-field quantum Monte Carlo (AFQMC) is typically formulated as an open-ended random walk in an overcomplete space of Slater determinants, implemented through a Langevin equation. However, the explicit form of the underlying Fokker-Planck equation governing the walker population distribution has remained unknown. Here, in this Letter, we derive the Fokker-Planck equation for AFQMC and propose a novel numerical scheme to solve it. The solution of the Fokker-Planck equation reveals the wave function actually sampled by the AFQMC algorithm. Interestingly, we find that even when the exact ground state is used as a guiding wave function in constrained path AFQMC, contrary to the common assumption, the wave function sampled by AFQMC is not exact. Beyond clarifying several fundamental aspects of AFQMC, the availability of a Fokker-Planck equation formulation opens new avenues for systematically improving its accuracy, which we outline in this Letter.

Monte Carlo methods↗
DOE OSTI2026

Searching for synchrotron emission from the geminga TeV halo using the planck satellite

Pulsars convert a significant fraction of their total spin-down power into very high-energy electrons, leading to the formation of TeV halos. While these halos are well characterized at TeV energies, it remains unclear whether pulsars also accelerate electrons efficiently at lower energies and how these particles propagate through their surrounding environments. We aim to test whether synchrotron emission from $\sim 50$–$300 \, \textrm{GeV}$ electrons around the Geminga pulsar can be detected in the frequency range observed by the Planck satellite. This would help constrain low-energy particle acceleration and diffusion in the vicinity of pulsars. We model the expected synchrotron emission from Geminga’s TeV halo based on various diffusion and injection spectrum scenarios and compare these predictions to publicly available multi-frequency Planck data. We find no conclusive evidence of spatially extended synchrotron emission associated with Geminga in any of Planck’s frequency bands. Our calculations show that even under favorable diffusion and injection conditions, the predicted synchrotron flux lies well below Planck’s measured background levels.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

Simulating Charge Transport in Solid Oxide Mixed Ionic and Electronic Conductors: Nernst-Planck Theory vs Modified Fick's Law

With the assumption that the Fermi level (electrochemical potential of electrons) is uniform across the thickness of a mixed ionic and electronic conducting (MIEC) electrode, the charge-transport model in the electrode domain can be reduced to the modified Fick’s first law, which includes a thermodynamic factor A. A transient numerical solution of the Nernst-Planck theory was obtained for a symmetric cell with MIEC electrodes to illustrate the validity of the assumption of a uniform Fermi level. Subsequently, an impedance numerical solution based on the modified Fick’s first law is compared with that from the Nernst-Planck theory. The results show that Nernst-Planck charge-transport model is essentially the same as the modified Fick’s first law model as long as the MIEC electrodes have a predominant electronic conductivity. However, because of the invalidity of the uniform Fermi level assumption for aMIEC electrolyte with a predominant ionic conductivity, Nernst-Planck theory is needed to describe the charge transport behaviors.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗