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DOE OSTI2024

Bendability parameter for twisted ribbons to describe longitudinal wrinkling and delineate the near-threshold regime

We propose a dimensionless bendability parameter, ε -1 =[(h/W) 2 ⁢T -1 ] -1 , for wrinkling of thin, twisted ribbons with thickness h, width W, and tensional strain T. Bendability permits efficient collapse of data for wrinkle onset, wavelength, critical stress, and residual stress, demonstrating longitudinal wrinkling's primary dependence on this parameter. This parameter also allows us to distinguish the highly bendable range (ε -1 >20) from moderately bendable samples (ε -1 ϵ(0,20]). We identify scaling relations to describe longitudinal wrinkles that are valid across our entire set of simulated ribbons. When restricted to the highly bendable regime, simulations confirm theoretical near-threshold (NT) predictions for wrinkle onset and wavelength.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2026

Dispersive and nondispersive 𝐾-matrix formalisms

The modeling of coupled-channel effects has become increasingly important due to the availability of highly precise data for a large variety of hadronic (re)scattering processes. The 𝐾-matrix is a powerful, yet comparatively simple, method to describe scattering amplitudes, including coupled-channel effects, with the aim of interpreting experimental data. Throughout the literature, a range of dispersive and nondispersive 𝐾-matrix methods are employed. Here, we compare the dispersive and nondispersive formulations in the context of the N/D method. It is shown that the methods are equivalent in the physical region under 𝐾-matrix reparametrization. Differences away from the physical region are examined. Applications to synthetic data are used to illustrate the effects of model choices concerning form factors and the application of dispersion relations, with the goal of clarifying best practices. We find no clear preference with regard to dispersive modeling. In contrast, we find that interpretational ambiguity of the bare model parameters—and even of the form of the bare model—is endemic, and recommend a thorough sampling of data and model spaces to assess conclusion robustness.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2020

Combining Emergent Constraints for Climate Sensitivity

A method is proposed for combining information from several emergent constraints into a probabilistic estimate for a climate sensitivity proxy Y such as equilibrium climate sensitivity (ECS). The method is based on fitting a multivariate Gaussian PDF for Y and the emergent constraints using an ensemble of global climate models (GCMs); it can be viewed as a form of multiple linear regression of Y on the constraints. The method accounts for uncertainties in sampling this multidimensional PDF with a small number of models, for observational uncertainties in the constraints, and for overconfidence about the correlation of the constraints with the climate sensitivity. Its general form (Method C) accounts for correlations between the constraints. Method C becomes less robust when some constraints are too strongly related to each other; this can be mitigated using regularization approaches such as ridge regression. An illuminating special case, Method U, neglects any correlations between constraints except through their mutual relationship to the climate proxy; it is more robust to small GCM sample size and is appealingly interpretable. These methods are applied to ECS and the climate feedback parameter using a previously published set of 11 possible emergent constraints derived from climate models in the Coupled Model Intercomparison Project (CMIP). The ±2σ posterior range of ECS for Method C with no overconfidence adjustment is 4.3 ± 0.7 K. For Method U with a large overconfidence adjustment, it is 4.0 ± 1.3 K. This study adds confidence to past findings that most constraints predict higher climate sensitivity than the CMIP mean.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2025

pyTCR: A tropical cyclone rainfall model for python

pyTCR is a climatology software package developed in the Python programming language. It integrates the capabilities of several legacy physical models and increases computational efficiency to allow rapid estimation of tropical cyclone (TC) rainfall consistent with the large-scale environment. Specifically, pyTCR implements a horizontally distributed and vertically integrated model [Zhu et al., 2013] for simulating rainfall driven by TCs. Along storm tracks, rainfall is estimated by computing the cross-boundary-layer, upward water vapor transport caused by different mechanisms including frictional convergence, vortex stretching, large-scale baroclinic effect (i.e., wind shear), topographic forcing, and radiative cooling [Lu et al., 2018]. The package provides essential functionalities for modeling and interpreting spatio-temporal TC rainfall data. pyTCR requires a limited number of model input parameters, making it a convenient and useful tool for analyzing rainfall mechanisms driven by TCs. To sample rare (most intense) rainfall events that are often of great societal interest, pyTCR adapts and leverages outputs from a statistical-dynamical TC downscaling model [Lin et al., 2023] capable of rapidly generating a large number of synthetic TCs given a certain climate. As a result, pyTCR significantly reduces computational effort and improves the efficiency in capturing extreme TC rainfall events at the tail of the distributions from limited datasets. Furthermore, the TC downscaling model is forced entirely by large-scale environmental conditions from reanalysis data or coupled General Circulation Models (GCMs), simplifying the projection of TC-induced rainfall and wind speed under future climate using pyTCR. Finally, pyTCR can be coupled with hydrological and wind models to assess risks associated with independent and compound events (e.g., storm surges and freshwater flooding).

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2021

Aging and Lifetimes Milestone 7777, G.C. #4: Assess the ability of MRI to identify chemical and mechanical heterogeneity in polymers at various length scales

Polysiloxane foams utilized for stockpile applications experience changes over time induced by exposure to thermal, radiative, and mechanical stresses. The interplay of these stresses can lead to chemical and/or physical changes in the polymer, such as compression set and material degradation over time. Understanding the mechanisms of material aging and identifying material degradation prior to failure are critical in maintaining the integrity of the nuclear stockpile. Our prior work using solid-state NMR spectroscopy has shown that we can observe signatures of thermal, radiative, and mechanical aging of silicone elastomers using differences in NMR parameters such as relaxation (T1 and T2). However, most of our measurements have been on bulk samples and have only provided an average aging behavior of each sample. Here, we have used magnetic resonance imaging (MRI) to provide relaxation-weighted images that are a metric of structural heterogeneity (cross-link density) in polymers across multiple length scales. In addition, the larger sample size that can be accommodated in animal MRI scanners has the potential to make the technique adaptable to detecting heterogeneities whole parts.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

LLNL FY22 Aging and Lifetimes Exit Criteria: Milestone 8119, GC#01

Polysiloxane foams utilized for stockpile applications experience changes over time induced by exposure to thermal, radiative, and mechanical stresses. The interplay of these stresses can lead to chemical and/or physical changes in the polymer, such as compression set and material degradation over time. Understanding the mechanisms of material aging and identifying material degradation prior to failure are critical in maintaining the integrity of the nuclear stockpile. Our prior work using solid-state NMR spectroscopy has shown that we can observe signatures of thermal, radiative, and mechanical aging of silicone elastomers using differences in NMR parameters such as relaxation (T1 and T2). However, most of our measurements have been on bulk samples and have only provided an average aging behavior of each sample. Here, we have used magnetic resonance imaging (MRI) to provide relaxation-weighted images that are a metric of structural heterogeneity (crosslink density) in polymers across multiple length scales. In addition, the larger sample size that can be accommodated in animal MRI scanners has the potential to make the technique adaptable to detecting heterogeneities in whole parts.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Modulated Thermomechanical Analysis of Compression-Molded High-Density Polyethylene

Thermomechanical analysis (TMA) experiments conducted on high-density polyethylene (HDPE) show both reversible and irreversible dimensional changes. To further explore these reversible and irreversible processes, modulated thermomechanical analysis (MTMA) was used. Before reliable data on compression-molded HDPE was collected, a parameter optimization was performed to obtain a suitable MTMA method. Once a suitable method was obtained, several MTMA experiments were conducted on compression-molded HDPE. This work highlights the steps taken during the MTMA parameter optimization and the results obtained from MTMA experiments conducted on pristine compression-molded HDPE samples.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Worst Case Sabotage Consequence Modeling for Advanced Reactors

Under proposed rulemaking by the United States Nuclear Regulatory Commission, advanced reactor licensees may qualify for a reduction in onsite responders if the consequences from a sabotage attack do not exceed 25 rem at the reactor site boundary 2 hours after a release occurs. This work presents a preliminary assessment of the feasibility of meeting the 25 rem at the site boundary criteria. Using advanced reactor radionuclide inventories radiological release estimates created by collaborators at Oak Ridge National Laboratory, the MACCS consequence analysis code was used to investigate the distance at the dose from hypothetical sabotage events reaches 25 rem for different advanced reactor technologies. It was found that the distance to 25 rem depended heavily on sampled weather conditions and sabotage release fractions, and further refinement of release fractions and MACCS modeling parameters is recommended.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2023

Towards Low-Temperature CVD Synthesis and Characterization of Mono- or Few-Layer Molybdenum Disulfide

Molybdenum disulfide (MoS 2 ) transistors are a promising alternative for the semiconductor industry due to their large on/off current ratio (>10 10 ), immunity to short-channel effects, and unique switching characteristics. MoS 2 has drawn considerable interest due to its intriguing electrical, optical, sensing, and catalytic properties. Monolayer MoS 2 is a semiconducting material with a direct band gap of ~1.9 eV, which can be tuned. Commercially, the aim of synthesizing a novel material is to grow high-quality samples over a large area and at a low cost. Although chemical vapor deposition (CVD) growth techniques are associated with a low-cost pathway and large-area material growth, a drawback concerns meeting the high crystalline quality required for nanoelectronic and optoelectronic applications. This research presents a lower-temperature CVD for the repeatable synthesis of large-size mono- or few-layer MoS 2 using the direct vapor phase sulfurization of MoO 3 . The samples grown on Si/SiO 2 substrates demonstrate a uniform single-crystalline quality in Raman spectroscopy, photoluminescence (PL), scanning electron microscopy (SEM), atomic force microscopy (AFM), X-ray photoelectron spectroscopy (XPS), and scanning transmission electron microscopy. These characterization techniques were targeted to confirm the uniform thickness, stoichiometry, and lattice spacing of the MoS 2 layers. The MoS 2 crystals were deposited over the entire surface of the sample substrate. With a detailed discussion of the CVD setup and an explanation of the process parameters that influence nucleation and growth, this work opens a new platform for the repeatable synthesis of highly crystalline mono- or few-layer MoS 2 suitable for optoelectronic application.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2021

Relationships between the Stellar, Gaseous, and Star Formation Disks in LITTLE THINGS Dwarf Irregular Galaxies: Indirect Evidence for Substantial Fractions of Dark Molecular Gas

The stellar, gaseous and young stellar disks in the LITTLE THINGS sample of nearby dwarf irregular galaxies are fitted with functions to search for correlations between the parameters. We find that the H i radial profiles are generally flatter in the center and fall faster in the outer regions than the V-band profiles, while young stars are more centrally concentrated, especially if the H i is more centrally flat. This pattern suggests that the H i is turning into molecules in the center, and the molecular clouds are forming stars and FUV. A model that assumes the molecular surface density is proportional to the total gas surface density to a power of 1.5 or 2, in analogy with the Kennicutt–Schmidt relation, reproduces the relationship between the ratio of the visible to the H i scale length and the H i Sérsic index. The molecular fraction is estimated as a function of radius for each galaxy by converting the FUV to a molecular surface density using conventional calibrations. The average molecular fraction inside 3R {sub D} is 23% ± 17%. However, the break in the stellar surface brightness profile has no unified tracer related to star formation.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2021

Design and Optimization of a Gas-Cooled, Airfoil Fin Microchannel Heat Exchanger

High-performance microchannel heat exchangers are needed to supply heat for power conversion for nuclear microreactors. An airfoil fin microchannel design, constructed of Alloy 617 with helium as the working fluid, was analyzed and optimized using a design of experiments with artificial intelligence and machine learning techniques. The use of airfoil fins offers the potential to reduce pressure drop across the heat exchanger, as compared to other types of channel configurations. A framework for topology optimization of airfoil fin PCHEs has been developed that can be readily extended to different fin sizes and shapes, as well as different inlet and operating conditions, materials of construction, and working fluids. An optimization procedure was developed that employs computational fluid dynamics for a set of design points identified using Latin hypercube sampling. STAR-CCM+ was used to analyze a simplified two-channel configuration where five parameters were varied – inlet angle, fin scale, extent of staggering, transverse and longitudinal pitches. Two methods were compared for generating surrogate models – a 5D polynomial and a regression neural network. A response surface approximation was created from the surrogate models and input to a genetic algorithm. The genetic algorithm identified a set of optimal points on the Pareto front. The optimal geometry was found across six channel Reynolds numbers ranging from 1000 to 5000 to analyze how varying inlet conditions affects the optimal design. A set of optimal designs that maximizes heat transfer and minimizes pressure drop was identified, and a thermal stress analysis was performed on the optimal design. This work has developed a digital framework for the expedient topology design and evaluation of PCHE designs for gas-cooled microreactor applications. Correlations for the Nusselt number and Darcy friction factor were developed that can be useful for thermal hydraulic analyses using system codes. A thermal stress analysis was conducted and a brief discussion of the status of code cases of PCHEs for nuclear applications is given. Testing and thermomechanical modeling is needed to facilitate future code compliance of PCHEs for high pressure and high temperature applications.

42 ENGINEERING↗

DOE OSTI2022

An influence of manufacturing tolerances on Pin-Cell k-infinity of MOX fuel using data from the FUBILA experiment program

An influence of manufacturing tolerances (MTs) was evaluated on the pin-cell k-infinity of MOX fuel through the random sampling of CASMO5 calculations. The data from the FUBILA experiment program was used as the manufacturing parameters. For the uncertainties of element/isotope mass fractions, their covariance matrices were calculated by the generalized least square method. The total k-infinity uncertainty was 120-250 pcm (percent mille). From the breakdown of k-infinity uncertainty per materials, the MTs of fuel pellet had a dominant influence. The individual influences were also evaluated for element/isotope mass fractions, an inner/outer diameter, and a density. Those of element/isotope mass fractions were less than a few dozen pcm. Since the perturbations of fuel pellet diameter and density caused large variations to the total amount of heavy metals and effect of spatial self-shielding, they had a negative correlation with the k-infinity perturbation. On the AG3 (Al-Mg alloy) over-cladding, the inner/outer diameter perturbations had both negative and positive correlations. The negative one was due to decrease in amount of light water and the positive one was due to increase in amount of AG3. Since the effect of neutron slowing-down by light water had a dominant influence, the influence of the former negative correlation was larger than that of the latter positive correlation. It is, therefore, concluded that the consideration of the MTs that had a large influence on the effect of neutron slowing-down is important for precise quantification of the pin-cell k-infinity uncertainty of MOX fuel. (author)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2020

MESOSCALE THERMAL TRANSPORT MEASUREMENTS OF MULTI-PHASE AND POROUS NUCLEAR FUELS USING A SQUARE-WAVE PULSE THERMOREFLECTANCE TECHNIQUE

The safe and efficient operation of nuclear reactors require accurate knowledge of peak temperatures in the fuel assemblies. The temperature profiles are governed by the thermal transport properties of the fuel, namely the thermal conductivities (k) and thermal diffusivities (D). These values can be very difficult to measure as they are known to vary considerably from the measured bulk values of the fresh fuel, and quickly degrade with increasing burnup [1 -3] . Laser-based techniques have been effectively used for non-destructive and non-contact thermal transport measurements of a wide variety of materials, including nuclear materials [4-6] that would otherwise prove too hazardous or difficult to measure otherwise. In this study, a new thermoreflectance technique known as square-pulse transient thermoreflectance (SPTR) is described and used to determine the mesoscale thermal diffusivity of both uranium sesquisilicide (U3Si2) and uranium nitride (UN) phases in a composite fuel with micron level spatial resolution [7]. This technique employs a rapid train of square-wave pulses from an excitation laser to create a periodic heat flux on a gold coated sample surface. Surface adsorption results in transient film temperatures and hence rapid fluctuations in thermoreflectance that can be measured via a detection laser coupled with a digital oscilloscope. The lasers are coaxially focused on the sample surface, allowing for a sample measurement area of a single convolved laser spot size (~2 µm). A sensitivity analysis was conducted to identify key measurement parameters of this technique using reference materials with a range of thermal conductivities comparable to those of both ceramic, composite, and metal nuclear fuel types (1.4 – 27.2 W/m-K). The reference materials were measured using the new technique as well as a spatial-domain thermoreflectance technique (SDTR) previously reported for a comparison [8]. Additionally, measurements of several U3Si2 and UN phase regions of a polished UN/U3Si2 (70/30 vol.%) sample were taken, and the resulting calculated D values are reported, with both techniques showing excellent agreement between samples. This technique was used to scan a multiphase region at 5 micron increments to generate a local diffusivity map, demonstrating the utility of the techniques for measuring thermal transport properties in specimens with precipitates and secondary phases. Furthermore, the technique is currently being applied to measure thermal properties of Fast Flux Test Reactor (FFTR) irradiated metal fuel specimens whose porous microstructure make it very difficult to measure using other techniques. Comparison of the local scale measurements are compared with the pre-irradiated fuel samples to show the degradation of thermal transport in fuels due to pores from fission gas bubbles and other irradiation induced defects.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2021

The differences between mass- and light-derived structural parameters over time for MaNGA elliptical galaxies

ABSTRACT We apply stellar population synthesis analysis to obtain spatially resolved archaeological inferences for a large sample of ‘red and dead’ Elliptical galaxies (Classical Ellipticals, CLEs) from the MaNGA/SDSS-IV DR15 survey. From their 2D stellar light and mass maps, we explore the differences between the radial mass and light distributions in the rest-frame bands g, r, and i as functions of look-back time, tlb, or redshift, z. We characterize these differences through the ratios between the following mass- and light-derived global properties: sizes, concentrations, and effective surface densities. We find that the mass-to-light ratios of these properties change with tlb, more the more massive the galaxies are. The CLE galaxy archaeological progenitors are, on average, less compact, concentrated, and dense in light than in mass as z decreases. However, at later times, when also the evolution of the progenitors becomes passive at all radii, there is an upturn in these trends and the differences between mass and light in compactness/concentration decrease towards z ∼ 0. The trends in the ratios of mass-to-light sizes agree qualitatively with results from direct observations in galaxy surveys at different redshifts. We discuss the caveats and interpretations of our results, and speculate that the strong structural evolution found in some previous studies for early-type galaxies could be explained partially by photometric changes rather than by intrinsic structural changes.

Ibarra-Medel, H. (ORCID:0000000297906313)↗

DOE OSTI2022

Unsupervised learning approaches to characterizing heterogeneous samples using X-ray single-particle imaging

One of the outstanding analytical problems in X-ray single-particle imaging (SPI) is the classification of structural heterogeneity, which is especially difficult given the low signal-to-noise ratios of individual patterns and the fact that even identical objects can yield patterns that vary greatly when orientation is taken into consideration. Proposed here are two methods which explicitly account for this orientation-induced variation and can robustly determine the structural landscape of a sample ensemble. The first, termed common-line principal component analysis (PCA), provides a rough classification which is essentially parameter free and can be run automatically on any SPI dataset. The second method, utilizing variation auto-encoders (VAEs), can generate 3D structures of the objects at any point in the structural landscape. Both these methods are implemented in combination with the noise-tolerant expand–maximize–compress (EMC) algorithm and its utility is demonstrated by applying it to an experimental dataset from gold nanoparticles with only a few thousand photons per pattern. Both discrete structural classes and continuous deformations are recovered. These developments diverge from previous approaches of extracting reproducible subsets of patterns from a dataset and open up the possibility of moving beyond the study of homogeneous sample sets to addressing open questions on topics such as nanocrystal growth and dynamics, as well as phase transitions which have not been externally triggered.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2021

Following O and OH in He/O 2 and He/H 2 O gas mixtures—from the gas phase through the liquid phase to modifications on a biological sample

Abstract Applied cold atmospheric plasma allows for the controlled delivery of reactive oxygen and nitrogen species tailored for specific applications. Through the manipulation of the plasma parameters, feed gases, and careful consideration of the environment surrounding the treatment target, selective chemistries that preferentially influence the target can be produced and delivered. To demonstrate this, the COST reference microscale atmospheric pressure plasma jet is used to study the generation and transport of O and ⋅ OH from the gas phase through the liquid to the biological model target cysteine. Relative and absolute species densities of ⋅ OH and O are measured in the gas phase through laser induced fluorescence (LIF) and two-photon absorption LIF respectively. The transport of these species is followed into the liquid phase by hydrogen peroxide quantification and visualized by a fluorescence assay. Modifications to the model biological sample cysteine exposed to ⋅ OH and H 2 O 2 dominated chemistry (He/H 2 O (0.25%)) and O dominated chemistry (He/O 2 (0.6%)) is measured by FTIR spectroscopy. The origin of these species that modify cysteine is considered through the use of heavy water (H 2 18 O) and mass spectrometry. It is found that the reaction pathways differ significantly for He/O 2 and He/H 2 O. Hydrogen peroxide is formed mainly in the liquid phase in the presence of a substrate for He/O 2 whereas for He/H 2 O it forms in the gas phase. The liquid chemistry resulting from the He/O 2 admixture mainly targets the sulfur moiety of cysteine for oxidation up to irreversible oxidation states, while He/H 2 O treatment leads preferentially to reversible oxidation products. The more O or OH/H 2 O 2 dominated chemistry produced by the two gas admixtures studied offers the possibility to select species for target modification.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

Bayesian sparse learning with preconditioned stochastic gradient MCMC and its applications

Deep neural networks have been successfully employed in an extensive variety of research areas, including solving partial differential equations. Despite its significant success, there are some challenges in effectively training DNN, such as avoiding overfitting in over-parameterized DNNs and accelerating the optimization in DNNs with pathological curvature. Here, we propose a Bayesian type sparse deep learning algorithm. The algorithm utilizes a set of spike-and-slab priors for the parameters in the deep neural network. The hierarchical Bayesian mixture will be trained using an adaptive empirical method. That is, one will alternatively sample from the posterior using preconditioned stochastic gradient Langevin Dynamics (PSGLD), and optimize the latent variables via stochastic approximation. The sparsity of the network is achieved while optimizing the hyperparameters with adaptive searching and penalizing. A popular SG-MCMC approach is Stochastic gradient Langevin dynamics (SGLD). However, considering the complex geometry in the model parameter space in nonconvex learning, updating parameters using a universal step size in each component as in SGLD may cause slow mixing. To address this issue, we apply a computationally manageable preconditioner in the updating rule, which provides a step-size parameter to adapt to local geometric properties. Moreover, by smoothly optimizing the hyperparameter in the preconditioning matrix, our proposed algorithm ensures a decreasing bias, which is introduced by ignoring the correction term in the preconditioned SGLD. According to the existing theoretical framework, we show that the proposed algorithm can asymptotically converge to the correct distribution with a controllable bias under mild conditions. Numerical tests are performed on both synthetic regression problems and learning solutions of elliptic PDE, which demonstrate the accuracy and efficiency of the present work.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2023

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

We present cosmological parameter constraints estimated using the Bayesian BEYONDPLANCK 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 1σ when considering only temperature multipoles between 30 ≤ ℓ ≤ 600. In cases where there are differences, we note that the BEYONDPLANCK 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 BEYONDPLANCK 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.

79 ASTRONOMY AND ASTROPHYSICS↗