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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

High Resolution Polar Kerr Effect Studies of CsV 3 Sb 5 : Tests for Time-Reversal Symmetry Breaking below the Charge-Order Transition

We report high resolution polar Kerr effect measurements on CsV 3 Sb 5 single crystals in search for signatures of spontaneous time reversal symmetry breaking below the charge order transition at T * = 94 K. Utilizing two different versions of zero-area loop Sagnac interferometers operating at 1550 nm wavelength, each with the fundamental attribute that without a time reversal symmetry breaking sample at its path, the interferometer is perfectly reciprocal, we find no observable Kerr effect to within the noise floor limit of the apparatus at 30 nanoradians. Simultaneous coherent reflection ratio measurements confirm the sharpness of the charge order transition in the same optical volume as the Kerr measurements. At finite magnetic field we observe a sharp onset of a diamagnetic shift in the Kerr signal at T *, which persists down to the lowest temperature without change in trend. Since 1550 nm is an energy that was shown to capture all features of the optical properties of the material that interact with the charge order transition, we are led to conclude that it is highly unlikely that time reversal symmetry is broken in the charge ordered state in CsV 3 Sb 5 .

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Effect of Many Modes on Self-Polarization and Photochemical Suppression in Cavities

The standard description of cavity-modified molecular reactions typically involves a single (resonant) mode, while in reality the quantum cavity supports a range of photon modes. In this work we demonstrate that as more photon modes are accounted for, physico-chemical phenomena can dramatically change, as illustrated by the cavity-induced suppression of the important and ubiquitous process of proton-coupled electron-transfer. Using a multi-trajectory Ehrenfest treatment for the photonmodes, we find that self-polarization effects become essential, and we introduce the concept of selfpolarization- modified Born-Oppenheimer surfaces as a new construct to analyze dynamics. As the number of cavity photon modes increases, the increasing deviation of these surfaces from the cavityfree Born-Oppenheimer surfaces, together with the interplay between photon emission and absorption inside the widening bands of these surfaces, leads to enhanced suppression. The present findings are general and will have implications for the description and control of cavity-driven physical processes of molecules, nanostructures and solids embedded in cavities.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

High-throughput computation of electric polarization in solids via Berry flux diagonalization

Electric polarization in the absence of an externally applied electric field is a key property of polar materials, but the standard interpolation-based ab initio approach to compute polarization differences within the modern theory of polarization presents challenges for automated high-throughput calculations. Berry flux diagonalization [J. Bonini et al., Phys. Rev. B 102, 045141 (2020)] has been proposed as an efficient and reliable alternative, though it has yet to be widely deployed. Here, we assess Berry flux diagonalization using ab initio calculations of a large set of materials, introducing and validating heuristics that ensure branch alignment with a minimal number of intermediate interpolated structures. Our automated implementation of Berry flux diagonalization succeeds in cases where prior interpolation-based workflows fail due to band-gap closures or branch ambiguities. Benchmarking with ab initio calculations of 176 candidate ferroelectrics, we demonstrate the efficacy of the approach on a broad range of insulating materials and obtain accurate effective polarization values with fewer interpolated structures than prior automated interpolation-based workflows. Our real-space heuristics that can predict gauge stability a priori from ionic displacements enable a general automated framework for reliable polarization calculations and efficient high-throughput screening of chemically and structurally diverse polar insulators. These results establish Berry flux diagonalization as a robust and efficient method to compute the effective polarization of solids and to accelerate the data-driven discovery of functional polar materials.

Poteshman, Abigail N. [University of Chicago, IL (↗
DOE OSTI2025

A tale of two polarization paradoxes: The diamagnetic polarization paradox

An accurate calculation of the total polarization charge density in a plasma is essential for a self-consistent determination of the electric field. Yet, the “diamagnetic polarization paradox” refers to the fact that there is a paradoxical factor of 1/2 difference between the pressure-driven “diamagnetic polarization” density calculated using real space drift theory vs action-angle space guiding center and gyrokinetic theory that has not been explained before. Here, we show that both results can be made consistent with one another. Half of the diamagnetic polarization is due to the transformation from the guiding center density to the real space density. The other half is due to the fact that, within the drift kinetic ordering assumptions, the guiding center density should be expressed as the gyroaverage of the density in the limit of vanishing Larmor radius. A comprehensive review of polarization is presented to complete the derivation, and then we derive results that are required for the polarization calculations to agree. Expressions for the diamagnetic polarization density are given that are accurate to first order in amplitude and all orders in gyroradius within the gyrokinetic theory for a constant magnetic field. Applications to Maxwell–Boltzmann particle distribution functions (PDFs), including anisotropic temperature, are presented. Local invariants, like total energy and toroidal momentum, do not generate net polarization effects; the electric and thermodynamic polarizations must precisely cancel. In contrast, anisotropic dependence on the magnetic moment generates a net polarization proportional to the temperature anisotropy. Finally, when sources are present, the equilibrium PDF is approximately the ratio of two orbit averages.

adiabatic theory↗
DOE OSTI2023

Synchrotron Polarization Signatures of Surface Waves in Supermassive Black Hole Jets

Abstract Supermassive black holes in active galactic nuclei are known to launch relativistic jets, which are observed across the entire electromagnetic spectrum and thought to be efficient particle accelerators. Their primary radiation mechanism for radio emission is polarized synchrotron emission produced by a population of nonthermal electrons. In this Letter, we present a global general relativistic magnetohydrodynamical (GRMHD) simulation of a magnetically arrested disk (MAD). After the simulation reaches the MAD state, we show that waves are continuously launched from the vicinity of the black hole and propagate along the interface between the jet and the wind. At this interface, a steep gradient in velocity is present between the mildly relativistic wind and the highly relativistic jet. The interface is, therefore, a shear layer, and due to the shear, the waves generate roll-ups that alter the magnetic field configuration and the shear layer geometry. We then perform polarized radiation transfer calculations of our GRMHD simulation and find signatures of the waves in both total intensity and linear polarization, effectively lowering the fully resolved polarization fraction. The telltale polarization signatures of the waves could be observable by future very long baseline interferometric observations, e.g., the next-generation Event Horizon Telescope.

Astronomy & Astrophysics↗
DOE OSTI2025

Strain-Modulated Exciton Localization and Enhanced Emission in Multilayer GaSe

Strain engineering is one of the most effective routes for tuning the electrical and optical properties of two-dimensional layered materials. Besides reproducing the results of other groups on the tunability and photoluminescence (PL) enhancement of free and bound excitons under mechanical deformation or thermal effects, we systematically studied the mechanical strain (wrinkle) and local thermal strain (laser heating) effects on the PL lifetime and polarization in GaSe multilayers and their interplay, revealing their coupled impact on excitonic dynamics. Here, the PL intensity of localized excitons in the wrinkle region of GaSe increases superlinearly with the excitation laser power. The polarization effect has been observed for the bound exciton in GaSe under mechanical strain, but not in GaSe under thermal strain. Fluorescence lifetime imaging (FLIM) measurements reveal strain-tunable lifetimes for both free and bound excitons, and the lifetime of the bound exciton is longer than the free exciton in the mechanical strain region, correlating with the enhanced emission of the bound exciton. These results highlight previously uncharacterized optoelectronic tunability in GaSe and broaden the design space for strain (or thermally)-controlled 2D layered devices.

, GaSe, Exciton localization↗
DOE OSTI2026

Measurement of the Neutron Elastic Electromagnetic Form Factor Ratio at Large Momentum Transfer

Exploring nucleon structure is vital both for understanding its origin and existence as well as for the advancement of the sciences. It helps us answer key questions such as how quark and gluon dynamics create 99% of the nucleon mass. Electron- nucleon scattering has been widely used for precision studies of the nucleon and nuclear structure since the Nobel Prize winning investigations by Robert Hofstadter and collaborators in the 1950s. These studies provide information about the spatial charge and current densities of the nucleon in terms of the electromagnetic form factors. The form factors are functions of four momentum transfer squared (Q2). Extending the electromagnetic form factor measurements to higher Q2 plays a critical role in furthering the understanding of nucleon structure. This motivated the Super BigBite Spectrometer (SBS) program at Jefferson Lab. The open nature of the spectrometers and the direct line of sight from the target to the tracking detector locations in experimental setups such as SBS creates high levels of background at the detectors. This necessitates the use of tracking detectors with high rate capability and good position resolution. Gas Electron Multiplier (GEM) detectors are an excellent choice for tracking detectors in such experiments. Understanding the performance of the GEM detectors is important not just for SBS experiments but also for future high-luminosity experiments. This thesis reports the exploratory results from the measurement of the neutron elastic electromagnetic form factor ratio (Gn E/Gn M) at high momentum transfer. A longitudinally polarized electron beam was scattered off a polarized 3He target, used as an effective polarized neutron target. In this experiment, the polarized 3He target achieved a world record polarization weighted luminosity at a beam current of 45 µA. Double spin asymmetry of the scattered neutron events is used to extract the neutron form factor ratio. Measurements were taken at Q2 = 3.0, 6.8, 9.8 (GeV/c)2. The lowest Q2 measurement is in good agreement with the existing world data, and the higher-Q2 measurements extend the Q2 reach well beyond the existing world data and are expected to remain unmatched for a long time.

Gamage, Vimukthi Haththotuwa [Univ. of Virginia, C↗
DOE OSTI2022

Gamma-ray Spectra from a 3x3 CsPbBr 3 Array

CsPbBr 3 is a promising semiconductor material for X- and γ-ray detection at room temperature due to a wide bandgap of 2.3eV, high stopping power, and relatively high mobility-lifetime products of electrons and holes, and the capability of growing large crystals. In this paper we report on fabrication and testing of a 3.8 mm thick, 3 X 3 array with 1.2 mm pitch. Raw 137 Cs spectra were acquired with applied bias of 400 V, 500 V, and 600 V. Energy resolution of between 2 and 3 % FWHM at 662 keV was obtained from most pixels without any correction at room temperature. After 15 days under continuous bias at 600 V, no polarization effects were observed.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Measurement of the Neutron Electromagnetic Form Factor Ratio at High Momentum Transfer

The inner structure of the nucleon (proton and neutron) remains a topic of great interest in nuclear and particle physics, after many decades of study. For example, understanding the quark-gluon dynamics inside the nucleon would shed light on how 99% of the nucleon mass is created. The neutron electromagnetic form factors, Gn E and Gn M , give important insights into the neutron structure. The Super BigBite Spectrometer (SBS) program at Jefferson Lab (JLab) seeks to extend the form factor measurements for both the proton and the neutron. The neutron electric form actor, Gn E , has been historically difficult to measure due to the short lifetime of the free neutron and the small value of Gn E . The GEn-II experiment is part of the SBS program and seeks to measure Gn E , significantly increasing the high momentum transfer coverage. A newly designed polarized 3He target increased the figure of merit by three times compared to previous measurements. The analysis of this data is especially challenging due to the unprecedented high-rate environment caused by the open nature of the spectrometer with a direct line of sight to the target. This required developing new Gas Electron Multiplier (GEM) particle trackers which can cover large areas demanded by this setup and handle particle rates up to 500 kHz/cm2. Rates this high over a large area is unprecedented in particle tracking systems and came with a number of challenges. Data taken in the SBS program was critical to understanding hardware and software solutions that improved the track reconstruction efficiency to be >97% with a position resolution of 70 ?m. In previous experiments the proton electromagnetic form factors, Gp E and Gp M were measured up to Q2 = 8.5 GeV2 and Q2 = 30 GeV2, respectively, while Gn E has only been measured up to Q2 = 3.4 GeV2. The GEn-II experiment has measured the neutron form factor ratio, Gn E/Gn M, at Q2 values of 2.90, 6.50, and 9.47 GeV2 by scattering a polarized electron beam with a polarized 3He target, used here as an effective polarized neutron target, and measuring the double spin asymmetry of the cross section. Previous Gn E measurements do not extend above Q2 = 3.4 GeV2, and therefore this analysis has extended the world data by almost three times. The background correction is especially difficult at the higher Q2 settings leading to large systematic errors. As very exploratory results from this early analysis of the data, we find for Q2 = 2.90 GeV2, Gn E = 0.0157 ±stat 0.0016 ±sys 0.0011, for Q2 = 6.50 GeV2, Gn E = 0.0067 ±stat 0.0019 ±sys 0.0005, and for Q2 = 9.46 GeV2, Gn E = 0.0046 ±stat 0.0023 ±sys 0.0005. These results are compared to predictions from the Dyson-Schwinger Equations (DSE) model and a Relativistic Constituent Quark Model (RCQM).

Jeffas, Sean↗
DOE OSTI2022

Linking the Salmonella enterica 1,2-Propanediol Utilization Bacterial Microcompartment Shell to the Enzymatic Core via the Shell Protein PduB

Bacterial microcompartments (MCPs) are protein-based organelles that house the enzymatic machinery for metabolism of niche carbon sources, allowing enteric pathogens to outcompete native microbiota during host colonization. While much progress has been made toward understanding MCP biogenesis, questions still remain regarding the mechanism by which core MCP enzymes are enveloped within the MCP protein shell. Here, we explore the hypothesis that the shell protein PduB is responsible for linking the shell of the 1,2-propanediol utilization (Pdu) MCP from Salmonella enterica serovar Typhimurium LT2 to its enzymatic core. Using fluorescent reporters, we demonstrate that all members of the Pdu enzymatic core are encapsulated in Pdu MCPs. We also demonstrate that PduB is critical for linking the entire Pdu enzyme core to the MCP shell. Using MCP purifications, transmission electron microscopy, and fluorescence microscopy, we find that shell assembly can be decoupled from the enzymatic core, as apparently empty MCPs are formed in Salmonella strains lacking PduB. Mutagenesis studies reveal that PduB is incorporated into the Pdu MCP shell via a conserved, lysine-mediated hydrogen bonding mechanism. Finally, growth assays and system-level pathway modeling reveal that unencapsulated pathway performance is strongly impacted by enzyme concentration, highlighting the importance of minimizing polar effects when conducting these functional assays. Together, these results provide insight into the mechanism of enzyme encapsulation within Pdu MCPs and demonstrate that the process of enzyme encapsulation and shell assembly are separate processes in this system, a finding that will aid future efforts to understand MCP biogenesis.

1, 2-propanediol utilization↗
DOE OSTI2025

Polarization Switching on the Open Surfaces of the Wurtzite Ferroelectric Nitrides: Ferroelectric Subsystems and Electrochemical Reactivity

Binary ferroelectric nitrides are promising materials for information technologies and power electronics. However, polarization switching in these materials is highly unusual. From the structural perspective, polarization reversal is associated with the change of the effective polarity at the surfaces and interfaces from N‐to‐M terminated, suggesting strong coupling between ferroelectric and chemical phenomena. Phenomenologically, macroscopic studies demonstrate the presence of complex time dependent phenomena including wake‐up. Here, in this study, the polarization switching using the multidimensional high‐resolution piezoresponse force microscopy (PFM) and spectroscopy is explored, detecting both the evolution of induced ferroelectric domain, electromechanical response, and surface deformation during first‐order reversal curve measurements. The presence of two weakly coupled ferroelectric subsystems are demonstrated and the bias‐induced electrochemical reactivity. The observed behaviors are very similar to the recent studies of other wurtzite system but additionally include electrochemical reactivity, suggesting the universality of these behaviors for the wurtzite binary ferroelectrics. These studies suggest potential of high‐resolution multimodal PFM spectroscopies to resolve complex coupled polarization dynamics in materials. Furthermore, these PFM based studies are fully consistent with the recent electron microscopy observations of the shark‐teeth like ferroelectric domains in nitrides. Hence, it is believed that these studies establish the universal phenomenological picture of polarization switching in binary wurtzite.

36 MATERIALS SCIENCE↗
DOE OSTI2024

From Feast to Famine: A Systematic Study of Accretion onto Oblique Pulsars with 3D GRMHD Simulations

Disk-fed accretion onto neutron stars can power a wide range of astrophysical sources ranging from X-ray binaries, to accretion-powered millisecond pulsars, ultraluminous X-ray sources, and gamma-ray bursts. A crucial parameter controlling the gas–magnetosphere interaction is the strength of the stellar dipole. In addition, coherent X-ray pulsations in many neutron star systems indicate that the star's dipole moment is oblique relative to its rotation axis. Therefore, it is critical to systematically explore the 2D parameter space of the star's magnetic field strength and obliquity, which is what this work does, for the first time, in the framework of 3D general-relativistic magnetohydrodynamics. If the accretion disk carries its own vertical magnetic field, this introduces an additional factor: the relative polarity of the disk and stellar magnetic fields. We find that depending on the strength of the stellar dipole and the star–disk relative polarity, the neutron star's jet power can either increase or decrease with increasing obliquity. For weak dipole strength (equivalently, high accretion rate), the parallel polarity results in a positive correlation between jet power and obliquity, whereas the antiparallel orientation displays the opposite trend. For stronger dipoles, the relative-polarity effect disappears, and jet power always decreases with increasing obliquity. The influence of the relative polarity gradually disappears as obliquity increases. Highly oblique pulsars tend to have an increased magnetospheric radius, a lower mass accretion rate, and enter the propeller regime at lower magnetic moments than aligned stars.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Solvent–Solvent Correlations across Graphene: The Effect of Image Charges

Wetting experiments show pure graphene to be weakly hydrophilic, but its contact angle (CA) also reflects the character of the supporting material. Measurements and Molecular Dynamics simulations on suspended and supported graphene often reveal a CA reduction due to the presence of the supporting substrate. A similar reduction is consistently observed when graphene is wetted from both sides. The effect has been attributed to transparency to molecular interactions across the graphene sheet, however, the possibility of substrate-induced graphene polarization has also been considered. Computer simulations of CA on graphene have so far been determined by ignoring the material’s conducting properties. We improve the graphene model by incorporating its conductivity according to the Constant Applied Potential Molecular Dynamics. Using this method, we compare the wettabilities of suspended graphene and graphene supported by water by measuring the CA of cylindrical water drops on the sheets. The inclusion of graphene conductivity and concomitant polarization effects lead to a lower CA on suspended graphene but the CA reduction is significantly bigger when the sheets are also wetted from the opposite side. The stronger adhesion is accompanied by a profound change in the correlations among water molecules across the sheet. While partial charges on water molecules interacting across an insulator sheet attract charges of the opposite sign, apparent attraction among like charges is manifested across the conducting graphene. The change is associated with graphene polarization, as the image charges inside the conductor attract equally signed partial charges of water molecules on both sides of the sheet. Additionally, by using a non-polar liquid (diiodomethane), we affirm a detectable wetting translucency when liquid-liquid forces are dominated by dispersive interactions. Furthermore, our findings are important for predictive modeling toward a variety of applications including sensors, fuel cell membranes, water filtration, and graphene-based electrode materials in high-performance supercapacitors.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2020

High temperature operation to 500 °C of AlGaN graded polarization-doped field-effect transistors

AlGaN polarization-doped field-effect transistors were characterized by DC and pulsed measurements from room temperature to 500 °C in ambient. DC current-voltage characteristics demonstrated only a 70% reduction in on-state current from 25 to 500 °C and full gate modulation, regardless of the operating temperature. Near ideal gate lag measurement was realized across the temperature range that is indicative of a high-quality substrate and sufficient surface passivation. The ability for operation at high temperature is enabled by the high Schottky barrier height from the Ni/Au gate contact, with values of 2.05 and 2.76 eV at 25 and 500 °C, respectively. The high barrier height due to the insulatorlike aluminum nitride layer leads to an ION/IOFF ratio of 1.5 × 10 9 and 6 × 10 3 at room temperature and 500 °C, respectively. Transmission electron microscopy was used to confirm the stability of the heterostructure even after an extended high-temperature operation with only minor interdiffusion of the Ni/Au Schottky contact. The use of refractory metals in all contacts will be key to ensure a stable extended high-temperature operation.

36 MATERIALS SCIENCE↗
DOE OSTI2021

The effects of laser polarization and wavelength on injection dynamics of a laser wakefield accelerator

Here, we investigate the effects of laser polarization and wavelength on electron injection dynamics in a laser wakefield accelerator. During the ionization process, electrons gain residual momentum and kinetic energy via above threshold ionization, which has a strong dependence on laser polarization. A circularly polarized laser pulse results in a much higher residual momentum and kinetic energy gain for the ionized electrons compared with the linearly polarized case. This residual momentum results in particle injection because of the sensitivity of particle trapping to the initial conditions and enhanced the total injected beam charge in both experiments and particle-in-cell simulations. Due to the strong correlation of above threshold ionization with laser wavelength, in this work we extended the investigation to long wavelength (up to 20 μm) drive pulses using particle-in-cell simulations. Owing to the gain in kinetic energy, it may be expected that the charge trapped would consistently increase for circular polarization with increasing laser wavelength, but this was not observed. Instead, there are oscillations with wavelength in the relative trapped charge between linear and circular polarization cases, which arise because of ionization and heating effects on the plasma. Our studies highlight the complex interplay between several different physical effects, including injection regimes—above threshold ionization assisted injection, wave-breaking injection by carrier-envelope-phase effects and ionization injection—ionization gradient induced laser pulse evolution, and thermal modifications to the wake structure that need considering when extrapolating laser wakefield acceleration to different wavelength regimes.

Ma, Y. (ORCID:0000000239194856)↗
DOE OSTI2023

Beyond the Condon limit: Condensed phase optical spectra from atomistic simulations

While dark transitions made bright by molecular motions determine the optoelectronic properties of many materials, simulating such non-Condon effects in condensed phase spectroscopy remains a fundamental challenge. We derive a Gaussian theory to predict and analyze condensed phase optical spectra beyond the Condon limit. Our theory introduces novel quantities that encode how nuclear motions modulate the energy gap and transition dipole of electronic transitions in the form of spectral densities. By formulating the theory through a statistical framework of thermal averages and fluctuations, we circumvent the limitations of widely used microscopically harmonic theories, allowing us to tackle systems with generally anharmonic atomistic interactions and non-Condon fluctuations of arbitrary strength. We show how to calculate these spectral densities using first-principles simulations, capturing realistic molecular interactions and incorporating finite-temperature, disorder, and dynamical effects. Our theory accurately predicts the spectra of systems known to exhibit strong non-Condon effects (phenolate in various solvents) and reveals distinct mechanisms for electronic peak splitting: timescale separation of modes that tune non-Condon effects and spectral interference from correlated energy gap and transition dipole fluctuations. We further introduce analysis tools to identify how intramolecular vibrations, solute–solvent interactions, and environmental polarization effects impact dark transitions. Moreover, we prove an upper bound on the strength of cross correlated energy gap and transition dipole fluctuations, thereby elucidating a simple condition that a system must follow for our theory to accurately predict its spectrum.

Chemistry↗
DOE OSTI2020

A Measurement of the CMB E-mode Angular Power Spectrum at Subdegree Scales from 670 Square Degrees of POLARBEAR Data

In this work, we report a measurement of the E-mode polarization power spectrum of the cosmic microwave background (CMB) using 150 GHz data taken from 2014 July to 2016 December with the POLARBEAR experiment. We reach an effective polarization map noise level of 32 μK-arcmin across an observation area of 670 square degrees. We measure the EE power spectrum over the angular multipole range 500 ≤ ℓ < 3000, tracing the third to seventh acoustic peaks with high sensitivity. The statistical uncertainty on E-mode bandpowers is ~2.3 μK 2 at ℓ ~ 1000, with a systematic uncertainty of 0.5 mK 2 . Furthermore, the data are consistent with the standard ΛCDM cosmological model with a probability-to-exceed of 0.38. We combine recent CMB E-mode measurements and make inferences about cosmological parameters in ΛCDM as well as in extensions to ΛCDM. Adding the ground-based CMB polarization measurements to the Planck data set reduces the uncertainty on the Hubble constant by a factor of 1.2 to H0 = 67.20 ±0.57 km s -1 Mpc -1 . When allowing the number of relativistic species (Neff ) to vary, we find N eff = 2.94 ±0.16, which is in good agreement with the standard value of 3.046. Instead allowing the primordial helium abundance (Y He ) to vary, the data favor Y He = 0.248 ±0.012. This is very close to the expectation of 0.2467 from big bang nucleosynthesis. When varying both Y He and N eff , we find N eff = 2.70 ±0.26 and Y He = 0.262 ±0.015.

79 ASTRONOMY AND ASTROPHYSICS↗